skia2/docs/SkPath_Reference.bmh

#Topic Path
#Alias Path_Reference ##
#Alias Paths ##

#Class SkPath

#Code
#Populate
##

Paths contain geometry. Paths may be empty, or contain one or more Verbs that
outline a figure. Path always starts with a move verb to a Cartesian_Coordinate,
and may be followed by additional verbs that add lines or curves.
Adding a close verb makes the geometry into a continuous loop, a closed contour.
Paths may contain any number of contours, each beginning with a move verb.

Path contours may contain only a move verb, or may also contain lines,
Quadratic_Beziers, Conics, and Cubic_Beziers. Path contours may be open or
closed.

When used to draw a filled area, Path describes whether the fill is inside or
outside the geometry. Path also describes the winding rule used to fill
overlapping contours.

Internally, Path lazily computes metrics likes bounds and convexity. Call
SkPath::updateBoundsCache to make Path thread safe.

#Subtopic Verb
#Alias Verbs ##
#Line # line and curve type ##
#Enum Verb
#Line # controls how Path Points are interpreted ##

#Code
    enum Verb {
        kMove_Verb,
        kLine_Verb,
        kQuad_Verb,
        kConic_Verb,
        kCubic_Verb,
        kClose_Verb,
        kDone_Verb,
    };
##

Verb instructs Path how to interpret one or more Point and optional Conic_Weight;
manage Contour, and terminate Path.

#Const kMove_Verb 0
#Line # starts new Contour at next Point ##
    Consecutive kMove_Verb are preserved but all but the last kMove_Verb is
    ignored. kMove_Verb after other Verbs implicitly closes the previous Contour
    if SkPaint::kFill_Style is set when drawn; otherwise, stroke is drawn open.
    kMove_Verb as the last Verb is preserved but ignored.
##
#Const kLine_Verb 1
#Line # adds Line from Last_Point to next Point ##
    Line is a straight segment from Point to Point. Consecutive kLine_Verb
    extend Contour. kLine_Verb at same position as prior kMove_Verb is
    preserved, and draws Point if SkPaint::kStroke_Style is set, and
    SkPaint::Cap is SkPaint::kSquare_Cap or SkPaint::kRound_Cap. kLine_Verb
    at same position as prior line or curve Verb is preserved but is ignored.
##
#Const kQuad_Verb 2
#Line # adds Quad from Last_Point ##
    Adds Quad from Last_Point, using control Point, and end Point.
    Quad is a parabolic section within tangents from Last_Point to control Point,
    and control Point to end Point.
##
#Const kConic_Verb 3
#Line # adds Conic from Last_Point ##
    Adds Conic from Last_Point, using control Point, end Point, and Conic_Weight.
    Conic is a elliptical, parabolic, or hyperbolic section within tangents
    from Last_Point to control Point, and control Point to end Point, constrained
    by Conic_Weight. Conic_Weight less than one is elliptical; equal to one is
    parabolic (and identical to Quad); greater than one hyperbolic.
##
#Const kCubic_Verb 4
#Line # adds Cubic from Last_Point ##
    Adds Cubic from Last_Point, using two control Points, and end Point.
    Cubic is a third-order Bezier_Curve section within tangents from Last_Point
    to first control Point, and from second control Point to end Point.
##
#Const kClose_Verb 5
#Line # closes Contour ##
    Closes Contour, connecting Last_Point to kMove_Verb Point. Consecutive
    kClose_Verb are preserved but only first has an effect. kClose_Verb after
    kMove_Verb has no effect.
##
#Const kDone_Verb 6
#Line # terminates Path ##
    Not in Verb_Array, but returned by Path iterator.
##

Each Verb has zero or more Points stored in Path.
Path iterator returns complete curve descriptions, duplicating shared Points
for consecutive entries.

#Table
#Legend
# Verb        # Allocated Points # Iterated Points # Weights ##
##
# kMove_Verb  # 1                # 1               # 0       ##
# kLine_Verb  # 1                # 2               # 0       ##
# kQuad_Verb  # 2                # 3               # 0       ##
# kConic_Verb # 2                # 3               # 1       ##
# kCubic_Verb # 3                # 4               # 0       ##
# kClose_Verb # 0                # 1               # 0       ##
# kDone_Verb  # --               # 0               # 0       ##
##

#Example
void draw(SkCanvas* canvas) {
    SkPath path;
    path.lineTo(20, 20);
    path.quadTo(-10, -10, 30, 30);
    path.close();
    path.cubicTo(1, 2, 3, 4, 5, 6);
    path.conicTo(0, 0, 0, 0, 2);
    uint8_t verbs[7];
    int count = path.getVerbs(verbs, (int) SK_ARRAY_COUNT(verbs));
    const char* verbStr[] = { "Move", "Line", "Quad", "Conic", "Cubic", "Close" };
    SkDebugf("verb count: %d\nverbs: ", count);
    for (int i = 0; i < count; ++i) {
        SkDebugf("k%s_Verb ", verbStr[verbs[i]]);
    }
    SkDebugf("\n");
}
#StdOut
verb count: 7
verbs: kMove_Verb kLine_Verb kQuad_Verb kClose_Verb kMove_Verb kCubic_Verb kConic_Verb
##
##

#Enum Verb ##
#Subtopic Verb ##

# ------------------------------------------------------------------------------
#Subtopic Direction
#Line # contour orientation, clockwise or counterclockwise ##
#Alias Directions ##

#Enum Direction
#Line # sets Contour clockwise or counterclockwise ##

#Code
    enum Direction {
        kCW_Direction,
        kCCW_Direction,
    };
##

Direction describes whether Contour is clockwise or counterclockwise.
When Path contains multiple overlapping Contours, Direction together with
Fill_Type determines whether overlaps are filled or form holes.

Direction also determines how Contour is measured. For instance, dashing
measures along Path to determine where to start and stop stroke; Direction
will change dashed results as it steps clockwise or counterclockwise.

Closed Contours like Rect, Round_Rect, Circle, and Oval added with
kCW_Direction travel clockwise; the same added with kCCW_Direction
travel counterclockwise.

#Const kCW_Direction 0
#Line # contour travels clockwise ##
##
#Const kCCW_Direction 1
#Line # contour travels counterclockwise ##
##


#Example
#Height 100
void draw(SkCanvas* canvas) {
    const SkPoint arrow[] = { {40, -5}, {45, 0}, {40, 5} };
    const SkRect rect = {10, 10, 90, 90};
    SkPaint rectPaint;
    rectPaint.setAntiAlias(true);
    SkPaint textPaint(rectPaint);
    textPaint.setTextAlign(SkPaint::kCenter_Align);
    rectPaint.setStyle(SkPaint::kStroke_Style);
    SkPaint arrowPaint(rectPaint);
    SkPath arrowPath;
    arrowPath.addPoly(arrow, SK_ARRAY_COUNT(arrow), true);
    arrowPaint.setPathEffect(SkPath1DPathEffect::Make(arrowPath, 320, 0,
                             SkPath1DPathEffect::kRotate_Style));
    for (auto direction : { SkPath::kCW_Direction, SkPath::kCCW_Direction } ) {
        canvas->drawRect(rect, rectPaint);
        for (unsigned start : { 0, 1, 2, 3 } ) {
           SkPath path;
           path.addRect(rect, direction, start);
           canvas->drawPath(path, arrowPaint);
       }
       canvas->drawString(SkPath::kCW_Direction == direction ? "CW" : "CCW",  rect.centerX(),
            rect.centerY(), textPaint);
       canvas->translate(120, 0);
    }
}
##

#SeeAlso arcTo rArcTo isRect isNestedFillRects addRect addOval

#Enum Direction ##
#Subtopic Direction ##

# ------------------------------------------------------------------------------

#Method SkPath()
#In Constructors
#Line # constructs with default values ##
Constucts an empty Path. By default, Path has no Verbs, no Points, and no Weights.
Fill_Type is set to kWinding_FillType.

#Return  empty Path ##

#Example
    SkPath path;
    SkDebugf("path is " "%s" "empty", path.isEmpty() ? "" : "not ");
#StdOut
path is empty
##
##

#SeeAlso reset rewind

##

# ------------------------------------------------------------------------------

#Method SkPath(const SkPath& path)
#In Constructors
#Line # makes a shallow copy ##
Constructs a copy of an existing path.
Copy constructor makes two paths identical by value. Internally, path and
the returned result share pointer values. The underlying Verb_Array, Point_Array
and Weights are copied when modified.

Creating a Path copy is very efficient and never allocates memory.
Paths are always copied by value from the interface; the underlying shared
pointers are not exposed.

#Param path  Path to copy by value ##

#Return  copy of Path ##

#Example
#Description
    Modifying one path does not effect another, even if they started as copies
    of each other.
##
    SkPath path;
    path.lineTo(20, 20);
    SkPath path2(path);
    path2.close();
    SkDebugf("path verbs: %d\n", path.countVerbs());
    SkDebugf("path2 verbs: %d\n", path2.countVerbs());
    path.reset();
    SkDebugf("after reset\n" "path verbs: %d\n", path.countVerbs());
    SkDebugf("path2 verbs: %d\n", path2.countVerbs());
#StdOut
path verbs: 2
path2 verbs: 3
after reset
path verbs: 0
path2 verbs: 3
##
##

#SeeAlso operator=(const SkPath& path)

##

# ------------------------------------------------------------------------------

#Method ~SkPath()

#Line # decreases Reference_Count of owned objects ##
Releases ownership of any shared data and deletes data if Path is sole owner.

#Example
#Description
delete calls Path Destructor, but copy of original in path2 is unaffected.
##
void draw(SkCanvas* canvas) {
    SkPath* path = new SkPath();
    path->lineTo(20, 20);
    SkPath path2(*path);
    delete path;
    SkDebugf("path2 is " "%s" "empty", path2.isEmpty() ? "" : "not ");
}
##

#SeeAlso SkPath() SkPath(const SkPath& path) operator=(const SkPath& path)

##

# ------------------------------------------------------------------------------

#Method SkPath& operator=(const SkPath& path)

#Line # makes a shallow copy ##
Constructs a copy of an existing path.
Path assignment makes two paths identical by value. Internally, assignment
shares pointer values. The underlying Verb_Array, Point_Array and Weights
are copied when modified.

Copying Paths by assignment is very efficient and never allocates memory.
Paths are always copied by value from the interface; the underlying shared
pointers are not exposed.

#Param path  Verb_Array, Point_Array, Weights, and Fill_Type to copy ##

#Return  Path copied by value ##

#Example
SkPath path1;
path1.addRect({10, 20, 30, 40});
SkPath path2 = path1;
const SkRect& b1 = path1.getBounds();
SkDebugf("path1 bounds = %g, %g, %g, %g\n", b1.fLeft, b1.fTop, b1.fRight, b1.fBottom);
const SkRect& b2 = path2.getBounds();
SkDebugf("path2 bounds = %g, %g, %g, %g\n", b2.fLeft, b2.fTop, b2.fRight, b2.fBottom);
#StdOut
path1 bounds = 10, 20, 30, 40
path2 bounds = 10, 20, 30, 40
#StdOut ##
##

#SeeAlso swap SkPath(const SkPath& path)

##

# ------------------------------------------------------------------------------

#Method bool operator==(const SkPath& a, const SkPath& b)

#Line # compares Paths for equality ##
Compares a and b; returns true if Fill_Type, Verb_Array, Point_Array, and Weights
are equivalent.

#Param a  Path to compare ##
#Param b  Path to compare ##

#Return  true if Path pair are equivalent ##

#Example
#Description
Rewind removes Verb_Array but leaves storage; since storage is not compared,
Path pair are equivalent.
##
void draw(SkCanvas* canvas) {
    auto debugster = [](const char* prefix, const SkPath& a, const SkPath& b) -> void {
                SkDebugf("%s one %c= two\n", prefix, a == b ? '=' : '!');
    };
    SkPath one;
    SkPath two;
    debugster("empty", one, two);
    one.moveTo(0, 0);
    debugster("moveTo", one, two);
    one.rewind();
    debugster("rewind", one, two);
    one.moveTo(0, 0);
    one.reset();
    debugster("reset", one, two);
}
#StdOut
empty one == two
moveTo one != two
rewind one == two
reset one == two
##
##

#SeeAlso operator!=(const SkPath& a, const SkPath& b) operator=(const SkPath& path)

##

# ------------------------------------------------------------------------------

#Method bool operator!=(const SkPath& a, const SkPath& b)

#Line # compares paths for inequality ##
Compares a and b; returns true if Fill_Type, Verb_Array, Point_Array, and Weights
are not equivalent.

#Param a  Path to compare ##
#Param b  Path to compare ##

#Return  true if Path pair are not equivalent ##

#Example
#Description
Path pair are equal though their convexity is not equal.
##
void draw(SkCanvas* canvas) {
    auto debugster = [](const char* prefix, const SkPath& a, const SkPath& b) -> void {
                SkDebugf("%s one %c= two\n", prefix, a != b ? '!' : '=');
    };
    SkPath one;
    SkPath two;
    debugster("empty", one, two);
    one.addRect({10, 20, 30, 40});
    two.addRect({10, 20, 30, 40});
    debugster("add rect", one, two);
    one.setConvexity(SkPath::kConcave_Convexity);
    debugster("setConvexity", one, two);
    SkDebugf("convexity %c=\n", one.getConvexity() == two.getConvexity() ? '=' : '!');
}
#StdOut
empty one == two
add rect one == two
setConvexity one == two
convexity !=
##
##

##

# ------------------------------------------------------------------------------

#Subtopic Property
#Line # metrics and attributes ##
##

#Method bool isInterpolatable(const SkPath& compare) const
#In Property
#In Interpolate
#Line # returns if pair contains equal counts of Verb_Array and Weights ##
Returns true if Paths contain equal Verbs and equal Weights.
If Paths contain one or more Conics, the Weights must match.

conicTo may add different Verbs depending on Conic_Weight, so it is not
trivial to interpolate a pair of Paths containing Conics with different
Conic_Weight values.

#Param compare  Path to compare ##

#Return  true if Paths Verb_Array and Weights are equivalent ##

#Example
    SkPath path, path2;
    path.moveTo(20, 20);
    path.lineTo(40, 40);
    path.lineTo(20, 20);
    path.lineTo(40, 40);
    path.close();
    path2.addRect({20, 20, 40, 40});
    SkDebugf("paths are " "%s" "interpolatable", path.isInterpolatable(path2) ? "" : "not ");
#StdOut
paths are interpolatable
##
##

#SeeAlso isInterpolatable

##

# ------------------------------------------------------------------------------

#Subtopic Interpolate
#Line # weighted average of Path pair ##
##

#Method bool interpolate(const SkPath& ending, SkScalar weight, SkPath* out) const
#In Interpolate
#Line # interpolates between Path pair ##
Interpolates between Paths with Point_Array of equal size.
Copy Verb_Array and Weights to out, and set out Point_Array to a weighted
average of this Point_Array and ending Point_Array, using the formula:
#Formula # (Path Point * weight) + ending Point * (1 - weight) ##.

weight is most useful when between zero (ending Point_Array) and
one (this Point_Array); will work with values outside of this
range.

interpolate() returns false and leaves out unchanged if Point_Array is not
the same size as ending Point_Array. Call isInterpolatable to check Path
compatibility prior to calling interpolate().

#Param ending  Point_Array averaged with this Point_Array ##
#Param weight  contribution of this Point_Array, and
               one minus contribution of ending Point_Array
##
#Param out     Path replaced by interpolated averages ##

#Return  true if Paths contain same number of Points ##

#Example
#Height 60
void draw(SkCanvas* canvas) {
    SkPaint paint;
    paint.setAntiAlias(true);
    paint.setStyle(SkPaint::kStroke_Style);
    SkPath path, path2;
    path.moveTo(20, 20);
    path.lineTo(40, 40);
    path.lineTo(20, 40);
    path.lineTo(40, 20);
    path.close();
    path2.addRect({20, 20, 40, 40});
    for (SkScalar i = 0; i <= 1; i += 1.f / 6) {
      SkPath interp;
      path.interpolate(path2, i, &interp);
      canvas->drawPath(interp, paint);
      canvas->translate(30, 0);
    }
}
##

#SeeAlso isInterpolatable

##

# ------------------------------------------------------------------------------

#Method bool unique() const
#Deprecated soon
Only valid for Android framework.
##

# ------------------------------------------------------------------------------
#Subtopic Fill_Type
#Line # fill rule, normal and inverted ##

#Enum FillType
#Line # sets winding rule and inverse fill ##

#Code
    enum FillType {
        kWinding_FillType,
        kEvenOdd_FillType,
        kInverseWinding_FillType,
        kInverseEvenOdd_FillType,
    };
##

Fill_Type selects the rule used to fill Path. Path set to kWinding_FillType
fills if the sum of Contour edges is not zero, where clockwise edges add one, and
counterclockwise edges subtract one. Path set to kEvenOdd_FillType fills if the
number of Contour edges is odd. Each Fill_Type has an inverse variant that
reverses the rule:
kInverseWinding_FillType fills where the sum of Contour edges is zero;
kInverseEvenOdd_FillType fills where the number of Contour edges is even.

#Example
#Height 100
#Description
The top row has two clockwise rectangles. The second row has one clockwise and
one counterclockwise rectangle. The even-odd variants draw the same. The
winding variants draw the top rectangle overlap, which has a winding of 2, the
same as the outer parts of the top rectangles, which have a winding of 1.
##
void draw(SkCanvas* canvas) {
   SkPath path;
   path.addRect({10, 10, 30, 30}, SkPath::kCW_Direction);
   path.addRect({20, 20, 40, 40}, SkPath::kCW_Direction);
   path.addRect({10, 60, 30, 80}, SkPath::kCW_Direction);
   path.addRect({20, 70, 40, 90}, SkPath::kCCW_Direction);
   SkPaint strokePaint;
   strokePaint.setStyle(SkPaint::kStroke_Style);
   SkRect clipRect = {0, 0, 51, 100};
   canvas->drawPath(path, strokePaint);
   SkPaint fillPaint;
   for (auto fillType : { SkPath::kWinding_FillType, SkPath::kEvenOdd_FillType,
                      SkPath::kInverseWinding_FillType, SkPath::kInverseEvenOdd_FillType } ) {
        canvas->translate(51, 0);
        canvas->save();
        canvas->clipRect(clipRect);
        path.setFillType(fillType);
        canvas->drawPath(path, fillPaint);
        canvas->restore();
    }
}
##

#Const kWinding_FillType 0
#Line # is enclosed by a non-zero sum of Contour Directions ##
##
#Const kEvenOdd_FillType 1
#Line # is enclosed by an odd number of Contours ##
##
#Const kInverseWinding_FillType 2
#Line # is enclosed by a zero sum of Contour Directions ##
##
#Const kInverseEvenOdd_FillType 3
#Line # is enclosed by an even number of Contours ##
##

#Example
#Height 230
void draw(SkCanvas* canvas) {
   SkPath path;
   path.addRect({20, 10, 80, 70}, SkPath::kCW_Direction);
   path.addRect({40, 30, 100, 90}, SkPath::kCW_Direction);
   SkPaint strokePaint;
   strokePaint.setStyle(SkPaint::kStroke_Style);
   SkRect clipRect = {0, 0, 128, 128};
   canvas->drawPath(path, strokePaint);
   canvas->drawLine({0, 50}, {120, 50}, strokePaint);
   SkPaint textPaint;
   textPaint.setAntiAlias(true);
   textPaint.setTextAlign(SkPaint::kCenter_Align);
   SkScalar textHPos[] = { 10, 30, 60, 90, 110 };
   canvas->drawPosTextH("01210", 5, textHPos, 48, textPaint);
   textPaint.setTextSize(18);
   canvas->translate(0, 128);
   canvas->scale(.5f, .5f);
   canvas->drawString("inverse", 384, 150, textPaint);
   SkPaint fillPaint;
   for (auto fillType : { SkPath::kWinding_FillType, SkPath::kEvenOdd_FillType,
                      SkPath::kInverseWinding_FillType, SkPath::kInverseEvenOdd_FillType } ) {
        canvas->save();
        canvas->clipRect(clipRect);
        path.setFillType(fillType);
        canvas->drawPath(path, fillPaint);
        canvas->restore();
        canvas->drawString(fillType & 1 ? "even-odd" : "winding", 64, 170, textPaint);
        canvas->translate(128, 0);
    }
}
##

#SeeAlso SkPaint::Style Direction getFillType setFillType

##

# ------------------------------------------------------------------------------

#Method FillType getFillType() const

#In Fill_Type
#Line # returns Fill_Type: winding, even-odd, inverse ##
Returns FillType, the rule used to fill Path. FillType of a new Path is
kWinding_FillType.

#Return  one of: kWinding_FillType, kEvenOdd_FillType,  kInverseWinding_FillType,
kInverseEvenOdd_FillType
##

#Example
    SkPath path;
    SkDebugf("default path fill type is %s\n",
            path.getFillType() == SkPath::kWinding_FillType ? "kWinding_FillType" :
            path.getFillType() == SkPath::kEvenOdd_FillType ? "kEvenOdd_FillType" :
            path.getFillType() == SkPath::kInverseWinding_FillType ? "kInverseWinding_FillType" :
                                                                     "kInverseEvenOdd_FillType");
#StdOut
default path fill type is kWinding_FillType
##
##

#SeeAlso FillType setFillType isInverseFillType

##

# ------------------------------------------------------------------------------

#Method void setFillType(FillType ft)

#In Fill_Type
#Line # sets Fill_Type: winding, even-odd, inverse ##
Sets FillType, the rule used to fill Path. While there is no check
that ft is legal, values outside of FillType are not supported.

#Param ft  one of: kWinding_FillType, kEvenOdd_FillType,  kInverseWinding_FillType,
kInverseEvenOdd_FillType
##

#Example
#Description
If empty Path is set to inverse FillType, it fills all pixels.
##
#Height 64
     SkPath path;
     path.setFillType(SkPath::kInverseWinding_FillType);
     SkPaint paint;
     paint.setColor(SK_ColorBLUE);
     canvas->drawPath(path, paint);
##

#SeeAlso FillType getFillType toggleInverseFillType

##

# ------------------------------------------------------------------------------

#Method bool isInverseFillType() const

#In Fill_Type
#Line # returns if Fill_Type fills outside geometry ##
Returns if FillType describes area outside Path geometry. The inverse fill area
extends indefinitely.

#Return  true if FillType is kInverseWinding_FillType or kInverseEvenOdd_FillType ##

#Example
    SkPath path;
    SkDebugf("default path fill type is inverse: %s\n",
            path.isInverseFillType() ? "true" : "false");
#StdOut
default path fill type is inverse: false
##
##

#SeeAlso FillType getFillType setFillType toggleInverseFillType

##

# ------------------------------------------------------------------------------

#Method void toggleInverseFillType()

#In Fill_Type
#Line # toggles Fill_Type between inside and outside geometry ##
Replaces FillType with its inverse. The inverse of FillType describes the area
unmodified by the original FillType.

#Table
#Legend
# FillType                 # toggled FillType         ##
##
# kWinding_FillType        # kInverseWinding_FillType ##
# kEvenOdd_FillType        # kInverseEvenOdd_FillType ##
# kInverseWinding_FillType # kWinding_FillType        ##
# kInverseEvenOdd_FillType # kEvenOdd_FillType        ##
##

#Example
#Description
Path drawn normally and through its inverse touches every pixel once.
##
#Height 100
SkPath path;
SkPaint paint;
paint.setColor(SK_ColorRED);
paint.setTextSize(80);
paint.getTextPath("ABC", 3, 20, 80, &path);
canvas->drawPath(path, paint);
path.toggleInverseFillType();
paint.setColor(SK_ColorGREEN);
canvas->drawPath(path, paint);
##

#SeeAlso FillType getFillType setFillType isInverseFillType

##

#Subtopic Fill_Type ##

# ------------------------------------------------------------------------------

#Subtopic Convexity
#Line # if Path is concave or convex ##

#Enum Convexity
#Line # returns if Path is convex or concave ##

#Code
    enum Convexity : uint8_t {
        kUnknown_Convexity,
        kConvex_Convexity,
        kConcave_Convexity,
    };
##

Path is convex if it contains one Contour and Contour loops no more than
360 degrees, and Contour angles all have same Direction. Convex Path
may have better performance and require fewer resources on GPU_Surface.

Path is concave when either at least one Direction change is clockwise and
another is counterclockwise, or the sum of the changes in Direction is not 360
degrees.

Initially Path Convexity is kUnknown_Convexity. Path Convexity is computed
if needed by destination Surface.

#Const kUnknown_Convexity 0
#Line # indicates Convexity has not been determined ##
##
#Const kConvex_Convexity 1
#Line # one Contour made of a simple geometry without indentations ##
##
#Const kConcave_Convexity 2
#Line # more than one Contour, or a geometry with indentations ##
##

#Example
void draw(SkCanvas* canvas) {
    SkPaint paint;
    SkPoint quad[] = {{70, 70}, {20, 20}, {120, 20}, {120, 120}};
    const char* labels[] = { "unknown", "convex", "concave" };
    for (SkScalar x : { 40, 100 } ) {
        SkPath path;
        quad[0].fX = x;
        path.addPoly(quad, SK_ARRAY_COUNT(quad), true);
        canvas->drawPath(path, paint);
        canvas->drawString(labels[(int) path.getConvexity()], 30, 100, paint);
        canvas->translate(100, 100);
    }
}
##

#SeeAlso Contour Direction getConvexity getConvexityOrUnknown setConvexity isConvex

#Enum Convexity ##

#Method Convexity getConvexity() const

#In Convexity
#Line # returns geometry convexity, computing if necessary ##
Computes Convexity if required, and returns stored value.
Convexity is computed if stored value is kUnknown_Convexity,
or if Path has been altered since Convexity was computed or set.

#Return  computed or stored Convexity ##

#Example
void draw(SkCanvas* canvas) {
    auto debugster = [](const char* prefix, const SkPath& path) -> void {
        SkDebugf("%s path convexity is %s\n", prefix,
                SkPath::kUnknown_Convexity == path.getConvexity() ? "unknown" :
                SkPath::kConvex_Convexity == path.getConvexity() ? "convex" : "concave"); };
    SkPath path;
    debugster("initial", path);
    path.lineTo(50, 0);
    debugster("first line", path);
    path.lineTo(50, 50);
    debugster("second line", path);
    path.lineTo(100, 50);
    debugster("third line", path);
}
##

#SeeAlso Convexity Contour Direction getConvexityOrUnknown setConvexity isConvex

##

# ------------------------------------------------------------------------------

#Method Convexity getConvexityOrUnknown() const

#In Convexity
#Line # returns geometry convexity if known ##
Returns last computed Convexity, or kUnknown_Convexity if
Path has been altered since Convexity was computed or set.

#Return  stored Convexity ##

#Example
#Description
Convexity is unknown unless getConvexity is called without a subsequent call
that alters the path.
##
void draw(SkCanvas* canvas) {
    auto debugster = [](const char* prefix, const SkPath& path) -> void {
        SkDebugf("%s path convexity is %s\n", prefix,
            SkPath::kUnknown_Convexity == path.getConvexityOrUnknown() ? "unknown" :
            SkPath::kConvex_Convexity == path.getConvexityOrUnknown() ? "convex" : "concave"); };
    SkPath path;
    debugster("initial", path);
    path.lineTo(50, 0);
    debugster("first line", path);
    path.getConvexity();
    path.lineTo(50, 50);
    debugster("second line", path);
    path.lineTo(100, 50);
    path.getConvexity();
    debugster("third line", path);
}
##

#SeeAlso Convexity Contour Direction getConvexity setConvexity isConvex

##

# ------------------------------------------------------------------------------

#Method void setConvexity(Convexity convexity)

#In Convexity
#Line # sets if geometry is convex to avoid future computation ##
Stores convexity so that it is later returned by getConvexity or getConvexityOrUnknown.
convexity may differ from getConvexity, although setting an incorrect value may
cause incorrect or inefficient drawing.

If convexity is kUnknown_Convexity: getConvexity will
compute Convexity, and getConvexityOrUnknown will return kUnknown_Convexity.

If convexity is kConvex_Convexity or kConcave_Convexity, getConvexity
and getConvexityOrUnknown will return convexity until the path is
altered.

#Param convexity  one of: kUnknown_Convexity, kConvex_Convexity, or kConcave_Convexity ##

#Example
void draw(SkCanvas* canvas) {
    auto debugster = [](const char* prefix, const SkPath& path) -> void {
        SkDebugf("%s path convexity is %s\n", prefix,
                SkPath::kUnknown_Convexity == path.getConvexity() ? "unknown" :
                SkPath::kConvex_Convexity == path.getConvexity() ? "convex" : "concave"); };
        SkPoint quad[] = {{70, 70}, {20, 20}, {120, 20}, {120, 120}};
        SkPath path;
        path.addPoly(quad, SK_ARRAY_COUNT(quad), true);
        debugster("initial", path);
        path.setConvexity(SkPath::kConcave_Convexity);
        debugster("after forcing concave", path);
        path.setConvexity(SkPath::kUnknown_Convexity);
        debugster("after forcing unknown", path);
}
##

#SeeAlso Convexity Contour Direction getConvexity getConvexityOrUnknown isConvex

##

# ------------------------------------------------------------------------------

#Method bool isConvex() const

#In Convexity
#Line # returns if geometry is convex ##
Computes Convexity if required, and returns true if value is kConvex_Convexity.
If setConvexity was called with kConvex_Convexity or kConcave_Convexity, and
the path has not been altered, Convexity is not recomputed.

#Return  true if Convexity stored or computed is kConvex_Convexity ##

#Example
#Description
Concave shape is erroneously considered convex after a forced call to
setConvexity.
##
void draw(SkCanvas* canvas) {
    SkPaint paint;
    SkPoint quad[] = {{70, 70}, {20, 20}, {120, 20}, {120, 120}};
    for (SkScalar x : { 40, 100 } ) {
        SkPath path;
        quad[0].fX = x;
        path.addPoly(quad, SK_ARRAY_COUNT(quad), true);
        path.setConvexity(SkPath::kConvex_Convexity);
        canvas->drawPath(path, paint);
        canvas->drawString(path.isConvex() ? "convex" : "not convex", 30, 100, paint);
        canvas->translate(100, 100);
    }
}
##

#SeeAlso Convexity Contour Direction getConvexity getConvexityOrUnknown setConvexity

##

#Subtopic Convexity ##

# ------------------------------------------------------------------------------

#Method bool isOval(SkRect* bounds) const
#In Property
#Line # returns if describes Oval ##

Returns true if this path is recognized as an oval or circle.

bounds receives bounds of Oval.

bounds is unmodified if Oval is not found.

#Param bounds  storage for bounding Rect of Oval; may be nullptr ##

#Return  true if Path is recognized as an oval or circle ##

#Example
void draw(SkCanvas* canvas) {
    SkPaint paint;
    SkPath path;
    path.addOval({20, 20, 220, 220});
    SkRect bounds;
    if (path.isOval(&bounds)) {
        paint.setColor(0xFF9FBFFF);
        canvas->drawRect(bounds, paint);
    }
    paint.setColor(0x3f000000);
    canvas->drawPath(path, paint);
}
##

#SeeAlso Oval addCircle addOval

##

# ------------------------------------------------------------------------------

#Method bool isRRect(SkRRect* rrect) const
#In Property
#Line # returns if describes Round_Rect ##

Returns true if this path is recognized as a SkRRect (but not an oval/circle or rect).

rrect receives bounds of Round_Rect.

rrect is unmodified if Round_Rect is not found.

#Param rrect  storage for bounding Rect of Round_Rect; may be nullptr ##

#Return  true if Path contains only Round_Rect ##

#Example
#Description
Draw rounded rectangle and its bounds.
##
void draw(SkCanvas* canvas) {
    SkPaint paint;
    SkPath path;
    path.addRRect(SkRRect::MakeRectXY({20, 20, 220, 220}, 30, 50));
    SkRRect rrect;
    if (path.isRRect(&rrect)) {
        const SkRect& bounds = rrect.rect();
        paint.setColor(0xFF9FBFFF);
        canvas->drawRect(bounds, paint);
    }
    paint.setColor(0x3f000000);
    canvas->drawPath(path, paint);
}
##

#SeeAlso Round_Rect addRoundRect addRRect

##

# ------------------------------------------------------------------------------

#Method SkPath& reset()
#In Constructors
#Line # removes Verb_Array, Point_Array, and Weights; frees memory ##
Sets Path to its initial state.
Removes Verb_Array, Point_Array, and Weights, and sets FillType to kWinding_FillType.
Internal storage associated with Path is released.

#Return reference to Path ##

#Example
   SkPath path1, path2;
   path1.setFillType(SkPath::kInverseWinding_FillType);
   path1.addRect({10, 20, 30, 40});
   SkDebugf("path1 %c= path2\n", path1 == path2 ? '=' : '!');
   path1.reset();
   SkDebugf("path1 %c= path2\n", path1 == path2 ? '=' : '!');
##

#SeeAlso rewind()

##

# ------------------------------------------------------------------------------

#Method SkPath& rewind()
#In Constructors
#Line # removes Verb_Array, Point_Array, and Weights, keeping memory ##
Sets Path to its initial state, preserving internal storage.
Removes Verb_Array, Point_Array, and Weights, and sets FillType to kWinding_FillType.
Internal storage associated with Path is retained.

Use rewind() instead of reset() if Path storage will be reused and performance
is critical.

#Return reference to Path ##

#Example
#Description
Although path1 retains its internal storage, it is indistinguishable from
a newly initialized path.
##
   SkPath path1, path2;
   path1.setFillType(SkPath::kInverseWinding_FillType);
   path1.addRect({10, 20, 30, 40});
   SkDebugf("path1 %c= path2\n", path1 == path2 ? '=' : '!');
   path1.rewind();
   SkDebugf("path1 %c= path2\n", path1 == path2 ? '=' : '!');
##

#SeeAlso reset()

##

# ------------------------------------------------------------------------------

#Method bool isEmpty() const
#In Property
#Line # returns if verb count is zero ##
Returns if Path is empty.
Empty Path may have FillType but has no SkPoint, Verb, or Conic_Weight.
SkPath() constructs empty Path; reset() and rewind() make Path empty.

#Return  true if the path contains no Verb array  ##

#Example
void draw(SkCanvas* canvas) {
    auto debugster = [](const char* prefix, const SkPath& path) -> void {
        SkDebugf("%s path is %s" "empty\n", prefix, path.isEmpty() ? "" : "not ");
    };
    SkPath path;
    debugster("initial", path);
    path.moveTo(0, 0);
    debugster("after moveTo", path);
    path.rewind();
    debugster("after rewind", path);
    path.lineTo(0, 0);
    debugster("after lineTo", path);
    path.reset();
    debugster("after reset", path);
}
#StdOut
initial path is empty
after moveTo path is not empty
after rewind path is empty
after lineTo path is not empty
after reset path is empty
##
##

#SeeAlso SkPath() reset() rewind()

##

# ------------------------------------------------------------------------------

#Method bool isLastContourClosed() const
#In Property
#Line # returns if final Contour forms a loop ##
Returns if Contour is closed.
Contour is closed if Path Verb array was last modified by close(). When stroked,
closed Contour draws Paint_Stroke_Join instead of Paint_Stroke_Cap at first and
last Point.

#Return  true if the last Contour ends with a kClose_Verb ##

#Example
#Description
close() has no effect if Path is empty; isLastContourClosed() returns
false until Path has geometry followed by close().
##
void draw(SkCanvas* canvas) {
    auto debugster = [](const char* prefix, const SkPath& path) -> void {
        SkDebugf("%s last contour is %s" "closed\n", prefix,
                 path.isLastContourClosed() ? "" : "not ");
    };
    SkPath path;
    debugster("initial", path);
    path.close();
    debugster("after close", path);
    path.lineTo(0, 0);
    debugster("after lineTo", path);
    path.close();
    debugster("after close", path);
}
#StdOut
initial last contour is not closed
after close last contour is not closed
after lineTo last contour is not closed
after close last contour is closed
##
##

#SeeAlso close()

##

# ------------------------------------------------------------------------------

#Method bool isFinite() const
#In Property
#Line # returns if all Point values are finite ##
Returns true for finite Point array values between negative SK_ScalarMax and
positive SK_ScalarMax. Returns false for any Point array value of
SK_ScalarInfinity, SK_ScalarNegativeInfinity, or SK_ScalarNaN.

#Return  true if all Point values are finite ##

#Example
void draw(SkCanvas* canvas) {
    auto debugster = [](const char* prefix, const SkPath& path) -> void {
        SkDebugf("%s path is %s" "finite\n", prefix, path.isFinite() ? "" : "not ");
    };
    SkPath path;
    debugster("initial", path);
    path.lineTo(SK_ScalarMax, SK_ScalarMax);
    debugster("after line", path);
    SkMatrix matrix;
    matrix.setScale(2, 2);
    path.transform(matrix);
    debugster("after scale", path);
}
#StdOut
initial path is finite
after line path is finite
after scale path is not finite
##
##

#SeeAlso SkScalar
##

# ------------------------------------------------------------------------------

#Method bool isVolatile() const
#In Property
#In Volatile
#Line # returns if Device should not cache ##
Returns true if the path is volatile; it will not be altered or discarded
by the caller after it is drawn. Paths by default have volatile set false, allowing
Surface to attach a cache of data which speeds repeated drawing. If true, Surface
may not speed repeated drawing.

#Return  true if caller will alter Path after drawing ##

#Example
    SkPath path;
    SkDebugf("volatile by default is %s\n", path.isVolatile() ? "true" : "false");
#StdOut
volatile by default is false
##
##

#SeeAlso setIsVolatile

##

# ------------------------------------------------------------------------------
#Subtopic Volatile
#Line # caching attribute ##
##

#Method void setIsVolatile(bool isVolatile)
#In Volatile
#Line # sets if Device should not cache ##
Specifies whether Path is volatile; whether it will be altered or discarded
by the caller after it is drawn. Paths by default have volatile set false, allowing
Device to attach a cache of data which speeds repeated drawing.

Mark temporary paths, discarded or modified after use, as volatile
to inform Device that the path need not be cached.

Mark animating Path volatile to improve performance.
Mark unchanging Path non-volatile to improve repeated rendering.

Raster_Surface Path draws are affected by volatile for some shadows.
GPU_Surface Path draws are affected by volatile for some shadows and concave geometries.

#Param isVolatile  true if caller will alter Path after drawing ##

#Example
#Height 50
#Width 50
    SkPaint paint;
    paint.setStyle(SkPaint::kStroke_Style);
    SkPath path;
    path.setIsVolatile(true);
    path.lineTo(40, 40);
    canvas->drawPath(path, paint);
    path.rewind();
    path.moveTo(0, 40);
    path.lineTo(40, 0);
    canvas->drawPath(path, paint);
##

#ToDo tie example to bench to show how volatile affects speed or dm to show resource usage ##

#SeeAlso isVolatile

##

# ------------------------------------------------------------------------------

#Method static bool IsLineDegenerate(const SkPoint& p1, const SkPoint& p2, bool exact)
#In Property
#Line # returns if Line is very small ##
Tests if Line between Point pair is degenerate.
Line with no length or that moves a very short distance is degenerate; it is
treated as a point.

exact changes the equality test. If true, returns true only if p1 equals p2.
If false, returns true if p1 equals or nearly equals p2.

#Param p1     line start point ##
#Param p2     line end point ##
#Param exact  if false, allow nearly equals ##

#Return  true if Line is degenerate; its length is effectively zero ##

#Example
#Description
As single precision floats, 100 and 100.000001 have the same bit representation,
and are exactly equal. 100 and 100.0001 have different bit representations, and
are not exactly equal, but are nearly equal.
##
void draw(SkCanvas* canvas) {
    SkPoint points[] = { {100, 100}, {100.000001f, 100.000001f}, {100.0001f, 100.0001f} };
    for (size_t i = 0; i < SK_ARRAY_COUNT(points) - 1; ++i) {
        for (bool exact : { false, true } ) {
            SkDebugf("line from (%1.8g,%1.8g) to (%1.8g,%1.8g) is %s" "degenerate, %s\n",
                    points[i].fX, points[i].fY, points[i + 1].fX, points[i + 1].fY,
                    SkPath::IsLineDegenerate(points[i], points[i + 1], exact)
                    ? "" : "not ", exact ? "exactly" : "nearly");
        }
    }
}
#StdOut
line from (100,100) to (100,100) is degenerate, nearly
line from (100,100) to (100,100) is degenerate, exactly
line from (100,100) to (100.0001,100.0001) is degenerate, nearly
line from (100,100) to (100.0001,100.0001) is not degenerate, exactly
#StdOut ##
##

#SeeAlso IsQuadDegenerate IsCubicDegenerate
##

# ------------------------------------------------------------------------------

#Method static bool IsQuadDegenerate(const SkPoint& p1, const SkPoint& p2,
                                 const SkPoint& p3, bool exact)
#In Property
#Line # returns if Quad is very small ##

Tests if Quad is degenerate.
Quad with no length or that moves a very short distance is degenerate; it is
treated as a point.

#Param p1  Quad start point ##
#Param p2  Quad control point ##
#Param p3  Quad end point ##
#Param exact  if true, returns true only if p1, p2, and p3 are equal;
              if false, returns true if p1, p2, and p3 are equal or nearly equal
##

#Return  true if Quad is degenerate; its length is effectively zero ##

#Example
#Description
As single precision floats: 100, 100.00001, and 100.00002 have different bit representations
but nearly the same value. Translating all three by 1000 gives them the same bit representation;
the fractional portion of the number can not be represented by the float and is lost.
##
void draw(SkCanvas* canvas) {
    auto debugster = [](const SkPath& path, bool exact) -> void {
        SkDebugf("quad (%1.8g,%1.8g), (%1.8g,%1.8g), (%1.8g,%1.8g) is %s" "degenerate, %s\n",
            path.getPoint(0).fX, path.getPoint(0).fY, path.getPoint(1).fX,
            path.getPoint(1).fY, path.getPoint(2).fX, path.getPoint(2).fY,
            SkPath::IsQuadDegenerate(path.getPoint(0), path.getPoint(1), path.getPoint(2), exact) ?
            "" : "not ", exact ? "exactly" : "nearly");
    };
    SkPath path, offset;
    path.moveTo({100, 100});
    path.quadTo({100.00001f, 100.00001f}, {100.00002f, 100.00002f});
    offset.addPath(path, 1000, 1000);
    for (bool exact : { false, true } ) {
        debugster(path, exact);
        debugster(offset, exact);
    }
}
#StdOut
quad (100,100), (100.00001,100.00001), (100.00002,100.00002) is degenerate, nearly
quad (1100,1100), (1100,1100), (1100,1100) is degenerate, nearly
quad (100,100), (100.00001,100.00001), (100.00002,100.00002) is not degenerate, exactly
quad (1100,1100), (1100,1100), (1100,1100) is degenerate, exactly
#StdOut ##
##

#SeeAlso IsLineDegenerate IsCubicDegenerate
##

# ------------------------------------------------------------------------------

#Method static bool IsCubicDegenerate(const SkPoint& p1, const SkPoint& p2,
                                  const SkPoint& p3, const SkPoint& p4, bool exact)
#In Property
#Line # returns if Cubic is very small ##

Tests if Cubic is degenerate.
Cubic with no length or that moves a very short distance is degenerate; it is
treated as a point.

#Param p1  Cubic start point ##
#Param p2  Cubic control point 1 ##
#Param p3  Cubic control point 2 ##
#Param p4  Cubic end point ##
#Param exact  if true, returns true only if p1, p2, p3, and p4 are equal;
              if false, returns true if p1, p2, p3, and p4 are equal or nearly equal
##

#Return  true if Cubic is degenerate; its length is effectively zero ##

#Example
void draw(SkCanvas* canvas) {
    SkPoint points[] = {{1, 0}, {0, 0}, {0, 0}, {0, 0}};
    SkScalar step = 1;
    SkScalar prior, length = 0, degenerate = 0;
    do {
        prior = points[0].fX;
        step /= 2;
        if (SkPath::IsCubicDegenerate(points[0], points[1], points[2], points[3], false)) {
            degenerate = prior;
            points[0].fX += step;
        } else {
            length = prior;
            points[0].fX -= step;
        }
    } while (prior != points[0].fX);
    SkDebugf("%1.8g is degenerate\n", degenerate);
    SkDebugf("%1.8g is length\n", length);
}
#StdOut
0.00024414062 is degenerate
0.00024414065 is length
#StdOut ##
##

##

# ------------------------------------------------------------------------------

#Method bool isLine(SkPoint line[2]) const
#In Property
#Line # returns if describes Line ##
Returns true if Path contains only one Line;
Path_Verb array has two entries: kMove_Verb, kLine_Verb.
If Path contains one Line and line is not nullptr, line is set to
Line start point and Line end point.
Returns false if Path is not one Line; line is unaltered.

#Param line  storage for Line. May be nullptr ##

#Return  true if Path contains exactly one Line ##

#Example
void draw(SkCanvas* canvas) {
    auto debugster = [](const char* prefix, const SkPath& path) -> void {
        SkPoint line[2];
        if (path.isLine(line)) {
            SkDebugf("%s is line (%1.8g,%1.8g) (%1.8g,%1.8g)\n", prefix,
                 line[0].fX, line[0].fY, line[1].fX, line[1].fY);
        } else {
            SkDebugf("%s is not line\n", prefix);
        }
    };
    SkPath path;
    debugster("empty", path);
    path.lineTo(0, 0);
    debugster("zero line", path);
    path.rewind();
    path.moveTo(10, 10);
    path.lineTo(20, 20);
    debugster("line", path);
    path.moveTo(20, 20);
    debugster("second move", path);
}
#StdOut
empty is not line
zero line is line (0,0) (0,0)
line is line (10,10) (20,20)
second move is not line
##
##

##

# ------------------------------------------------------------------------------

#Subtopic Point_Array
#Line # end points and control points for lines and curves ##
#Substitute SkPoint array

Point_Array contains Points satisfying the allocated Points for
each Verb in Verb_Array. For instance, Path containing one Contour with Line
and Quad is described by Verb_Array: Verb::kMoveTo, Verb::kLineTo, Verb::kQuadTo; and
one Point for move, one Point for Line, two Points for Quad; totaling four Points.

Point_Array may be read directly from Path with getPoints, or inspected with
getPoint, with Iter, or with RawIter.

#Method int getPoints(SkPoint points[], int max) const

#In Point_Array
#Line # returns Point_Array ##
Returns number of points in Path. Up to max points are copied.
points may be nullptr; then, max must be zero.
If max is greater than number of points, excess points storage is unaltered.

#Param points  storage for Path Point array. May be nullptr ##
#Param max  maximum to copy; must be greater than or equal to zero ##

#Return  Path Point array length ##

#Example
void draw(SkCanvas* canvas) {
    auto debugster = [](const char* prefix, const SkPath& path, SkPoint* points, int max) -> void {
         int count = path.getPoints(points, max);
         SkDebugf("%s point count: %d  ", prefix, count);
         for (int i = 0; i < SkTMin(count, max) && points; ++i) {
             SkDebugf("(%1.8g,%1.8g) ", points[i].fX, points[i].fY);
         }
         SkDebugf("\n");
    };
    SkPath path;
    path.lineTo(20, 20);
    path.lineTo(-10, -10);
    SkPoint points[3];
    debugster("no points",  path, nullptr, 0);
    debugster("zero max",  path, points, 0);
    debugster("too small",  path, points, 2);
    debugster("just right",  path, points, path.countPoints());
}
#StdOut
no points point count: 3
zero max point count: 3
too small point count: 3  (0,0) (20,20)
just right point count: 3  (0,0) (20,20) (-10,-10)
##
##

#SeeAlso countPoints getPoint
##

#Method int countPoints() const

#In Point_Array
#Line # returns Point_Array length ##
Returns the number of points in Path.
Point count is initially zero.

#Return  Path Point array length ##

#Example
void draw(SkCanvas* canvas) {
    auto debugster = [](const char* prefix, const SkPath& path) -> void {
         SkDebugf("%s point count: %d\n", prefix, path.countPoints());
    };
    SkPath path;
    debugster("empty", path);
    path.lineTo(0, 0);
    debugster("zero line", path);
    path.rewind();
    path.moveTo(10, 10);
    path.lineTo(20, 20);
    debugster("line", path);
    path.moveTo(20, 20);
    debugster("second move", path);
}
#StdOut
empty point count: 0
zero line point count: 2
line point count: 2
second move point count: 3
##
##

#SeeAlso getPoints
##

#Method SkPoint getPoint(int index) const

#In Point_Array
#Line # returns entry from Point_Array ##
Returns Point at index in Point_Array. Valid range for index is
0 to countPoints - 1.
Returns (0, 0) if index is out of range.

#Param index  Point array element selector ##

#Return  Point array value or (0, 0) ##

#Example
void draw(SkCanvas* canvas) {
    SkPath path;
    path.lineTo(20, 20);
    path.offset(-10, -10);
    for (int i= 0; i < path.countPoints(); ++i) {
         SkDebugf("point %d: (%1.8g,%1.8g)\n", i, path.getPoint(i).fX, path.getPoint(i).fY);
    }
}
#StdOut
point 0: (-10,-10)
point 1: (10,10)
##
##

#SeeAlso countPoints getPoints
##


#Subtopic Point_Array ##

# ------------------------------------------------------------------------------
#Subtopic Verb_Array
#Line # line and curve type for points ##

Verb_Array always starts with kMove_Verb.
If kClose_Verb is not the last entry, it is always followed by kMove_Verb;
the quantity of kMove_Verb equals the Contour count.
Verb_Array does not include or count kDone_Verb; it is a convenience
returned when iterating through Verb_Array.

Verb_Array may be read directly from Path with getVerbs, or inspected with Iter,
or with RawIter.

#Method int countVerbs() const

#In Verb_Array
#Line # returns Verb_Array length ##
Returns the number of Verbs: kMove_Verb, kLine_Verb, kQuad_Verb, kConic_Verb,
kCubic_Verb, and kClose_Verb; added to Path.

#Return  length of Verb_Array ##

#Example
SkPath path;
SkDebugf("empty verb count: %d\n", path.countVerbs());
path.addRoundRect({10, 20, 30, 40}, 5, 5);
SkDebugf("round rect verb count: %d\n", path.countVerbs());
#StdOut
empty verb count: 0
round rect verb count: 10
##
##

#SeeAlso getVerbs Iter RawIter

##

#Method int getVerbs(uint8_t verbs[], int max) const

#In Verb_Array
#Line # returns Verb_Array ##
Returns the number of verbs in the path. Up to max verbs are copied. The
verbs are copied as one byte per verb.

#Param verbs  storage for verbs, may be nullptr ##
#Param max    maximum number to copy into verbs ##

#Return  the actual number of verbs in the path ##

#Example
void draw(SkCanvas* canvas) {
    auto debugster = [](const char* prefix, const SkPath& path, uint8_t* verbs, int max) -> void {
         int count = path.getVerbs(verbs, max);
         SkDebugf("%s verb count: %d  ", prefix, count);
         const char* verbStr[] = { "move", "line", "quad", "conic", "cubic", "close" };
         for (int i = 0; i < SkTMin(count, max) && verbs; ++i) {
             SkDebugf("%s ", verbStr[verbs[i]]);
         }
         SkDebugf("\n");
    };
    SkPath path;
    path.lineTo(20, 20);
    path.lineTo(-10, -10);
    uint8_t verbs[3];
    debugster("no verbs",  path, nullptr, 0);
    debugster("zero max",  path, verbs, 0);
    debugster("too small",  path, verbs, 2);
    debugster("just right",  path, verbs, path.countVerbs());
}
#StdOut
no verbs verb count: 3
zero max verb count: 3
too small verb count: 3  move line
just right verb count: 3  move line line
##
##

#SeeAlso countVerbs getPoints Iter RawIter
##

#Subtopic Verb_Array ##

# ------------------------------------------------------------------------------

#Method void swap(SkPath& other)
#In Operators
#Line # exchanges Path pair ##
Exchanges the Verb_Array, Point_Array, Weights, and Fill_Type with other.
Cached state is also exchanged. swap() internally exchanges pointers, so
it is lightweight and does not allocate memory.

swap() usage has largely been replaced by operator=(const SkPath& path).
Paths do not copy their content on assignment until they are written to,
making assignment as efficient as swap().

#Param other  Path exchanged by value ##

#Example
SkPath path1, path2;
path1.addRect({10, 20, 30, 40});
path1.swap(path2);
const SkRect& b1 = path1.getBounds();
SkDebugf("path1 bounds = %g, %g, %g, %g\n", b1.fLeft, b1.fTop, b1.fRight, b1.fBottom);
const SkRect& b2 = path2.getBounds();
SkDebugf("path2 bounds = %g, %g, %g, %g\n", b2.fLeft, b2.fTop, b2.fRight, b2.fBottom);
#StdOut
path1 bounds = 0, 0, 0, 0
path2 bounds = 10, 20, 30, 40
#StdOut ##
##

#SeeAlso operator=(const SkPath& path)

##

# ------------------------------------------------------------------------------

#Method const SkRect& getBounds() const
#In Property
#Line # returns maximum and minimum of Point_Array ##
Returns minimum and maximum axes values of Point_Array.
Returns (0, 0, 0, 0) if Path contains no points. Returned bounds width and height may
be larger or smaller than area affected when Path is drawn.

Rect returned includes all Points added to Path, including Points associated with
kMove_Verb that define empty Contours.

#Return  bounds of all Points in Point_Array ##

#Example
#Description
Bounds of upright Circle can be predicted from center and radius.
Bounds of rotated Circle includes control Points outside of filled area.
##
    auto debugster = [](const char* prefix, const SkPath& path) -> void {
            const SkRect& bounds = path.getBounds();
            SkDebugf("%s bounds = %g, %g, %g, %g\n", prefix,
                     bounds.fLeft, bounds.fTop, bounds.fRight, bounds.fBottom);
    };
    SkPath path;
    debugster("empty", path);
    path.addCircle(50, 45, 25);
    debugster("circle", path);
    SkMatrix matrix;
    matrix.setRotate(45, 50, 45);
    path.transform(matrix);
    debugster("rotated circle", path);
#StdOut
empty bounds = 0, 0, 0, 0
circle bounds = 25, 20, 75, 70
rotated circle bounds = 14.6447, 9.64466, 85.3553, 80.3553
##
##

#SeeAlso computeTightBounds updateBoundsCache

##

# ------------------------------------------------------------------------------
#Subtopic Utility
#Line # rarely called management functions ##
##

#Method void updateBoundsCache() const
#In Utility
#Line # refreshes result of getBounds ##
Updates internal bounds so that subsequent calls to getBounds are instantaneous.
Unaltered copies of Path may also access cached bounds through getBounds.

For now, identical to calling getBounds and ignoring the returned value.

Call to prepare Path subsequently drawn from multiple threads,
to avoid a race condition where each draw separately computes the bounds.

#Example
    double times[2] = { 0, 0 };
    for (int i = 0; i < 10000; ++i) {
      SkPath path;
      for (int j = 1; j < 100; ++ j) {
        path.addCircle(50 + j, 45 + j, 25 + j);
      }
      if (1 & i) {
        path.updateBoundsCache();
      }
      double start = SkTime::GetNSecs();
      (void) path.getBounds();
      times[1 & i] += SkTime::GetNSecs() - start;
    }
    SkDebugf("uncached avg: %g ms\n", times[0] * 1e-6);
    SkDebugf("cached avg: %g ms\n", times[1] * 1e-6);
#StdOut
#Volatile
uncached avg: 0.18048 ms
cached avg: 0.182784 ms
##
##

#SeeAlso getBounds
#ToDo the results don't make sense, need to profile to figure this out ##

##

# ------------------------------------------------------------------------------

#Method SkRect computeTightBounds() const
#In Property
#Line # returns extent of geometry ##
Returns minimum and maximum axes values of the lines and curves in Path.
Returns (0, 0, 0, 0) if Path contains no points.
Returned bounds width and height may be larger or smaller than area affected
when Path is drawn.

Includes Points associated with kMove_Verb that define empty
Contours.

Behaves identically to getBounds when Path contains
only lines. If Path contains curves, computed bounds includes
the maximum extent of the Quad, Conic, or Cubic; is slower than getBounds;
and unlike getBounds, does not cache the result.

#Return  tight bounds of curves in Path ##

#Example
    auto debugster = [](const char* prefix, const SkPath& path) -> void {
            const SkRect& bounds = path.computeTightBounds();
            SkDebugf("%s bounds = %g, %g, %g, %g\n", prefix,
                     bounds.fLeft, bounds.fTop, bounds.fRight, bounds.fBottom);
    };
    SkPath path;
    debugster("empty", path);
    path.addCircle(50, 45, 25);
    debugster("circle", path);
    SkMatrix matrix;
    matrix.setRotate(45, 50, 45);
    path.transform(matrix);
    debugster("rotated circle", path);
#StdOut
empty bounds = 0, 0, 0, 0
circle bounds = 25, 20, 75, 70
rotated circle bounds = 25, 20, 75, 70
##
##

#SeeAlso getBounds

##

# ------------------------------------------------------------------------------

#Method bool conservativelyContainsRect(const SkRect& rect) const
#In Property
#Line # returns true if Rect may be inside ##
Returns true if rect is contained by Path.
May return false when rect is contained by Path.

For now, only returns true if Path has one Contour and is convex.
rect may share points and edges with Path and be contained.
Returns true if rect is empty, that is, it has zero width or height; and
the Point or Line described by rect is contained by Path.

#Param rect  Rect, Line, or Point checked for containment ##

#Return  true if rect is contained ##

#Example
#Height 140
#Description
Rect is drawn in blue if it is contained by red Path.
##
void draw(SkCanvas* canvas) {
    SkPath path;
    path.addRoundRect({10, 20, 54, 120}, 10, 20);
    SkRect tests[] = {
      { 10, 40, 54, 80 },
      { 25, 20, 39, 120 },
      { 15, 25, 49, 115 },
      { 13, 27, 51, 113 },
    };
    for (unsigned i = 0; i < SK_ARRAY_COUNT(tests); ++i) {
      SkPaint paint;
      paint.setColor(SK_ColorRED);
      canvas->drawPath(path, paint);
      bool rectInPath = path.conservativelyContainsRect(tests[i]);
      paint.setColor(rectInPath ? SK_ColorBLUE : SK_ColorBLACK);
      canvas->drawRect(tests[i], paint);
      canvas->translate(64, 0);
    }
}
##

#SeeAlso contains Op Rect Convexity

##

# ------------------------------------------------------------------------------

#Method void incReserve(int extraPtCount)
#In Utility
#Line # reserves space for additional data ##
Grows Path Verb_Array and Point_Array to contain extraPtCount additional Points.
May improve performance and use less memory by
reducing the number and size of allocations when creating Path.

#Param extraPtCount  number of additional Points to allocate ##

#Example
#Height 192
void draw(SkCanvas* canvas) {
    auto addPoly = [](int sides, SkScalar size, SkPath* path) -> void {
        path->moveTo(size, 0);
        for (int i = 1; i < sides; i++) {
            SkScalar c, s = SkScalarSinCos(SK_ScalarPI * 2 * i / sides, &c);
            path->lineTo(c * size, s * size);
        }
        path->close();
    };
    SkPath path;
    path.incReserve(3 + 4 + 5 + 6 + 7 + 8 + 9);
    for (int sides = 3; sides < 10; ++sides) {
       addPoly(sides, sides, &path);
    }
    SkMatrix matrix;
    matrix.setScale(10, 10, -10, -10);
    path.transform(matrix);
    SkPaint paint;
    paint.setStyle(SkPaint::kStroke_Style);
    canvas->drawPath(path, paint);
}
##

#SeeAlso Point_Array

##

#Method void shrinkToFit()
#In Utility
#Line # removes unused reserved space ##
Shrinks Path Verb_Array and Point_Array storage to discard unused capacity.
May reduce the heap overhead for Paths known to be fully constructed.

#NoExample
#Height 192
void draw(SkCanvas* canvas) {
    SkPath skinnyPath;
    skinnyPath.lineTo(100, 100);
    skinnyPath.shrinkToFit();

    SkDebugf("no wasted Path capacity in my house!\n");
}
##

#SeeAlso incReserve

##

# ------------------------------------------------------------------------------
#Subtopic Build
#Line # adds points and verbs to path ##
##

#Method SkPath& moveTo(SkScalar x, SkScalar y)
#In Build
#Line # starts Contour ##
Adds beginning of Contour at Point (x, y).

#Param x  x-axis value of Contour start ##
#Param y  y-axis value of Contour start ##

#Return reference to Path ##

#Example
    #Width 140
    #Height 100
    void draw(SkCanvas* canvas) {
        SkRect rect = { 20, 20, 120, 80 };
        SkPath path;
        path.addRect(rect);
        path.moveTo(rect.fLeft, rect.fTop);
        path.lineTo(rect.fRight, rect.fBottom);
        path.moveTo(rect.fLeft, rect.fBottom);
        path.lineTo(rect.fRight, rect.fTop);
        SkPaint paint;
        paint.setStyle(SkPaint::kStroke_Style);
        canvas->drawPath(path, paint);
    }
##

#SeeAlso Contour lineTo rMoveTo quadTo conicTo cubicTo close()

##

#Method SkPath& moveTo(const SkPoint& p)

Adds beginning of Contour at Point p.

#Param p  contour start ##

#Return reference to Path ##

#Example
    #Width 128
    #Height 128
void draw(SkCanvas* canvas) {
    SkPoint data[][3] = {{{30,40},{60,60},{90,30}}, {{30,120},{60,100},{90,120}},
                         {{60,100},{60,40},{70,30}}, {{60,40},{50,20},{70,30}}};
    SkPath path;
    for (unsigned i = 0; i < SK_ARRAY_COUNT(data); ++i) {
        path.moveTo(data[i][0]);
        path.lineTo(data[i][1]);
        path.lineTo(data[i][2]);
    }
    SkPaint paint;
    paint.setStyle(SkPaint::kStroke_Style);
    canvas->drawPath(path, paint);
}
##

#SeeAlso Contour lineTo rMoveTo quadTo conicTo cubicTo close()

##

#Method SkPath& rMoveTo(SkScalar dx, SkScalar dy)
#In Build
#Line # starts Contour relative to Last_Point ##
Adds beginning of Contour relative to Last_Point.
If Path is empty, starts Contour at (dx, dy).
Otherwise, start Contour at Last_Point offset by (dx, dy).
Function name stands for "relative move to".

#Param dx  offset from Last_Point to Contour start on x-axis ##
#Param dy  offset from Last_Point to Contour start on y-axis ##

#Return reference to Path ##

#Example
    #Height 100
    SkPath path;
    path.addRect({20, 20, 80, 80}, SkPath::kCW_Direction, 2);
    path.rMoveTo(25, 2);
    SkVector arrow[] = {{0, -4}, {-20, 0}, {0, -3}, {-5, 5}, {5, 5}, {0, -3}, {20, 0}};
    for (unsigned i = 0; i < SK_ARRAY_COUNT(arrow); ++i) {
        path.rLineTo(arrow[i].fX, arrow[i].fY);
    }
    SkPaint paint;
    canvas->drawPath(path, paint);
    SkPoint lastPt;
    path.getLastPt(&lastPt);
    canvas->drawString("start", lastPt.fX, lastPt.fY, paint);
##

#SeeAlso Contour lineTo moveTo quadTo conicTo cubicTo close()

##

# ------------------------------------------------------------------------------

#Method SkPath& lineTo(SkScalar x, SkScalar y)
#In Build
#Line # appends Line ##
Adds Line from Last_Point to (x, y). If Path is empty, or last Verb is
kClose_Verb, Last_Point is set to (0, 0) before adding Line.

lineTo appends kMove_Verb to Verb_Array and (0, 0) to Point_Array, if needed.
lineTo then appends kLine_Verb to Verb_Array and (x, y) to Point_Array.

#Param x  end of added Line in x ##
#Param y  end of added Line in y ##

#Return reference to Path ##

#Example
#Height 100
###$
void draw(SkCanvas* canvas) {
    SkPaint paint;
    paint.setAntiAlias(true);
    paint.setTextSize(72);
    canvas->drawString("#", 120, 80, paint);
    paint.setStyle(SkPaint::kStroke_Style);
    paint.setStrokeWidth(5);
    SkPath path;
    SkPoint hash[] = {{58, 28}, {43, 80}, {37, 45}, {85, 45}};
    SkVector offsets[] = {{0, 0}, {17, 0}, {0, 0}, {-5, 17}};
    unsigned o = 0;
    for (unsigned i = 0; i < SK_ARRAY_COUNT(hash); i += 2) {
        for (unsigned j = 0; j < 2; o++, j++) {
            path.moveTo(hash[i].fX + offsets[o].fX, hash[i].fY + offsets[o].fY);
            path.lineTo(hash[i + 1].fX + offsets[o].fX, hash[i + 1].fY + offsets[o].fY);
        }
    }
    canvas->drawPath(path, paint);
}
$$$#
##

#SeeAlso Contour moveTo rLineTo addRect

##

# ------------------------------------------------------------------------------

#Method SkPath& lineTo(const SkPoint& p)

Adds Line from Last_Point to Point p. If Path is empty, or last Verb is
kClose_Verb, Last_Point is set to (0, 0) before adding Line.

lineTo first appends kMove_Verb to Verb_Array and (0, 0) to Point_Array, if needed.
lineTo then appends kLine_Verb to Verb_Array and Point p to Point_Array.

#Param p  end Point of added Line ##

#Return reference to Path ##

#Example
#Height 100
    SkPath path;
    SkVector oxo[] = {{25, 25}, {35, 35}, {25, 35}, {35, 25},
                      {40, 20}, {40, 80}, {60, 20}, {60, 80},
                      {20, 40}, {80, 40}, {20, 60}, {80, 60}};
    for (unsigned i = 0; i < SK_ARRAY_COUNT(oxo); i += 2) {
        path.moveTo(oxo[i]);
        path.lineTo(oxo[i + 1]);
    }
    SkPaint paint;
    paint.setStyle(SkPaint::kStroke_Style);
    canvas->drawPath(path, paint);
##

#SeeAlso Contour moveTo rLineTo addRect

##

# ------------------------------------------------------------------------------

#Method SkPath& rLineTo(SkScalar dx, SkScalar dy)
#In Build
#Line # appends Line relative to Last_Point ##
Adds Line from Last_Point to Vector (dx, dy). If Path is empty, or last Verb is
kClose_Verb, Last_Point is set to (0, 0) before adding Line.

Appends kMove_Verb to Verb_Array and (0, 0) to Point_Array, if needed;
then appends kLine_Verb to Verb_Array and Line end to Point_Array.
Line end is Last_Point plus Vector (dx, dy).
Function name stands for "relative line to".

#Param dx  offset from Last_Point to Line end on x-axis ##
#Param dy  offset from Last_Point to Line end on y-axis ##

#Return reference to Path ##

#Example
#Height 128
void draw(SkCanvas* canvas) {
    SkPaint paint;
    paint.setAntiAlias(true);
    paint.setStyle(SkPaint::kStroke_Style);
    SkPath path;
    path.moveTo(10, 98);
    SkScalar x = 0, y = 0;
    for (int i = 10; i < 100; i += 5) {
        x += i * ((i & 2) - 1);
        y += i * (((i + 1) & 2) - 1);
        path.rLineTo(x, y);

    }
    canvas->drawPath(path, paint);
}
##

#SeeAlso Contour moveTo lineTo addRect

##

# ------------------------------------------------------------------------------
#Subtopic Quad
#Alias Quad ##
#Alias Quads ##
#Alias Quadratic_Bezier ##
#Alias Quadratic_Beziers ##
#Line # curve described by second-order polynomial ##

Quad describes a quadratic Bezier, a second-order curve identical to a section
of a parabola. Quad begins at a start Point, curves towards a control Point,
and then curves to an end Point.

#Example
#Height 110
void draw(SkCanvas* canvas) {
    SkPaint paint;
    paint.setAntiAlias(true);
    paint.setStyle(SkPaint::kStroke_Style);
    SkPoint quadPts[] = {{20, 90}, {120, 10}, {220, 90}};
    canvas->drawLine(quadPts[0], quadPts[1], paint);
    canvas->drawLine(quadPts[1], quadPts[2], paint);
    SkPath path;
    path.moveTo(quadPts[0]);
    path.quadTo(quadPts[1], quadPts[2]);
    paint.setStrokeWidth(3);
    canvas->drawPath(path, paint);
}
##

Quad is a special case of Conic where Conic_Weight is set to one.

Quad is always contained by the triangle connecting its three Points. Quad
begins tangent to the line between start Point and control Point, and ends
tangent to the line between control Point and end Point.

#Example
#Height 160
void draw(SkCanvas* canvas) {
    SkPaint paint;
    paint.setAntiAlias(true);
    paint.setStyle(SkPaint::kStroke_Style);
    SkPoint quadPts[] = {{20, 150}, {120, 10}, {220, 150}};
    SkColor colors[] = { 0xff88ff00, 0xff0088bb, 0xff6600cc, 0xffbb3377 };
    for (unsigned i = 0; i < SK_ARRAY_COUNT(colors); ++i) {
        paint.setColor(0x7fffffff & colors[i]);
        paint.setStrokeWidth(1);
        canvas->drawLine(quadPts[0], quadPts[1], paint);
        canvas->drawLine(quadPts[1], quadPts[2], paint);
        SkPath path;
        path.moveTo(quadPts[0]);
        path.quadTo(quadPts[1], quadPts[2]);
        paint.setStrokeWidth(3);
        paint.setColor(colors[i]);
        canvas->drawPath(path, paint);
        quadPts[1].fY += 30;
   }
}
##

#Method SkPath& quadTo(SkScalar x1, SkScalar y1, SkScalar x2, SkScalar y2)

#In Quad
#Line # appends Quad ##
    Adds Quad from Last_Point towards (x1, y1), to (x2, y2).
    If Path is empty, or last Verb is kClose_Verb, Last_Point is set to (0, 0)
    before adding Quad.

    Appends kMove_Verb to Verb_Array and (0, 0) to Point_Array, if needed;
    then appends kQuad_Verb to Verb_Array; and (x1, y1), (x2, y2)
    to Point_Array.

    #Param x1  control Point of Quad in x ##
    #Param y1  control Point of Quad in y ##
    #Param x2  end Point of Quad in x ##
    #Param y2  end Point of Quad in y ##

    #Return reference to Path ##

    #Example
    void draw(SkCanvas* canvas) {
        SkPaint paint;
        paint.setAntiAlias(true);
        paint.setStyle(SkPaint::kStroke_Style);
        SkPath path;
        path.moveTo(0, -10);
        for (int i = 0; i < 128; i += 16) {
            path.quadTo( 10 + i, -10 - i,  10 + i,       0);
            path.quadTo( 14 + i,  14 + i,       0,  14 + i);
            path.quadTo(-18 - i,  18 + i, -18 - i,       0);
            path.quadTo(-22 - i, -22 - i,       0, -22 - i);
        }
        path.offset(128, 128);
        canvas->drawPath(path, paint);
    }
    ##

    #SeeAlso Contour moveTo conicTo rQuadTo

##

#Method SkPath& quadTo(const SkPoint& p1, const SkPoint& p2)
#In Build
#In Quad
    Adds Quad from Last_Point towards Point p1, to Point p2.
    If Path is empty, or last Verb is kClose_Verb, Last_Point is set to (0, 0)
    before adding Quad.

    Appends kMove_Verb to Verb_Array and (0, 0) to Point_Array, if needed;
    then appends kQuad_Verb to Verb_Array; and Points p1, p2
    to Point_Array.

    #Param p1  control Point of added Quad ##
    #Param p2  end Point of added Quad ##

    #Return reference to Path ##

    #Example
    void draw(SkCanvas* canvas) {
        SkPaint paint;
        paint.setStyle(SkPaint::kStroke_Style);
        paint.setAntiAlias(true);
        SkPath path;
        SkPoint pts[] = {{128, 10}, {10, 214}, {236, 214}};
        path.moveTo(pts[1]);
        for (int i = 0; i < 3; ++i) {
            path.quadTo(pts[i % 3],  pts[(i + 2) % 3]);
        }
        canvas->drawPath(path, paint);
    }
    ##

    #SeeAlso Contour moveTo conicTo rQuadTo

##

#Method SkPath& rQuadTo(SkScalar dx1, SkScalar dy1, SkScalar dx2, SkScalar dy2)
#In Build
#In Quad
#Line # appends Quad relative to Last_Point ##
    Adds Quad from Last_Point towards Vector (dx1, dy1), to Vector (dx2, dy2).
    If Path is empty, or last Verb
    is kClose_Verb, Last_Point is set to (0, 0) before adding Quad.

    Appends kMove_Verb to Verb_Array and (0, 0) to Point_Array,
    if needed; then appends kQuad_Verb to Verb_Array; and appends Quad
    control and Quad end to Point_Array.
    Quad control is Last_Point plus Vector (dx1, dy1).
    Quad end is Last_Point plus Vector (dx2, dy2).
    Function name stands for "relative quad to".

    #Param dx1  offset from Last_Point to Quad control on x-axis ##
    #Param dy1  offset from Last_Point to Quad control on y-axis ##
    #Param dx2  offset from Last_Point to Quad end on x-axis ##
    #Param dy2  offset from Last_Point to Quad end on y-axis ##

    #Return reference to Path ##

    #Example
    void draw(SkCanvas* canvas) {
        SkPaint paint;
        paint.setAntiAlias(true);
        SkPath path;
        path.moveTo(128, 20);
        path.rQuadTo(-6, 10, -7, 10);
        for (int i = 1; i < 32; i += 4) {
           path.rQuadTo(10 + i, 10 + i, 10 + i * 4, 10);
           path.rQuadTo(-10 - i, 10 + i, -10 - (i + 2) * 4, 10);
        }
        path.quadTo(92, 220, 128, 215);
        canvas->drawPath(path, paint);
    }
    ##

    #SeeAlso Contour moveTo conicTo quadTo

##

#Subtopic Quad ##

# ------------------------------------------------------------------------------

#Subtopic Conic
#Line # conic section defined by three points and a weight ##
#Alias Conics ##

Conic describes a conical section: a piece of an ellipse, or a piece of a
parabola, or a piece of a hyperbola. Conic begins at a start Point,
curves towards a control Point, and then curves to an end Point. The influence
of the control Point is determined by Conic_Weight.

Each Conic in Path adds two Points and one Conic_Weight. Conic_Weights in Path
may be inspected with Iter, or with RawIter.

#Subtopic Weight
#Alias Conic_Weights ##
#Alias Weights ##
#Line # strength of Conic control Point ##

Weight determines both the strength of the control Point and the type of Conic.
Weight varies from zero to infinity. At zero, Weight causes the control Point to
have no effect; Conic is identical to a line segment from start Point to end
point. If Weight is less than one, Conic follows an elliptical arc.
If Weight is exactly one, then Conic is identical to Quad; Conic follows a
parabolic arc. If Weight is greater than one, Conic follows a hyperbolic
arc. If Weight is infinity, Conic is identical to two line segments, connecting
start Point to control Point, and control Point to end Point.

#Example
#Description
When Conic_Weight is one, Quad is added to path; the two are identical.
##
void draw(SkCanvas* canvas) {
    const char* verbNames[] = { "move", "line", "quad", "conic", "cubic", "close", "done" };
    const int pointCount[]  = {     1 ,     2 ,     3 ,      3 ,      4 ,      1 ,     0  };
    SkPath path;
    path.conicTo(20, 30, 50, 60, 1);
    SkPath::Iter iter(path, false);
    SkPath::Verb verb;
    do {
       SkPoint points[4];
       verb = iter.next(points);
       SkDebugf("%s ", verbNames[(int) verb]);
       for (int i = 0; i < pointCount[(int) verb]; ++i) {
            SkDebugf("{%g, %g}, ", points[i].fX, points[i].fY);
       }
       if (SkPath::kConic_Verb == verb) {
           SkDebugf("weight = %g", iter.conicWeight());
       }
       SkDebugf("\n");
    } while (SkPath::kDone_Verb != verb);
}
#StdOut
move {0, 0},
quad {0, 0}, {20, 30}, {50, 60},
done
##
##

If weight is less than one, Conic is an elliptical segment.

#Example
#Description
A 90 degree circular arc has the weight #Formula # 1 / sqrt(2) ##.
##
void draw(SkCanvas* canvas) {
    const char* verbNames[] = { "move", "line", "quad", "conic", "cubic", "close", "done" };
    const int pointCount[]  = {     1 ,     2 ,     3 ,      3 ,      4 ,      1 ,     0  };
    SkPath path;
    path.arcTo(20, 0, 20, 20, 20);
    SkPath::Iter iter(path, false);
    SkPath::Verb verb;
    do {
       SkPoint points[4];
       verb = iter.next(points);
       SkDebugf("%s ", verbNames[(int) verb]);
       for (int i = 0; i < pointCount[(int) verb]; ++i) {
            SkDebugf("{%g, %g}, ", points[i].fX, points[i].fY);
       }
       if (SkPath::kConic_Verb == verb) {
           SkDebugf("weight = %g", iter.conicWeight());
       }
       SkDebugf("\n");
    } while (SkPath::kDone_Verb != verb);
}
#StdOut
move {0, 0},
conic {0, 0}, {20, 0}, {20, 20}, weight = 0.707107
done
##
##

If weight is greater than one, Conic is a hyperbolic segment. As weight gets large,
a hyperbolic segment can be approximated by straight lines connecting the
control Point with the end Points.

#Example
void draw(SkCanvas* canvas) {
    const char* verbNames[] = { "move", "line", "quad", "conic", "cubic", "close", "done" };
    const int pointCount[]  = {     1 ,     2 ,     3 ,      3 ,      4 ,      1 ,     0  };
    SkPath path;
    path.conicTo(20, 0, 20, 20, SK_ScalarInfinity);
    SkPath::Iter iter(path, false);
    SkPath::Verb verb;
    do {
       SkPoint points[4];
       verb = iter.next(points);
       SkDebugf("%s ", verbNames[(int) verb]);
       for (int i = 0; i < pointCount[(int) verb]; ++i) {
            SkDebugf("{%g, %g}, ", points[i].fX, points[i].fY);
       }
       if (SkPath::kConic_Verb == verb) {
           SkDebugf("weight = %g", iter.conicWeight());
       }
       SkDebugf("\n");
    } while (SkPath::kDone_Verb != verb);
}
#StdOut
move {0, 0},
line {0, 0}, {20, 0},
line {20, 0}, {20, 20},
done
##
##

#Subtopic Weight ##

#Method SkPath& conicTo(SkScalar x1, SkScalar y1, SkScalar x2, SkScalar y2,
                 SkScalar w)
#In Conic
#In Build
#Line # appends Conic ##

    Adds Conic from Last_Point towards (x1, y1), to (x2, y2), weighted by w.
    If Path is empty, or last Verb is kClose_Verb, Last_Point is set to (0, 0)
    before adding Conic.

    Appends kMove_Verb to Verb_Array and (0, 0) to Point_Array, if needed.

    If w is finite and not one, appends kConic_Verb to Verb_Array;
    and (x1, y1), (x2, y2) to Point_Array; and w to Conic_Weights.

    If w is one, appends kQuad_Verb to Verb_Array, and
    (x1, y1), (x2, y2) to Point_Array.

    If w is not finite, appends kLine_Verb twice to Verb_Array, and
    (x1, y1), (x2, y2) to Point_Array.

    #Param x1  control Point of Conic in x ##
    #Param y1  control Point of Conic in y ##
    #Param x2  end Point of Conic in x ##
    #Param y2  end Point of Conic in y ##
    #Param w   weight of added Conic ##

    #Return reference to Path ##

    #Example
    #Height 160
    #Description
    As weight increases, curve is pulled towards control point.
    The bottom two curves are elliptical; the next is parabolic; the
    top curve is hyperbolic.
    ##
void draw(SkCanvas* canvas) {
    SkPaint paint;
    paint.setAntiAlias(true);
    paint.setStyle(SkPaint::kStroke_Style);
    SkPoint conicPts[] = {{20, 150}, {120, 10}, {220, 150}};
    canvas->drawLine(conicPts[0], conicPts[1], paint);
    canvas->drawLine(conicPts[1], conicPts[2], paint);
    SkColor colors[] = { 0xff88ff00, 0xff0088bb, 0xff6600cc, 0xffbb3377 };
    paint.setStrokeWidth(3);
    SkScalar weight = 0.5f;
    for (unsigned i = 0; i < SK_ARRAY_COUNT(colors); ++i) {
        SkPath path;
        path.moveTo(conicPts[0]);
        path.conicTo(conicPts[1], conicPts[2], weight);
        paint.setColor(colors[i]);
        canvas->drawPath(path, paint);
        weight += 0.25f;
   }
}
    ##

    #SeeAlso rConicTo arcTo addArc quadTo

##

#Method SkPath& conicTo(const SkPoint& p1, const SkPoint& p2, SkScalar w)
#In Build
#In Conic
    Adds Conic from Last_Point towards Point p1, to Point p2, weighted by w.
    If Path is empty, or last Verb is kClose_Verb, Last_Point is set to (0, 0)
    before adding Conic.

    Appends kMove_Verb to Verb_Array and (0, 0) to Point_Array, if needed.

    If w is finite and not one, appends kConic_Verb to Verb_Array;
    and Points p1, p2 to Point_Array; and w to Conic_Weights.

    If w is one, appends kQuad_Verb to Verb_Array, and Points p1, p2
    to Point_Array.

    If w is not finite, appends kLine_Verb twice to Verb_Array, and
    Points p1, p2 to Point_Array.

    #Param p1  control Point of added Conic ##
    #Param p2  end Point of added Conic ##
    #Param w   weight of added Conic ##

    #Return reference to Path ##

    #Example
    #Height 128
    #Description
    Conics and arcs use identical representations. As the arc sweep increases
    the Conic_Weight also increases, but remains smaller than one.
    ##
void draw(SkCanvas* canvas) {
    SkPaint paint;
    paint.setAntiAlias(true);
    paint.setStyle(SkPaint::kStroke_Style);
    SkRect oval = {0, 20, 120, 140};
    SkPath path;
    for (int i = 0; i < 4; ++i) {
        path.moveTo(oval.centerX(), oval.fTop);
        path.arcTo(oval, -90, 90 - 20 * i, false);
        oval.inset(15, 15);
    }
    path.offset(100, 0);
    SkScalar conicWeights[] = { 0.707107f, 0.819152f, 0.906308f, 0.965926f };
    SkPoint conicPts[][3] = { { {40, 20}, {100, 20}, {100, 80} },
                              { {40, 35}, {71.509f, 35}, {82.286f, 64.6091f} },
                              { {40, 50}, {53.9892f, 50}, {62.981f, 60.7164f} },
                              { {40, 65}, {44.0192f, 65}, {47.5f, 67.0096f} } };
    for (int i = 0; i < 4; ++i) {
         path.moveTo(conicPts[i][0]);
         path.conicTo(conicPts[i][1], conicPts[i][2], conicWeights[i]);
    }
    canvas->drawPath(path, paint);
}
    ##

    #SeeAlso rConicTo arcTo addArc quadTo

##

#Method SkPath& rConicTo(SkScalar dx1, SkScalar dy1, SkScalar dx2, SkScalar dy2,
                  SkScalar w)
#In Build
#In Conic
#Line # appends Conic relative to Last_Point ##

    Adds Conic from Last_Point towards Vector (dx1, dy1), to Vector (dx2, dy2),
    weighted by w. If Path is empty, or last Verb
    is kClose_Verb, Last_Point is set to (0, 0) before adding Conic.

    Appends kMove_Verb to Verb_Array and (0, 0) to Point_Array,
    if needed.

    If w is finite and not one, next appends kConic_Verb to Verb_Array,
    and w is recorded as Conic_Weight; otherwise, if w is one, appends
    kQuad_Verb to Verb_Array; or if w is not finite, appends kLine_Verb
    twice to Verb_Array.

    In all cases appends Points control and end to Point_Array.
    control is Last_Point plus Vector (dx1, dy1).
    end is Last_Point plus Vector (dx2, dy2).

    Function name stands for "relative conic to".

    #Param dx1  offset from Last_Point to Conic control on x-axis ##
    #Param dy1  offset from Last_Point to Conic control on y-axis ##
    #Param dx2  offset from Last_Point to Conic end on x-axis ##
    #Param dy2  offset from Last_Point to Conic end on y-axis ##
    #Param w    weight of added Conic ##

    #Return reference to Path ##

    #Example
    #Height 140
    void draw(SkCanvas* canvas) {
        SkPaint paint;
        paint.setAntiAlias(true);
        paint.setStyle(SkPaint::kStroke_Style);
        SkPath path;
        path.moveTo(20, 80);
        path.rConicTo( 60,   0,  60,  60, 0.707107f);
        path.rConicTo(  0, -60,  60, -60, 0.707107f);
        path.rConicTo(-60,   0, -60, -60, 0.707107f);
        path.rConicTo(  0,  60, -60,  60, 0.707107f);
        canvas->drawPath(path, paint);
    }
    ##

    #SeeAlso conicTo arcTo addArc quadTo

##

#Subtopic Conic ##

# ------------------------------------------------------------------------------
#Subtopic Cubic
#Alias Cubic ##
#Alias Cubics ##
#Alias Cubic_Bezier ##
#Alias Cubic_Beziers ##
#Line # curve described by third-order polynomial ##

Cubic describes a Bezier_Curve segment described by a third-order polynomial.
Cubic begins at a start Point, curving towards the first control Point;
and curves from the end Point towards the second control Point.

#Example
#Height 160
void draw(SkCanvas* canvas) {
    SkPaint paint;
    paint.setAntiAlias(true);
    paint.setStyle(SkPaint::kStroke_Style);
    SkPoint cubicPts[] = {{20, 150}, {90, 10}, {160, 150}, {230, 10}};
    SkColor colors[] = { 0xff88ff00, 0xff0088bb, 0xff6600cc, 0xffbb3377 };
    for (unsigned i = 0; i < SK_ARRAY_COUNT(colors); ++i) {
        paint.setColor(0x7fffffff & colors[i]);
        paint.setStrokeWidth(1);
        for (unsigned j = 0; j < 3; ++j) {
            canvas->drawLine(cubicPts[j], cubicPts[j + 1], paint);
        }
        SkPath path;
        path.moveTo(cubicPts[0]);
        path.cubicTo(cubicPts[1], cubicPts[2], cubicPts[3]);
        paint.setStrokeWidth(3);
        paint.setColor(colors[i]);
        canvas->drawPath(path, paint);
        cubicPts[1].fY += 30;
        cubicPts[2].fX += 30;
   }
}
##

#Method SkPath& cubicTo(SkScalar x1, SkScalar y1, SkScalar x2, SkScalar y2,
                 SkScalar x3, SkScalar y3)
#In Build
#In Cubic
#Line # appends Cubic ##

Adds Cubic from Last_Point towards (x1, y1), then towards (x2, y2), ending at
(x3, y3). If Path is empty, or last Verb is kClose_Verb, Last_Point is set to
(0, 0) before adding Cubic.

Appends kMove_Verb to Verb_Array and (0, 0) to Point_Array, if needed;
then appends kCubic_Verb to Verb_Array; and (x1, y1), (x2, y2), (x3, y3)
to Point_Array.

#Param x1  first control Point of Cubic in x ##
#Param y1  first control Point of Cubic in y ##
#Param x2  second control Point of Cubic in x ##
#Param y2  second control Point of Cubic in y ##
#Param x3  end Point of Cubic in x ##
#Param y3  end Point of Cubic in y ##

#Return reference to Path ##

#Example
void draw(SkCanvas* canvas) {
    SkPaint paint;
    paint.setAntiAlias(true);
    paint.setStyle(SkPaint::kStroke_Style);
    SkPath path;
    path.moveTo(0, -10);
    for (int i = 0; i < 128; i += 16) {
        SkScalar c = i * 0.5f;
        path.cubicTo( 10 + c, -10 - i,  10 + i, -10 - c,  10 + i,       0);
        path.cubicTo( 14 + i,  14 + c,  14 + c,  14 + i,       0,  14 + i);
        path.cubicTo(-18 - c,  18 + i, -18 - i,  18 + c, -18 - i,       0);
        path.cubicTo(-22 - i, -22 - c, -22 - c, -22 - i,       0, -22 - i);
    }
    path.offset(128, 128);
    canvas->drawPath(path, paint);
}
##

#SeeAlso Contour moveTo rCubicTo quadTo

##

# ------------------------------------------------------------------------------

#Method SkPath& cubicTo(const SkPoint& p1, const SkPoint& p2, const SkPoint& p3)

#In Build
#In Cubic
Adds Cubic from Last_Point towards Point p1, then towards Point p2, ending at
Point p3. If Path is empty, or last Verb is kClose_Verb, Last_Point is set to
(0, 0) before adding Cubic.

Appends kMove_Verb to Verb_Array and (0, 0) to Point_Array, if needed;
then appends kCubic_Verb to Verb_Array; and Points p1, p2, p3
to Point_Array.

#Param p1  first control Point of Cubic ##
#Param p2  second control Point of Cubic ##
#Param p3  end Point of Cubic ##

#Return reference to Path ##

#Example
#Height 84
    SkPaint paint;
    paint.setAntiAlias(true);
    paint.setStyle(SkPaint::kStroke_Style);
    SkPoint pts[] = { {20, 20}, {300, 80}, {-140, 90}, {220, 10} };
    SkPath path;
    path.moveTo(pts[0]);
    path.cubicTo(pts[1], pts[2], pts[3]);
    canvas->drawPath(path, paint);
##

#SeeAlso Contour moveTo rCubicTo quadTo

##

# ------------------------------------------------------------------------------

#Method SkPath& rCubicTo(SkScalar x1, SkScalar y1, SkScalar x2, SkScalar y2,
                  SkScalar x3, SkScalar y3)
#In Build
#In Cubic
#Line # appends Cubic relative to Last_Point ##

    Adds Cubic from Last_Point towards Vector (dx1, dy1), then towards
    Vector (dx2, dy2), to Vector (dx3, dy3).
    If Path is empty, or last Verb
    is kClose_Verb, Last_Point is set to (0, 0) before adding Cubic.

    Appends kMove_Verb to Verb_Array and (0, 0) to Point_Array,
    if needed; then appends kCubic_Verb to Verb_Array; and appends Cubic
    control and Cubic end to Point_Array.
    Cubic control is Last_Point plus Vector (dx1, dy1).
    Cubic end is Last_Point plus Vector (dx2, dy2).
    Function name stands for "relative cubic to".

    #Param x1  offset from Last_Point to first Cubic control on x-axis ##
    #Param y1  offset from Last_Point to first Cubic control on y-axis ##
    #Param x2  offset from Last_Point to second Cubic control on x-axis ##
    #Param y2  offset from Last_Point to second Cubic control on y-axis ##
    #Param x3  offset from Last_Point to Cubic end on x-axis ##
    #Param y3  offset from Last_Point to Cubic end on y-axis ##

    #Return reference to Path ##

#Example
    void draw(SkCanvas* canvas) {
        SkPaint paint;
        paint.setAntiAlias(true);
        paint.setStyle(SkPaint::kStroke_Style);
        SkPath path;
        path.moveTo(24, 108);
        for (int i = 0; i < 16; i++) {
           SkScalar sx, sy;
           sx = SkScalarSinCos(i * SK_ScalarPI / 8, &sy);
           path.rCubicTo(40 * sx, 4 * sy, 4 * sx, 40 * sy, 40 * sx, 40 * sy);
        }
        canvas->drawPath(path, paint);
    }
##

#SeeAlso Contour moveTo cubicTo quadTo

##

#Subtopic Cubic ##

# ------------------------------------------------------------------------------

#Subtopic Arc
#Line # part of Oval or Circle ##
Arc can be constructed in a number of ways. Arc may be described by part of Oval and angles,
by start point and end point, and by radius and tangent lines. Each construction has advantages,
and some constructions correspond to Arc drawing in graphics standards.

All Arc draws are implemented by one or more Conic draws. When Conic_Weight is less than one,
Conic describes an Arc of some Oval or Circle.

arcTo(const SkRect& oval, SkScalar startAngle, SkScalar sweepAngle, bool forceMoveTo)
describes Arc as a piece of Oval, beginning at start angle, sweeping clockwise or counterclockwise,
which may continue Contour or start a new one. This construction is similar to PostScript and
HTML_Canvas arcs. Variation addArc always starts new Contour. Canvas::drawArc draws without
requiring Path.

arcTo(SkScalar x1, SkScalar y1, SkScalar x2, SkScalar y2, SkScalar radius)
describes Arc as tangent to the line (x0, y0), (x1, y1) and tangent to the line (x1, y1), (x2, y2)
where (x0, y0) is the last Point added to Path. This construction is similar to PostScript and
HTML_Canvas arcs.

arcTo(SkScalar rx, SkScalar ry, SkScalar xAxisRotate, ArcSize largeArc, Direction sweep,
      SkScalar x, SkScalar y)
describes Arc as part of Oval with radii (rx, ry), beginning at
last Point added to Path and ending at (x, y). More than one Arc satisfies this criteria,
so additional values choose a single solution. This construction is similar to SVG arcs.

conicTo describes Arc of less than 180 degrees as a pair of tangent lines and Conic_Weight.
conicTo can represent any Arc with a sweep less than 180 degrees at any rotation. All arcTo
constructions are converted to Conic data when added to Path.

#ToDo  example is spaced correctly on fiddle but spacing is too wide on pc
##

#Illustration

#List
# <sup>1</sup> arcTo(const SkRect& oval, SkScalar startAngle, SkScalar sweepAngle, bool forceMoveTo) ##
# <sup>2</sup> parameter sets force MoveTo  ##
# <sup>3</sup> start angle must be multiple of 90 degrees ##
# <sup>4</sup> arcTo(SkScalar x1, SkScalar y1, SkScalar x2, SkScalar y2, SkScalar radius) ##
# <sup>5</sup> arcTo(SkScalar rx, SkScalar ry, SkScalar xAxisRotate, ArcSize largeArc,
               Direction sweep, SkScalar x, SkScalar y) ##
#List ##

#Example
#Height 128
void draw(SkCanvas* canvas) {
    SkRect oval = {8, 8, 56, 56};
    SkPaint ovalPaint;
    ovalPaint.setAntiAlias(true);
    SkPaint textPaint(ovalPaint);
    ovalPaint.setStyle(SkPaint::kStroke_Style);
    SkPaint arcPaint(ovalPaint);
    arcPaint.setStrokeWidth(5);
    arcPaint.setColor(SK_ColorBLUE);
    canvas->translate(-64, 0);
    for (char arcStyle = '1'; arcStyle <= '6'; ++arcStyle) {
        '4' == arcStyle ? canvas->translate(-96, 55) : canvas->translate(64, 0);
        canvas->drawText(&arcStyle, 1, 30, 36, textPaint);
        canvas->drawOval(oval, ovalPaint);
        SkPath path;
        path.moveTo({56, 32});
        switch (arcStyle) {
            case '1':
                path.arcTo(oval, 0, 90, false);
                break;
            case '2':
                canvas->drawArc(oval, 0, 90, false, arcPaint);
                continue;
            case '3':
                path.addArc(oval, 0, 90);
                break;
            case '4':
                path.arcTo({56, 56}, {32, 56}, 24);
                break;
            case '5':
                path.arcTo({24, 24}, 0, SkPath::kSmall_ArcSize, SkPath::kCW_Direction, {32, 56});
                break;
            case '6':
                path.conicTo({56, 56}, {32, 56}, SK_ScalarRoot2Over2);
                break;
         }
         canvas->drawPath(path, arcPaint);
     }
}
#Example ##

In the example above:
#List
# 1 describes an arc from an oval, a starting angle, and a sweep angle. ##
# 2 is similar to 1, but does not require building a path to draw. ##
# 3 is similar to 1, but always begins new Contour. ##
# 4 describes an arc from a pair of tangent lines and a radius. ##
# 5 describes an arc from Oval center, arc start Point and arc end Point. ##
# 6 describes an arc from a pair of tangent lines and a Conic_Weight. ##
#List ##

#Method SkPath& arcTo(const SkRect& oval, SkScalar startAngle, SkScalar sweepAngle, bool forceMoveTo)
#In Build
#In Arc
#Line # appends Arc ##
Appends Arc to Path. Arc added is part of ellipse
bounded by oval, from startAngle through sweepAngle. Both startAngle and
sweepAngle are measured in degrees, where zero degrees is aligned with the
positive x-axis, and positive sweeps extends Arc clockwise.

arcTo adds Line connecting Path last Point to initial Arc Point if forceMoveTo
is false and Path is not empty. Otherwise, added Contour begins with first point
of Arc. Angles greater than -360 and less than 360 are treated modulo 360.

#Param oval        bounds of ellipse containing Arc ##
#Param startAngle  starting angle of Arc in degrees ##
#Param sweepAngle  sweep, in degrees. Positive is clockwise; treated modulo 360 ##
#Param forceMoveTo  true to start a new contour with Arc ##

#Return reference to Path ##

#Example
#Height 200
#Description
arcTo continues a previous contour when forceMoveTo is false and when Path
is not empty.
##
void draw(SkCanvas* canvas) {
    SkPaint paint;
    SkPath path;
    paint.setStyle(SkPaint::kStroke_Style);
    paint.setStrokeWidth(4);
    path.moveTo(0, 0);
    path.arcTo({20, 20, 120, 120}, -90, 90, false);
    canvas->drawPath(path, paint);
    path.rewind();
    path.arcTo({120, 20, 220, 120}, -90, 90, false);
    canvas->drawPath(path, paint);
    path.rewind();
    path.moveTo(0, 0);
    path.arcTo({20, 120, 120, 220}, -90, 90, true);
    canvas->drawPath(path, paint);
}
##

#SeeAlso addArc SkCanvas::drawArc conicTo

##

# ------------------------------------------------------------------------------

#Method SkPath& arcTo(SkScalar x1, SkScalar y1, SkScalar x2, SkScalar y2, SkScalar radius)
#In Build
#In Arc
Appends Arc to Path, after appending Line if needed. Arc is implemented by Conic
weighted to describe part of Circle. Arc is contained by tangent from
last Path point (x0, y0) to (x1, y1), and tangent from (x1, y1) to (x2, y2). Arc
is part of Circle sized to radius, positioned so it touches both tangent lines.

#ToDo  allow example to hide source and not be exposed as fiddle ##

#Example
#Height 226
void draw(SkCanvas* canvas) {
    SkPaint tangentPaint;
    tangentPaint.setAntiAlias(true);
    SkPaint textPaint(tangentPaint);
    tangentPaint.setStyle(SkPaint::kStroke_Style);
    tangentPaint.setColor(SK_ColorGRAY);
    SkPaint arcPaint(tangentPaint);
    arcPaint.setStrokeWidth(5);
    arcPaint.setColor(SK_ColorBLUE);
    SkPath path;
    SkPoint pts[] = { {56, 20}, {200, 20}, {90, 190} };
    SkScalar radius = 50;
    path.moveTo(pts[0]);
    path.arcTo(pts[1], pts[2], radius);
    canvas->drawLine(pts[0], pts[1], tangentPaint);
    canvas->drawLine(pts[1], pts[2], tangentPaint);
    SkPoint lastPt;
    (void) path.getLastPt(&lastPt);
    SkVector radial = pts[2] - pts[1];
    radial.setLength(radius);
    SkPoint center = { lastPt.fX - radial.fY, lastPt.fY + radial.fX };
    canvas->drawCircle(center, radius, tangentPaint);
    canvas->drawLine(lastPt, center, tangentPaint);
    radial = pts[1] - pts[0];
    radial.setLength(radius);
    SkPoint arcStart = { center.fX + radial.fY, center.fY - radial.fX };
    canvas->drawLine(center, arcStart, tangentPaint);
    canvas->drawPath(path, arcPaint);
    textPaint.setTextAlign(SkPaint::kRight_Align);
    canvas->drawString("(x0, y0)", pts[0].fX - 5, pts[0].fY, textPaint);
    textPaint.setTextAlign(SkPaint::kLeft_Align);
    canvas->drawString("(x1, y1)", pts[1].fX + 5, pts[1].fY, textPaint);
    textPaint.setTextAlign(SkPaint::kCenter_Align);
    canvas->drawString("(x2, y2)", pts[2].fX, pts[2].fY + 15, textPaint);
    textPaint.setTextAlign(SkPaint::kRight_Align);
    canvas->drawString("radius", center.fX + 15, center.fY + 25, textPaint);
    canvas->drawString("radius", center.fX - 3, center.fY - 16, textPaint);
}
##

If last Path Point does not start Arc, arcTo appends connecting Line to Path.
The length of Vector from (x1, y1) to (x2, y2) does not affect Arc.

#Example
#Height 128
void draw(SkCanvas* canvas) {
    SkPaint tangentPaint;
    tangentPaint.setAntiAlias(true);
    SkPaint textPaint(tangentPaint);
    tangentPaint.setStyle(SkPaint::kStroke_Style);
    tangentPaint.setColor(SK_ColorGRAY);
    SkPaint arcPaint(tangentPaint);
    arcPaint.setStrokeWidth(5);
    arcPaint.setColor(SK_ColorBLUE);
    SkPath path;
    SkPoint pts[] = { {156, 20}, {200, 20}, {170, 50} };
    SkScalar radius = 50;
    path.moveTo(pts[0]);
    path.arcTo(pts[1], pts[2], radius);
    canvas->drawLine(pts[0], pts[1], tangentPaint);
    canvas->drawLine(pts[1], pts[2], tangentPaint);
    SkPoint lastPt;
    (void) path.getLastPt(&lastPt);
    SkVector radial = pts[2] - pts[1];
    radial.setLength(radius);
    SkPoint center = { lastPt.fX - radial.fY, lastPt.fY + radial.fX };
    canvas->drawLine(lastPt, center, tangentPaint);
    radial = pts[1] - pts[0];
    radial.setLength(radius);
    SkPoint arcStart = { center.fX + radial.fY, center.fY - radial.fX };
    canvas->drawLine(center, arcStart, tangentPaint);
    canvas->drawPath(path, arcPaint);
    textPaint.setTextAlign(SkPaint::kCenter_Align);
    canvas->drawString("(x0, y0)", pts[0].fX, pts[0].fY - 7, textPaint);
    textPaint.setTextAlign(SkPaint::kLeft_Align);
    canvas->drawString("(x1, y1)", pts[1].fX + 5, pts[1].fY, textPaint);
    textPaint.setTextAlign(SkPaint::kCenter_Align);
    canvas->drawString("(x2, y2)", pts[2].fX, pts[2].fY + 15, textPaint);
    textPaint.setTextAlign(SkPaint::kRight_Align);
    canvas->drawString("radius", center.fX + 15, center.fY + 25, textPaint);
    canvas->drawString("radius", center.fX - 5, center.fY - 20, textPaint);
}
##

Arc sweep is always less than 180 degrees. If radius is zero, or if
tangents are nearly parallel, arcTo appends Line from last Path Point to (x1, y1).

arcTo appends at most one Line and one Conic.
arcTo implements the functionality of PostScript_Arct and HTML_Canvas_ArcTo.

#Param x1      x-axis value common to pair of tangents ##
#Param y1      y-axis value common to pair of tangents ##
#Param x2      x-axis value end of second tangent ##
#Param y2      y-axis value end of second tangent ##
#Param radius  distance from Arc to Circle center ##

#Return reference to Path ##

#Example
#Description
arcTo is represented by Line and circular Conic in Path.
##
void draw(SkCanvas* canvas) {
    SkPath path;
    path.moveTo({156, 20});
    path.arcTo(200, 20, 170, 50, 50);
    SkPath::Iter iter(path, false);
    SkPoint p[4];
    SkPath::Verb verb;
    while (SkPath::kDone_Verb != (verb = iter.next(p))) {
        switch (verb) {
            case SkPath::kMove_Verb:
                SkDebugf("move to (%g,%g)\n", p[0].fX, p[0].fY);
                break;
            case SkPath::kLine_Verb:
                SkDebugf("line (%g,%g),(%g,%g)\n", p[0].fX, p[0].fY, p[1].fX, p[1].fY);
                break;
            case SkPath::kConic_Verb:
                SkDebugf("conic (%g,%g),(%g,%g),(%g,%g) weight %g\n",
                         p[0].fX, p[0].fY, p[1].fX, p[1].fY, p[2].fX, p[2].fY, iter.conicWeight());
                break;
            default:
                SkDebugf("unexpected verb\n");
        }
    }
}
#StdOut
move to (156,20)
line (156,20),(79.2893,20)
conic (79.2893,20),(200,20),(114.645,105.355) weight 0.382683
##
##

#SeeAlso conicTo

##

# ------------------------------------------------------------------------------

#Method SkPath& arcTo(const SkPoint p1, const SkPoint p2, SkScalar radius)
#In Build
#In Arc
Appends Arc to Path, after appending Line if needed. Arc is implemented by Conic
weighted to describe part of Circle. Arc is contained by tangent from
last Path point to p1, and tangent from p1 to p2. Arc
is part of Circle sized to radius, positioned so it touches both tangent lines.

If last Path Point does not start Arc, arcTo appends connecting Line to Path.
The length of Vector from p1 to p2 does not affect Arc.

Arc sweep is always less than 180 degrees. If radius is zero, or if
tangents are nearly parallel, arcTo appends Line from last Path Point to p1.

arcTo appends at most one Line and one Conic.
arcTo implements the functionality of PostScript_Arct and HTML_Canvas_ArcTo.

#Param p1      Point common to pair of tangents ##
#Param p2      end of second tangent ##
#Param radius  distance from Arc to Circle center ##

#Return reference to Path ##

#Example
#Description
Because tangent lines are parallel, arcTo appends line from last Path Point to
p1, but does not append a circular Conic.
##
void draw(SkCanvas* canvas) {
    SkPath path;
    path.moveTo({156, 20});
    path.arcTo({200, 20}, {170, 20}, 50);
    SkPath::Iter iter(path, false);
    SkPoint p[4];
    SkPath::Verb verb;
    while (SkPath::kDone_Verb != (verb = iter.next(p))) {
        switch (verb) {
            case SkPath::kMove_Verb:
                SkDebugf("move to (%g,%g)\n", p[0].fX, p[0].fY);
                break;
            case SkPath::kLine_Verb:
                SkDebugf("line (%g,%g),(%g,%g)\n", p[0].fX, p[0].fY, p[1].fX, p[1].fY);
                break;
            case SkPath::kConic_Verb:
                SkDebugf("conic (%g,%g),(%g,%g),(%g,%g) weight %g\n",
                          p[0].fX, p[0].fY, p[1].fX, p[1].fY, p[2].fX, p[2].fY, iter.conicWeight());
                break;
            default:
                SkDebugf("unexpected verb\n");
        }
    }
}
#StdOut
move to (156,20)
line (156,20),(200,20)
##
##

#SeeAlso conicTo

##

# ------------------------------------------------------------------------------

#Enum ArcSize
#Line # used by arcTo variation ##

#Code
    enum ArcSize {
        kSmall_ArcSize,
        kLarge_ArcSize,
    };
##

Four Oval parts with radii (rx, ry) start at last Path Point and ends at (x, y).
ArcSize and Direction select one of the four Oval parts.

#Const kSmall_ArcSize 0
#Line # smaller of Arc pair ##
##
#Const kLarge_ArcSize 1
#Line # larger of Arc pair ##
##

#Example
#Height 160
#Description
Arc begins at top of Oval pair and ends at bottom. Arc can take four routes to get there.
Two routes are large, and two routes are counterclockwise. The one route both large
and counterclockwise is blue.
##
void draw(SkCanvas* canvas) {
    SkPaint paint;
    paint.setAntiAlias(true);
    paint.setStyle(SkPaint::kStroke_Style);
    for (auto sweep: { SkPath::kCW_Direction, SkPath::kCCW_Direction } ) {
        for (auto arcSize : { SkPath::kSmall_ArcSize, SkPath::kLarge_ArcSize } ) {
            SkPath path;
            path.moveTo({120, 50});
            path.arcTo(70, 40, 30, arcSize, sweep, 156, 100);
            if (SkPath::kCCW_Direction == sweep && SkPath::kLarge_ArcSize == arcSize) {
                paint.setColor(SK_ColorBLUE);
                paint.setStrokeWidth(3);
            }
            canvas->drawPath(path, paint);
         }
    }
}
##

#SeeAlso arcTo Direction

##

# ------------------------------------------------------------------------------

#Method SkPath& arcTo(SkScalar rx, SkScalar ry, SkScalar xAxisRotate, ArcSize largeArc,
               Direction sweep, SkScalar x, SkScalar y)
#In Build
#In Arc

Appends Arc to Path. Arc is implemented by one or more Conics weighted to
describe part of Oval with radii (rx, ry) rotated by xAxisRotate degrees. Arc
curves from last Path Point to (x, y), choosing one of four possible routes:
clockwise or counterclockwise, and smaller or larger.

Arc sweep is always less than 360 degrees. arcTo appends Line to (x, y) if
either radii are zero, or if last Path Point equals (x, y). arcTo scales radii
(rx, ry) to fit last Path Point and (x, y) if both are greater than zero but
too small.

arcTo appends up to four Conic curves.
arcTo implements the functionality of SVG_Arc, although SVG "sweep-flag" value
is opposite the integer value of sweep; SVG "sweep-flag" uses 1 for clockwise,
while kCW_Direction  cast to int is zero.

#Param rx           radius in x before x-axis rotation ##
#Param ry           radius in y before x-axis rotation ##
#Param xAxisRotate  x-axis rotation in degrees; positive values are clockwise ##
#Param largeArc     chooses smaller or larger Arc ##
#Param sweep        chooses clockwise or counterclockwise Arc ##
#Param x            end of Arc ##
#Param y            end of Arc ##

#Return reference to Path ##

#Example
#Height 160
void draw(SkCanvas* canvas) {
    SkPaint paint;
    paint.setAntiAlias(true);
    paint.setStyle(SkPaint::kStroke_Style);
    for (auto sweep: { SkPath::kCW_Direction, SkPath::kCCW_Direction } ) {
        for (auto arcSize : { SkPath::kSmall_ArcSize, SkPath::kLarge_ArcSize } ) {
            SkPath path;
            path.moveTo({120, 50});
            path.arcTo(70, 40, 30, arcSize, sweep, 120.1, 50);
            if (SkPath::kCCW_Direction == sweep && SkPath::kLarge_ArcSize == arcSize) {
                paint.setColor(SK_ColorBLUE);
                paint.setStrokeWidth(3);
            }
            canvas->drawPath(path, paint);
         }
    }
}
##

#SeeAlso rArcTo ArcSize Direction

##

# ------------------------------------------------------------------------------

#Method SkPath& arcTo(const SkPoint r, SkScalar xAxisRotate, ArcSize largeArc, Direction sweep,
               const SkPoint xy)
#In Build
#In Arc

Appends Arc to Path. Arc is implemented by one or more Conic weighted to describe
part of Oval with radii (r.fX, r.fY) rotated by xAxisRotate degrees. Arc curves
from last Path Point to (xy.fX, xy.fY), choosing one of four possible routes:
clockwise or counterclockwise,
and smaller or larger.

Arc sweep is always less than 360 degrees. arcTo appends Line to xy if either
radii are zero, or if last Path Point equals (x, y). arcTo scales radii r to fit
last Path Point and xy if both are greater than zero but too small to describe
an arc.

arcTo appends up to four Conic curves.
arcTo implements the functionality of SVG_Arc, although SVG "sweep-flag" value is
opposite the integer value of sweep; SVG "sweep-flag" uses 1 for clockwise, while
kCW_Direction cast to int is zero.

#Param r            radii on axes before x-axis rotation ##
#Param xAxisRotate  x-axis rotation in degrees; positive values are clockwise ##
#Param largeArc     chooses smaller or larger Arc ##
#Param sweep        chooses clockwise or counterclockwise Arc ##
#Param xy           end of Arc ##

#Return reference to Path ##

#Example
#Height 108
void draw(SkCanvas* canvas) {
    SkPaint paint;
    SkPath path;
    const SkPoint starts[] = {{20, 20}, {120, 20}, {70, 60}};
    for (auto start : starts) {
        path.moveTo(start.fX, start.fY);
        path.rArcTo(20, 20, 0, SkPath::kSmall_ArcSize, SkPath::kCCW_Direction, 60, 0);
    }
    canvas->drawPath(path, paint);
}
##

#SeeAlso rArcTo ArcSize Direction

##

# ------------------------------------------------------------------------------

#Method SkPath& rArcTo(SkScalar rx, SkScalar ry, SkScalar xAxisRotate, ArcSize largeArc,
                Direction sweep, SkScalar dx, SkScalar dy)
#In Build
#In Arc
#Line # appends Arc relative to Last_Point ##

Appends Arc to Path, relative to last Path Point. Arc is implemented by one or
more Conic, weighted to describe part of Oval with radii (rx, ry) rotated by
xAxisRotate degrees. Arc curves from last Path Point (x0, y0) to end Point:
#Formula # (x0 + dx, y0 + dy) ##, choosing one of four possible routes: clockwise or
counterclockwise, and smaller or larger. If Path is empty, the start Arc Point
is (0, 0).

Arc sweep is always less than 360 degrees. arcTo appends Line to end Point
if either radii are zero, or if last Path Point equals end Point.
arcTo scales radii (rx, ry) to fit last Path Point and end Point if both are
greater than zero but too small to describe an arc.

arcTo appends up to four Conic curves.
arcTo implements the functionality of SVG_Arc, although SVG "sweep-flag" value is
opposite the integer value of sweep; SVG "sweep-flag" uses 1 for clockwise, while
kCW_Direction cast to int is zero.

#Param rx           radius before x-axis rotation ##
#Param ry           radius before x-axis rotation ##
#Param xAxisRotate  x-axis rotation in degrees; positive values are clockwise ##
#Param largeArc     chooses smaller or larger Arc ##
#Param sweep        chooses clockwise or counterclockwise Arc ##
#Param dx           x-axis offset end of Arc from last Path Point ##
#Param dy           y-axis offset end of Arc from last Path Point ##

#Return reference to Path ##

#Example
#Height 108
void draw(SkCanvas* canvas) {
    SkPaint paint;
    SkPath path;
    const SkPoint starts[] = {{20, 20}, {120, 20}, {70, 60}};
    for (auto start : starts) {
        path.moveTo(start.fX, start.fY);
        path.rArcTo(20, 20, 0, SkPath::kSmall_ArcSize, SkPath::kCCW_Direction, 60, 0);
    }
    canvas->drawPath(path, paint);
}
##

#SeeAlso arcTo ArcSize Direction

##

#Subtopic Arc ##

# ------------------------------------------------------------------------------

#Method SkPath& close()
#In Build
#Line # makes last Contour a loop ##
Appends kClose_Verb to Path. A closed Contour connects the first and last Point
with Line, forming a continuous loop. Open and closed Contour draw the same
with SkPaint::kFill_Style. With SkPaint::kStroke_Style, open Contour draws
Paint_Stroke_Cap at Contour start and end; closed Contour draws
Paint_Stroke_Join at Contour start and end.

close() has no effect if Path is empty or last Path Verb is kClose_Verb.

#Return reference to Path ##

#Example
void draw(SkCanvas* canvas) {
    SkPaint paint;
    paint.setStrokeWidth(15);
    paint.setStrokeCap(SkPaint::kRound_Cap);
    SkPath path;
    const SkPoint points[] = {{20, 20}, {70, 20}, {40, 90}};
    path.addPoly(points, SK_ARRAY_COUNT(points), false);
    for (int loop = 0; loop < 2; ++loop) {
        for (auto style : {SkPaint::kStroke_Style, SkPaint::kFill_Style,
                SkPaint::kStrokeAndFill_Style} ) {
            paint.setStyle(style);
            canvas->drawPath(path, paint);
            canvas->translate(85, 0);
        }
        path.close();
        canvas->translate(-255, 128);
    }
}
##

#SeeAlso

##

# ------------------------------------------------------------------------------

#Method static bool IsInverseFillType(FillType fill)
#In Property
#Line # returns if Fill_Type represents outside geometry ##
Returns true if fill is inverted and Path with fill represents area outside
of its geometric bounds.

#Table
#Legend
# FillType                 # is inverse ##
##
# kWinding_FillType        # false      ##
# kEvenOdd_FillType        # false      ##
# kInverseWinding_FillType # true       ##
# kInverseEvenOdd_FillType # true       ##
##

#Param fill  one of: kWinding_FillType, kEvenOdd_FillType,
             kInverseWinding_FillType, kInverseEvenOdd_FillType
##

#Return  true if Path fills outside its bounds ##

#Example
#Function
###$
#define nameValue(fill) { SkPath::fill, #fill }

$$$#
##
void draw(SkCanvas* canvas) {
    struct {
        SkPath::FillType fill;
        const char* name;
    } fills[] = {
        nameValue(kWinding_FillType),
        nameValue(kEvenOdd_FillType),
        nameValue(kInverseWinding_FillType),
        nameValue(kInverseEvenOdd_FillType),
    };
    for (auto fill: fills ) {
        SkDebugf("IsInverseFillType(%s) == %s\n", fill.name, SkPath::IsInverseFillType(fill.fill) ?
                 "true" : "false");
    }
}
#StdOut
IsInverseFillType(kWinding_FillType) == false
IsInverseFillType(kEvenOdd_FillType) == false
IsInverseFillType(kInverseWinding_FillType) == true
IsInverseFillType(kInverseEvenOdd_FillType) == true
##
##

#SeeAlso FillType getFillType setFillType ConvertToNonInverseFillType

##

# ------------------------------------------------------------------------------

#Method static FillType ConvertToNonInverseFillType(FillType fill)
#In Utility
#Line # returns Fill_Type representing inside geometry ##
Returns equivalent Fill_Type representing Path fill inside its bounds.
.

#Table
#Legend
# FillType                 # inside FillType   ##
##
# kWinding_FillType        # kWinding_FillType ##
# kEvenOdd_FillType        # kEvenOdd_FillType ##
# kInverseWinding_FillType # kWinding_FillType ##
# kInverseEvenOdd_FillType # kEvenOdd_FillType ##
##

#Param fill  one of: kWinding_FillType, kEvenOdd_FillType,
             kInverseWinding_FillType, kInverseEvenOdd_FillType
##

#Return  fill, or kWinding_FillType or kEvenOdd_FillType if fill is inverted ##

#Example
#Function
###$
#define nameValue(fill) { SkPath::fill, #fill }

$$$#
##
void draw(SkCanvas* canvas) {
    struct {
        SkPath::FillType fill;
        const char* name;
    } fills[] = {
        nameValue(kWinding_FillType),
        nameValue(kEvenOdd_FillType),
        nameValue(kInverseWinding_FillType),
        nameValue(kInverseEvenOdd_FillType),
    };
    for (unsigned i = 0; i < SK_ARRAY_COUNT(fills); ++i) {
        if (fills[i].fill != (SkPath::FillType) i) {
            SkDebugf("fills array order does not match FillType enum order");
            break;
        }
        SkDebugf("ConvertToNonInverseFillType(%s) == %s\n", fills[i].name,
                fills[(int) SkPath::ConvertToNonInverseFillType(fills[i].fill)].name);
    }
}
#StdOut
ConvertToNonInverseFillType(kWinding_FillType) == kWinding_FillType
ConvertToNonInverseFillType(kEvenOdd_FillType) == kEvenOdd_FillType
ConvertToNonInverseFillType(kInverseWinding_FillType) == kWinding_FillType
ConvertToNonInverseFillType(kInverseEvenOdd_FillType) == kEvenOdd_FillType
##
##

#SeeAlso FillType getFillType setFillType IsInverseFillType

##

# ------------------------------------------------------------------------------

#Method static int ConvertConicToQuads(const SkPoint& p0, const SkPoint& p1, const SkPoint& p2,
                                   SkScalar w, SkPoint pts[], int pow2)
#In Utility
#Line # approximates Conic with Quad array ##

Approximates Conic with Quad array. Conic is constructed from start Point p0,
control Point p1, end Point p2, and weight w.
Quad array is stored in pts; this storage is supplied by caller.
Maximum Quad count is 2 to the pow2.
Every third point in array shares last Point of previous Quad and first Point of
next Quad. Maximum pts storage size is given by:
#Formula # (1 + 2 * (1 << pow2)) * sizeof(SkPoint) ##.

Returns Quad count used the approximation, which may be smaller
than the number requested.

Conic_Weight determines the amount of influence Conic control point has on the curve.
w less than one represents an elliptical section. w greater than one represents
a hyperbolic section. w equal to one represents a parabolic section.

Two Quad curves are sufficient to approximate an elliptical Conic with a sweep
of up to 90 degrees; in this case, set pow2 to one.

#Param p0    Conic start Point ##
#Param p1    Conic control Point ##
#Param p2    Conic end Point ##
#Param w     Conic weight ##
#Param pts   storage for Quad array ##
#Param pow2  Quad count, as power of two, normally 0 to 5 (1 to 32 Quad curves) ##

#Return  number of Quad curves written to pts ##

#Example
#Description
A pair of Quad curves are drawn in red on top of the elliptical Conic curve in black.
The middle curve is nearly circular. The top-right curve is parabolic, which can
be drawn exactly with a single Quad.
##
void draw(SkCanvas* canvas) {
      SkPaint conicPaint;
      conicPaint.setAntiAlias(true);
      conicPaint.setStyle(SkPaint::kStroke_Style);
      SkPaint quadPaint(conicPaint);
      quadPaint.setColor(SK_ColorRED);
      SkPoint conic[] = { {20, 170}, {80, 170}, {80, 230} };
      for (auto weight : { .25f, .5f, .707f, .85f, 1.f } ) {
          SkPoint quads[5];
          SkPath::ConvertConicToQuads(conic[0], conic[1], conic[2], weight, quads, 1);
          SkPath path;
          path.moveTo(conic[0]);
          path.conicTo(conic[1], conic[2], weight);
          canvas->drawPath(path, conicPaint);
          path.rewind();
          path.moveTo(quads[0]);
          path.quadTo(quads[1], quads[2]);
          path.quadTo(quads[3], quads[4]);
          canvas->drawPath(path, quadPaint);
          canvas->translate(50, -50);
      }
}
##

#SeeAlso Conic Quad

##

# ------------------------------------------------------------------------------

#Method bool isRect(SkRect* rect, bool* isClosed = nullptr, Direction* direction = nullptr) const
#In Property
#Line # returns if describes Rect ##
Returns true if Path is equivalent to Rect when filled.
If false: rect, isClosed, and direction are unchanged.
If true: rect, isClosed, and direction are written to if not nullptr.

rect may be smaller than the Path bounds. Path bounds may include kMove_Verb points
that do not alter the area drawn by the returned rect.

#Param rect       storage for bounds of Rect; may be nullptr ##
#Param isClosed   storage set to true if Path is closed; may be nullptr ##
#Param direction  storage set to Rect direction; may be nullptr ##

#Return  true if Path contains Rect ##

#Example
#Description
After addRect, isRect returns true. Following moveTo permits isRect to return true, but
following lineTo does not. addPoly returns true even though rect is not closed, and one
side of rect is made up of consecutive line segments.
##
void draw(SkCanvas* canvas) {
    auto debugster = [](const char* prefix, const SkPath& path) -> void {
        SkRect rect;
        SkPath::Direction direction;
        bool isClosed;
        path.isRect(&rect, &isClosed, &direction) ?
                SkDebugf("%s is rect (%g, %g, %g, %g); is %s" "closed; direction %s\n", prefix,
                         rect.fLeft, rect.fTop, rect.fRight, rect.fBottom, isClosed ? "" : "not ",
                         SkPath::kCW_Direction == direction ? "CW" : "CCW") :
                SkDebugf("%s is not rect\n", prefix);
    };
    SkPath path;
    debugster("empty", path);
    path.addRect({10, 20, 30, 40});
    debugster("addRect", path);
    path.moveTo(60, 70);
    debugster("moveTo", path);
    path.lineTo(60, 70);
    debugster("lineTo", path);
    path.reset();
    const SkPoint pts[] = { {0, 0}, {0, 80}, {80, 80}, {80, 0}, {40, 0}, {20, 0} };
    path.addPoly(pts, SK_ARRAY_COUNT(pts), false);
    debugster("addPoly", path);
}
#StdOut
empty is not rect
addRect is rect (10, 20, 30, 40); is closed; direction CW
moveTo is rect (10, 20, 30, 40); is closed; direction CW
lineTo is not rect
addPoly is rect (0, 0, 80, 80); is not closed; direction CCW
##
##

#SeeAlso computeTightBounds conservativelyContainsRect getBounds isConvex isLastContourClosed isNestedFillRects

##

# ------------------------------------------------------------------------------

#Method bool isNestedFillRects(SkRect rect[2], Direction dirs[2] = nullptr) const
#In Property
#Line # returns if describes Rect pair, one inside the other ##
Returns true if Path is equivalent to nested Rect pair when filled.
If false, rect and dirs are unchanged.
If true, rect and dirs are written to if not nullptr:
setting rect[0] to outer Rect, and rect[1] to inner Rect;
setting dirs[0] to Direction of outer Rect, and dirs[1] to Direction of inner
Rect.

#Param rect  storage for Rect pair; may be nullptr ##
#Param dirs  storage for Direction pair; may be nullptr ##

#Return  true if Path contains nested Rect pair ##

#Example
void draw(SkCanvas* canvas) {
    SkPaint paint;
    paint.setStyle(SkPaint::kStroke_Style);
    paint.setStrokeWidth(5);
    SkPath path;
    path.addRect({10, 20, 30, 40});
    paint.getFillPath(path, &path);
    SkRect rects[2];
    SkPath::Direction directions[2];
    if (path.isNestedFillRects(rects, directions)) {
        for (int i = 0; i < 2; ++i) {
            SkDebugf("%s (%g, %g, %g, %g); direction %s\n", i ? "inner" : "outer",
                     rects[i].fLeft, rects[i].fTop, rects[i].fRight, rects[i].fBottom,
                     SkPath::kCW_Direction == directions[i] ? "CW" : "CCW");
        }
    } else {
        SkDebugf("is not nested rectangles\n");
    }
}
#StdOut
outer (7.5, 17.5, 32.5, 42.5); direction CW
inner (12.5, 22.5, 27.5, 37.5); direction CCW
##
##

#SeeAlso computeTightBounds conservativelyContainsRect getBounds isConvex isLastContourClosed isRect

##

# ------------------------------------------------------------------------------

#Method SkPath& addRect(const SkRect& rect, Direction dir = kCW_Direction)
#In Build
#Line # adds one Contour containing Rect ##
Adds Rect to Path, appending kMove_Verb, three kLine_Verb, and kClose_Verb,
starting with top-left corner of Rect; followed by top-right, bottom-right,
and bottom-left if dir is kCW_Direction; or followed by bottom-left,
bottom-right, and top-right if dir is kCCW_Direction.

#Param rect  Rect to add as a closed contour ##
#Param dir   Direction to wind added contour ##

#Return reference to Path ##

#Example
#Description
The left Rect dashes starting at the top-left corner, to the right.
The right Rect dashes starting at the top-left corner, towards the bottom.
##
#Height 128
void draw(SkCanvas* canvas) {
    SkPaint paint;
    paint.setStrokeWidth(15);
    paint.setStrokeCap(SkPaint::kSquare_Cap);
    float intervals[] = { 5, 21.75f };
    paint.setStyle(SkPaint::kStroke_Style);
    paint.setPathEffect(SkDashPathEffect::Make(intervals, SK_ARRAY_COUNT(intervals), 0));
    SkPath path;
    path.addRect({20, 20, 100, 100}, SkPath::kCW_Direction);
    canvas->drawPath(path, paint);
    path.rewind();
    path.addRect({140, 20, 220, 100}, SkPath::kCCW_Direction);
    canvas->drawPath(path, paint);
}
##

#SeeAlso SkCanvas::drawRect Direction

##

# ------------------------------------------------------------------------------

#Method SkPath& addRect(const SkRect& rect, Direction dir, unsigned start)

Adds Rect to Path, appending kMove_Verb, three kLine_Verb, and kClose_Verb.
If dir is kCW_Direction, Rect corners are added clockwise; if dir is
kCCW_Direction, Rect corners are added counterclockwise.
start determines the first corner added.

#Table
#Legend
# start # first corner ##
#Legend ##
# 0     # top-left ##
# 1     # top-right ##
# 2     # bottom-right ##
# 3     # bottom-left ##
#Table ##

#Param rect   Rect to add as a closed contour ##
#Param dir    Direction to wind added contour ##
#Param start  initial corner of Rect to add ##

#Return reference to Path ##

#Example
#Height 128
#Description
The arrow is just after the initial corner and points towards the next
corner appended to Path.
##
void draw(SkCanvas* canvas) {
    const SkPoint arrow[] = { {5, -5}, {15, -5}, {20, 0}, {15, 5}, {5, 5}, {10, 0} };
    const SkRect rect = {10, 10, 54, 54};
    SkPaint rectPaint;
    rectPaint.setAntiAlias(true);
    rectPaint.setStyle(SkPaint::kStroke_Style);
    SkPaint arrowPaint(rectPaint);
    SkPath arrowPath;
    arrowPath.addPoly(arrow, SK_ARRAY_COUNT(arrow), true);
    arrowPaint.setPathEffect(SkPath1DPathEffect::Make(arrowPath, 176, 0,
                             SkPath1DPathEffect::kRotate_Style));
    for (auto direction : { SkPath::kCW_Direction, SkPath::kCCW_Direction } ) {
        for (unsigned start : { 0, 1, 2, 3 } ) {
           SkPath path;
           path.addRect(rect, direction, start);
           canvas->drawPath(path, rectPaint);
           canvas->drawPath(path, arrowPaint);
           canvas->translate(64, 0);
       }
       canvas->translate(-256, 64);
    }
}
##

#SeeAlso SkCanvas::drawRect Direction

##

# ------------------------------------------------------------------------------

#Method SkPath& addRect(SkScalar left, SkScalar top, SkScalar right, SkScalar bottom,
                 Direction dir = kCW_Direction)

Adds Rect (left, top, right, bottom) to Path,
appending kMove_Verb, three kLine_Verb, and kClose_Verb,
starting with top-left corner of Rect; followed by top-right, bottom-right,
and bottom-left if dir is kCW_Direction; or followed by bottom-left,
bottom-right, and top-right if dir is kCCW_Direction.

#Param left    smaller x-axis value of Rect ##
#Param top     smaller y-axis value of Rect ##
#Param right   larger x-axis value of Rect ##
#Param bottom  larger y-axis value of Rect ##
#Param dir     Direction to wind added contour ##

#Return reference to Path ##

#Example
#Description
The left Rect dashes start at the top-left corner, and continue to the right.
The right Rect dashes start at the top-left corner, and continue down.
##
#Height 128
void draw(SkCanvas* canvas) {
    SkPaint paint;
    paint.setStrokeWidth(15);
    paint.setStrokeCap(SkPaint::kSquare_Cap);
    float intervals[] = { 5, 21.75f };
    paint.setStyle(SkPaint::kStroke_Style);
    paint.setPathEffect(SkDashPathEffect::Make(intervals, SK_ARRAY_COUNT(intervals), 0));
    for (auto direction : { SkPath::kCW_Direction, SkPath::kCCW_Direction } ) {
        SkPath path;
        path.addRect(20, 20, 100, 100, direction);
        canvas->drawPath(path, paint);
        canvas->translate(128, 0);
    }
}
##

#SeeAlso SkCanvas::drawRect Direction

##

# ------------------------------------------------------------------------------

#Method SkPath& addOval(const SkRect& oval, Direction dir = kCW_Direction)
#In Build
#Line # adds one Contour containing Oval ##
Adds Oval to path, appending kMove_Verb, four kConic_Verb, and kClose_Verb.
Oval is upright ellipse bounded by Rect oval with radii equal to half oval width
and half oval height. Oval begins at (oval.fRight, oval.centerY()) and continues
clockwise if dir is kCW_Direction, counterclockwise if dir is kCCW_Direction.

#Param oval  bounds of ellipse added ##
#Param dir   Direction to wind ellipse ##

#Return reference to Path ##

#Example
#Height 120
    SkPaint paint;
    SkPath oval;
    oval.addOval({20, 20, 160, 80});
    canvas->drawPath(oval, paint);
##

#SeeAlso SkCanvas::drawOval Direction Oval

##

# ------------------------------------------------------------------------------

#Method SkPath& addOval(const SkRect& oval, Direction dir, unsigned start)

Adds Oval to Path, appending kMove_Verb, four kConic_Verb, and kClose_Verb.
Oval is upright ellipse bounded by Rect oval with radii equal to half oval width
and half oval height. Oval begins at start and continues
clockwise if dir is kCW_Direction, counterclockwise if dir is kCCW_Direction.

#Table
#Legend
# start # Point                        ##
#Legend ##
# 0     # oval.centerX(), oval.fTop    ##
# 1     # oval.fRight, oval.centerY()  ##
# 2     # oval.centerX(), oval.fBottom ##
# 3     # oval.fLeft, oval.centerY()   ##
#Table ##

#Param oval   bounds of ellipse added ##
#Param dir    Direction to wind ellipse ##
#Param start  index of initial point of ellipse ##

#Return reference to Path ##

#Example
#Height 160
void draw(SkCanvas* canvas) {
    const SkPoint arrow[] = { {0, -5}, {10, 0}, {0, 5} };
    const SkRect rect = {10, 10, 54, 54};
    SkPaint ovalPaint;
    ovalPaint.setAntiAlias(true);
    SkPaint textPaint(ovalPaint);
    textPaint.setTextAlign(SkPaint::kCenter_Align);
    ovalPaint.setStyle(SkPaint::kStroke_Style);
    SkPaint arrowPaint(ovalPaint);
    SkPath arrowPath;
    arrowPath.addPoly(arrow, SK_ARRAY_COUNT(arrow), true);
    arrowPaint.setPathEffect(SkPath1DPathEffect::Make(arrowPath, 176, 0,
                             SkPath1DPathEffect::kRotate_Style));
    for (auto direction : { SkPath::kCW_Direction, SkPath::kCCW_Direction } ) {
        for (unsigned start : { 0, 1, 2, 3 } ) {
           SkPath path;
           path.addOval(rect, direction, start);
           canvas->drawPath(path, ovalPaint);
           canvas->drawPath(path, arrowPaint);
           canvas->drawText(&"0123"[start], 1, rect.centerX(), rect.centerY() + 5, textPaint);
           canvas->translate(64, 0);
       }
       canvas->translate(-256, 72);
       canvas->drawString(SkPath::kCW_Direction == direction ? "clockwise" : "counterclockwise",
                          128, 0, textPaint);
    }
}
##

#SeeAlso SkCanvas::drawOval Direction Oval

##

# ------------------------------------------------------------------------------

#Method SkPath& addCircle(SkScalar x, SkScalar y, SkScalar radius,
                   Direction dir = kCW_Direction)
#In Build
#Line # adds one Contour containing Circle ##

Adds Circle centered at (x, y) of size radius to Path, appending kMove_Verb,
four kConic_Verb, and kClose_Verb. Circle begins at: #Formula # (x + radius, y) ##, continuing
clockwise if dir is kCW_Direction, and counterclockwise if dir is kCCW_Direction.

Has no effect if radius is zero or negative.

#Param x       center of Circle ##
#Param y       center of Circle  ##
#Param radius  distance from center to edge ##
#Param dir     Direction to wind Circle ##

#Return reference to Path ##

#Example
void draw(SkCanvas* canvas) {
    SkPaint paint;
    paint.setAntiAlias(true);
    paint.setStyle(SkPaint::kStroke_Style);
    paint.setStrokeWidth(10);
    for (int size = 10; size < 300; size += 20) {
        SkPath path;
        path.addCircle(128, 128, size, SkPath::kCW_Direction);
        canvas->drawPath(path, paint);
    }
}
##

#SeeAlso SkCanvas::drawCircle Direction Circle

##

# ------------------------------------------------------------------------------

#Method SkPath& addArc(const SkRect& oval, SkScalar startAngle, SkScalar sweepAngle)
#In Build
#Line # adds one Contour containing Arc ##
Appends Arc to Path, as the start of new Contour. Arc added is part of ellipse
bounded by oval, from startAngle through sweepAngle. Both startAngle and
sweepAngle are measured in degrees, where zero degrees is aligned with the
positive x-axis, and positive sweeps extends Arc clockwise.

If sweepAngle <= -360, or sweepAngle >= 360; and startAngle modulo 90 is nearly
zero, append Oval instead of Arc. Otherwise, sweepAngle values are treated
modulo 360, and Arc may or may not draw depending on numeric rounding.

#Param oval        bounds of ellipse containing Arc ##
#Param startAngle  starting angle of Arc in degrees ##
#Param sweepAngle  sweep, in degrees. Positive is clockwise; treated modulo 360 ##

#Return reference to Path ##

#Example
#Description
The middle row of the left and right columns draw differently from the entries
above and below because sweepAngle is outside of the range of +/-360,
and startAngle modulo 90 is not zero.
##
void draw(SkCanvas* canvas) {
    SkPaint paint;
    for (auto start : { 0, 90, 135, 180, 270 } ) {
        for (auto sweep : { -450.f, -180.f, -90.f, 90.f, 180.f, 360.1f } ) {
            SkPath path;
            path.addArc({10, 10, 35, 45}, start, sweep);
            canvas->drawPath(path, paint);
            canvas->translate(252 / 6, 0);
        }
        canvas->translate(-252, 255 / 5);
    }
}
##

#SeeAlso Arc arcTo SkCanvas::drawArc

##

# ------------------------------------------------------------------------------

#Method SkPath& addRoundRect(const SkRect& rect, SkScalar rx, SkScalar ry,
                      Direction dir = kCW_Direction)
#In Build
#Line # adds one Contour containing Round_Rect with common corner radii ##

Appends Round_Rect to Path, creating a new closed Contour. Round_Rect has bounds
equal to rect; each corner is 90 degrees of an ellipse with radii (rx, ry). If
dir is kCW_Direction, Round_Rect starts at top-left of the lower-left corner and
winds clockwise. If dir is kCCW_Direction, Round_Rect starts at the bottom-left
of the upper-left corner and winds counterclockwise.

If either rx or ry is too large, rx and ry are scaled uniformly until the
corners fit. If rx or ry is less than or equal to zero, addRoundRect appends
Rect rect to Path.

After appending, Path may be empty, or may contain: Rect, Oval, or RoundRect.

#Param rect  bounds of Round_Rect ##
#Param rx    x-axis radius of rounded corners on the Round_Rect ##
#Param ry    y-axis radius of rounded corners on the Round_Rect ##
#Param dir   Direction to wind Round_Rect ##

#Return reference to Path ##

#Example
#Description
If either radius is zero, path contains Rect and is drawn red.
If sides are only radii, path contains Oval and is drawn blue.
All remaining path draws are convex, and are drawn in gray; no
paths constructed from addRoundRect are concave, so none are
drawn in green.
##
void draw(SkCanvas* canvas) {
    SkPaint paint;
    paint.setAntiAlias(true);
    for (auto xradius : { 0, 7, 13, 20 } ) {
        for (auto yradius : { 0, 9, 18, 40 } ) {
            SkPath path;
            path.addRoundRect({10, 10, 36, 46}, xradius, yradius);
            paint.setColor(path.isRect(nullptr) ? SK_ColorRED : path.isOval(nullptr) ?
                           SK_ColorBLUE : path.isConvex() ? SK_ColorGRAY : SK_ColorGREEN);
            canvas->drawPath(path, paint);
            canvas->translate(64, 0);
        }
        canvas->translate(-256, 64);
    }
}
##

#SeeAlso addRRect SkCanvas::drawRoundRect

##

# ------------------------------------------------------------------------------

#Method SkPath& addRoundRect(const SkRect& rect, const SkScalar radii[],
                      Direction dir = kCW_Direction)

Appends Round_Rect to Path, creating a new closed Contour. Round_Rect has bounds
equal to rect; each corner is 90 degrees of an ellipse with radii from the
array.

#Table
#Legend
# radii index # location                        ##
#Legend ##
# 0           # x-axis radius of top-left corner     ##
# 1           # y-axis radius of top-left corner     ##
# 2           # x-axis radius of top-right corner    ##
# 3           # y-axis radius of top-right corner    ##
# 4           # x-axis radius of bottom-right corner ##
# 5           # y-axis radius of bottom-right corner ##
# 6           # x-axis radius of bottom-left corner  ##
# 7           # y-axis radius of bottom-left corner  ##
#Table ##

If dir is kCW_Direction, Round_Rect starts at top-left of the lower-left corner
and winds clockwise. If dir is kCCW_Direction, Round_Rect starts at the
bottom-left of the upper-left corner and winds counterclockwise.

If both radii on any side of rect exceed its length, all radii are scaled
uniformly until the corners fit. If either radius of a corner is less than or
equal to zero, both are treated as zero.

After appending, Path may be empty, or may contain: Rect, Oval, or RoundRect.

#Param rect   bounds of Round_Rect ##
#Param radii  array of 8 SkScalar values, a radius pair for each corner ##
#Param dir    Direction to wind Round_Rect ##

#Return reference to Path ##

#Example
void draw(SkCanvas* canvas) {
    SkPaint paint;
    paint.setAntiAlias(true);
    SkScalar radii[] = { 80, 100, 0, 0, 40, 60, 0, 0 };
    SkPath path;
    SkMatrix rotate90;
    rotate90.setRotate(90, 128, 128);
    for (int i = 0; i < 4; ++i) {
        path.addRoundRect({10, 10, 110, 110}, radii);
        path.transform(rotate90);
    }
    canvas->drawPath(path, paint);
}
##

#SeeAlso addRRect SkCanvas::drawRoundRect

##

# ------------------------------------------------------------------------------

#Method SkPath& addRRect(const SkRRect& rrect, Direction dir = kCW_Direction)
#In Build
#Line # adds one Contour containing Round_Rect ##
Adds rrect to Path, creating a new closed Contour. If
dir is kCW_Direction, rrect starts at top-left of the lower-left corner and
winds clockwise. If dir is kCCW_Direction, rrect starts at the bottom-left
of the upper-left corner and winds counterclockwise.

After appending, Path may be empty, or may contain: Rect, Oval, or Round_Rect.

#Param rrect  bounds and radii of rounded rectangle ##
#Param dir   Direction to wind Round_Rect ##

#Return reference to Path ##

#Example
void draw(SkCanvas* canvas) {
    SkPaint paint;
    paint.setAntiAlias(true);
    SkRRect rrect;
    SkVector radii[] = {{50, 50}, {0, 0}, {0, 0}, {50, 50}};
    rrect.setRectRadii({10, 10, 110, 110}, radii);
    SkPath path;
    SkMatrix rotate90;
    rotate90.setRotate(90, 128, 128);
    for (int i = 0; i < 4; ++i) {
        path.addRRect(rrect);
        path.transform(rotate90);
    }
    canvas->drawPath(path, paint);
}
##

#SeeAlso addRoundRect SkCanvas::drawRRect

##

# ------------------------------------------------------------------------------

#Method SkPath& addRRect(const SkRRect& rrect, Direction dir, unsigned start)

Adds rrect to Path, creating a new closed Contour. If dir is kCW_Direction, rrect
winds clockwise; if dir is kCCW_Direction, rrect winds counterclockwise.
start determines the first point of rrect to add.

#Table
#Legend
# start       # location                    ##
#Legend ##
# 0           # right of top-left corner    ##
# 1           # left of top-right corner    ##
# 2           # bottom of top-right corner  ##
# 3           # top of bottom-right corner  ##
# 4           # left of bottom-right corner ##
# 5           # right of bottom-left corner ##
# 6           # top of bottom-left corner   ##
# 7           # bottom of top-left corner   ##
#Table ##

After appending, Path may be empty, or may contain: Rect, Oval, or Round_Rect.

#Param rrect  bounds and radii of rounded rectangle ##
#Param dir    Direction to wind Round_Rect ##
#Param start  index of initial point of Round_Rect ##

#Return reference to Path ##

#Example
void draw(SkCanvas* canvas) {
    SkPaint paint;
    paint.setAntiAlias(true);
    SkRRect rrect;
    rrect.setRectXY({40, 40, 215, 215}, 50, 50);
    SkPath path;
    path.addRRect(rrect);
    canvas->drawPath(path, paint);
    for (int start = 0; start < 8; ++start) {
        SkPath textPath;
        textPath.addRRect(rrect, SkPath::kCW_Direction, start);
        SkPathMeasure pathMeasure(textPath, false);
        SkPoint position;
        SkVector tangent;
        if (!pathMeasure.getPosTan(0, &position, &tangent)) {
            continue;
        }
        SkRSXform rsxForm = SkRSXform::Make(tangent.fX, tangent.fY,
               position.fX + tangent.fY * 5, position.fY - tangent.fX * 5);
        canvas->drawTextRSXform(&"01234567"[start], 1, &rsxForm, nullptr, paint);
    }
}
##

#SeeAlso addRoundRect SkCanvas::drawRRect

##

# ------------------------------------------------------------------------------

#Method SkPath& addPoly(const SkPoint pts[], int count, bool close)
#In Build
#Line # adds one Contour containing connected lines ##
Adds Contour created from Line array, adding (count - 1) Line segments.
Contour added starts at pts[0], then adds a line for every additional Point
in pts array. If close is true, appends kClose_Verb to Path, connecting
pts[count - 1] and pts[0].

If count is zero, append kMove_Verb to path.
Has no effect if count is less than one.

#Param pts    array of Line sharing end and start Point ##
#Param count  length of Point array ##
#Param close  true to add Line connecting Contour end and start ##

#Return reference to Path ##

#Example
void draw(SkCanvas* canvas) {
    SkPaint paint;
    paint.setStrokeWidth(15);
    paint.setStrokeCap(SkPaint::kRound_Cap);
    const SkPoint points[] = {{20, 20}, {70, 20}, {40, 90}};
    for (bool close : { false, true } ) {
        SkPath path;
        path.addPoly(points, SK_ARRAY_COUNT(points), close);
        for (auto style : {SkPaint::kStroke_Style, SkPaint::kFill_Style,
                SkPaint::kStrokeAndFill_Style} ) {
            paint.setStyle(style);
            canvas->drawPath(path, paint);
            canvas->translate(85, 0);
        }
        canvas->translate(-255, 128);
    }
}
##

#SeeAlso SkCanvas::drawPoints

##

#Method SkPath& addPoly(const std::initializer_list<SkPoint>& list, bool close)

Adds Contour created from list. Contour added starts at list[0], then adds a line
for every additional Point in list. If close is true, appends kClose_Verb to Path,
connecting last and first Point in list.

If list is empty, append kMove_Verb to path.

#Param list   array of Points ##
#Param close  true to add Line connecting Contour end and start ##

#Return reference to Path ##

#Example
void draw(SkCanvas* canvas) {
    SkPaint paint;
    paint.setStrokeWidth(15);
    paint.setStrokeCap(SkPaint::kRound_Cap);
    for (bool close : { false, true } ) {
        SkPath path;
        path.addPoly({{20, 20}, {70, 20}, {40, 90}}, close);
        for (auto style : {SkPaint::kStroke_Style, SkPaint::kFill_Style,
                SkPaint::kStrokeAndFill_Style} ) {
            paint.setStyle(style);
            canvas->drawPath(path, paint);
            canvas->translate(85, 0);
        }
        canvas->translate(-255, 128);
    }
}
##

#SeeAlso SkCanvas::drawPoints

##

# ------------------------------------------------------------------------------

#Enum AddPathMode
#Line # sets addPath options ##

#Code
    enum AddPathMode {
        kAppend_AddPathMode,
        kExtend_AddPathMode,
    };
##

AddPathMode chooses how addPath appends. Adding one Path to another can extend
the last Contour or start a new Contour.

#Const kAppend_AddPathMode
#Line # appended to destination unaltered ##
    Path Verbs, Points, and Conic_Weights are appended to destination unaltered.
    Since Path Verb_Array begins with kMove_Verb if src is not empty, this
    starts a new Contour.
##
#Const kExtend_AddPathMode
#Line # add line if prior Contour is not closed ##
    If destination is closed or empty, start a new Contour. If destination
    is not empty, add Line from Last_Point to added Path first Point. Skip added
    Path initial kMove_Verb, then append remining Verbs, Points, and Conic_Weights.
##

#Example
#Description
test is built from path, open on the top row, and closed on the bottom row.
The left column uses kAppend_AddPathMode; the right uses kExtend_AddPathMode.
The top right composition is made up of one contour; the other three have two.
##
#Height 180
    SkPath path, path2;
    path.moveTo(20, 20);
    path.lineTo(20, 40);
    path.lineTo(40, 20);
    path2.moveTo(60, 60);
    path2.lineTo(80, 60);
    path2.lineTo(80, 40);
    SkPaint paint;
    paint.setStyle(SkPaint::kStroke_Style);
    for (int i = 0; i < 2; i++) {
        for (auto addPathMode : { SkPath::kAppend_AddPathMode, SkPath::kExtend_AddPathMode } ) {
            SkPath test(path);
            test.addPath(path2, addPathMode);
            canvas->drawPath(test, paint);
            canvas->translate(100, 0);
        }
        canvas->translate(-200, 100);
        path.close();
    }
##

#SeeAlso addPath reverseAddPath

##

# ------------------------------------------------------------------------------

#Method SkPath& addPath(const SkPath& src, SkScalar dx, SkScalar dy,
                 AddPathMode mode = kAppend_AddPathMode)
#In Build
#Line # adds contents of Path ##

Appends src to Path, offset by (dx, dy).

If mode is kAppend_AddPathMode, src Verb_Array, Point_Array, and Conic_Weights are
added unaltered. If mode is kExtend_AddPathMode, add Line before appending
Verbs, Points, and Conic_Weights.

#Param src  Path Verbs, Points, and Conic_Weights to add ##
#Param dx   offset added to src Point_Array x-axis coordinates ##
#Param dy   offset added to src Point_Array y-axis coordinates ##
#Param mode kAppend_AddPathMode or kExtend_AddPathMode ##

#Return reference to Path ##

#Example
#Height 180
    SkPaint paint;
    paint.setTextSize(128);
    paint.setFakeBoldText(true);
    SkPath dest, text;
    paint.getTextPath("O", 1, 50, 120, &text);
    for (int i = 0; i < 3; i++) {
        dest.addPath(text, i * 20, i * 20);
    }
    Simplify(dest, &dest);
    paint.setStyle(SkPaint::kStroke_Style);
    paint.setStrokeWidth(3);
    canvas->drawPath(dest, paint);
##

#SeeAlso AddPathMode offset reverseAddPath

##

# ------------------------------------------------------------------------------

#Method SkPath& addPath(const SkPath& src, AddPathMode mode = kAppend_AddPathMode)

Appends src to Path.

If mode is kAppend_AddPathMode, src Verb_Array, Point_Array, and Conic_Weights are
added unaltered. If mode is kExtend_AddPathMode, add Line before appending
Verbs, Points, and Conic_Weights.

#Param src  Path Verbs, Points, and Conic_Weights to add ##
#Param mode kAppend_AddPathMode or kExtend_AddPathMode ##

#Return reference to Path ##

#Example
#Height 80
    SkPaint paint;
    paint.setStyle(SkPaint::kStroke_Style);
    SkPath dest, path;
    path.addOval({-80, 20, 0, 60}, SkPath::kCW_Direction, 1);
    for (int i = 0; i < 2; i++) {
        dest.addPath(path, SkPath::kExtend_AddPathMode);
        dest.offset(100, 0);
    }
    canvas->drawPath(dest, paint);
##

#SeeAlso AddPathMode reverseAddPath

##

# ------------------------------------------------------------------------------

#Method SkPath& addPath(const SkPath& src, const SkMatrix& matrix, AddPathMode mode = kAppend_AddPathMode)

Appends src to Path, transformed by matrix. Transformed curves may have different
Verbs, Points, and Conic_Weights.

If mode is kAppend_AddPathMode, src Verb_Array, Point_Array, and Conic_Weights are
added unaltered. If mode is kExtend_AddPathMode, add Line before appending
Verbs, Points, and Conic_Weights.

#Param src     Path Verbs, Points, and Conic_Weights to add ##
#Param matrix  transform applied to src ##
#Param mode    kAppend_AddPathMode or kExtend_AddPathMode ##

#Return reference to Path ##

#Example
#Height 160
    SkPaint paint;
    paint.setStyle(SkPaint::kStroke_Style);
    SkPath dest, path;
    path.addOval({20, 20, 200, 120}, SkPath::kCW_Direction, 1);
    for (int i = 0; i < 6; i++) {
        SkMatrix matrix;
        matrix.reset();
        matrix.setPerspX(i / 400.f);
        dest.addPath(path, matrix);
    }
    canvas->drawPath(dest, paint);
##

#SeeAlso AddPathMode transform offset reverseAddPath

##

# ------------------------------------------------------------------------------

#Method SkPath& reverseAddPath(const SkPath& src)
#In Build
#Line # adds contents of Path back to front ##
Appends src to Path, from back to front.
Reversed src always appends a new Contour to Path.

#Param src     Path Verbs, Points, and Conic_Weights to add ##

#Return reference to Path ##

#Example
#Height 200
    SkPath path;
    path.moveTo(20, 20);
    path.lineTo(20, 40);
    path.lineTo(40, 20);
    SkPaint paint;
    paint.setStyle(SkPaint::kStroke_Style);
    for (int i = 0; i < 2; i++) {
        SkPath path2;
        path2.moveTo(60, 60);
        path2.lineTo(80, 60);
        path2.lineTo(80, 40);
        for (int j = 0; j < 2; j++) {
            SkPath test(path);
            test.reverseAddPath(path2);
            canvas->drawPath(test, paint);
            canvas->translate(100, 0);
            path2.close();
        }
        canvas->translate(-200, 100);
        path.close();
    }
##

#SeeAlso AddPathMode transform offset addPath

##

# ------------------------------------------------------------------------------

#Method void offset(SkScalar dx, SkScalar dy, SkPath* dst) const
#In Transform
#Line # translates Point_Array ##
Offsets Point_Array by (dx, dy). Offset Path replaces dst.
If dst is nullptr, Path is replaced by offset data.

#Param dx   offset added to Point_Array x-axis coordinates ##
#Param dy   offset added to Point_Array y-axis coordinates ##
#Param dst  overwritten, translated copy of Path; may be nullptr ##

#Example
#Height 60
    SkPath pattern;
    pattern.moveTo(20, 20);
    pattern.lineTo(20, 40);
    pattern.lineTo(40, 20);
    SkPaint paint;
    paint.setStyle(SkPaint::kStroke_Style);
    for (int i = 0; i < 10; i++) {
        SkPath path;
        pattern.offset(20 * i, 0, &path);
        canvas->drawPath(path, paint);
    }
##

#SeeAlso addPath transform

##

# ------------------------------------------------------------------------------
#Subtopic Transform
#Line # modify all points ##
##

#Method void offset(SkScalar dx, SkScalar dy)
#In Transform
Offsets Point_Array by (dx, dy). Path is replaced by offset data.

#Param dx  offset added to Point_Array x-axis coordinates ##
#Param dy  offset added to Point_Array y-axis coordinates ##

#Example
#Height 60
    SkPath path;
    path.moveTo(20, 20);
    path.lineTo(20, 40);
    path.lineTo(40, 20);
    SkPaint paint;
    paint.setStyle(SkPaint::kStroke_Style);
    for (int i = 0; i < 10; i++) {
        canvas->drawPath(path, paint);
        path.offset(20, 0);
    }
##

#SeeAlso addPath transform SkCanvas::translate()

##

# ------------------------------------------------------------------------------

#Method void transform(const SkMatrix& matrix, SkPath* dst) const
#In Transform
#Line # applies Matrix to Point_Array and Weights ##
Transforms Verb_Array, Point_Array, and weight by matrix.
transform may change Verbs and increase their number.
Transformed Path replaces dst; if dst is nullptr, original data
is replaced.

#Param matrix  Matrix to apply to Path ##
#Param dst     overwritten, transformed copy of Path; may be nullptr ##

#Example
#Height 200
    SkPath pattern;
    pattern.moveTo(100, 100);
    pattern.lineTo(100, 20);
    pattern.lineTo(20, 100);
    SkPaint paint;
    paint.setStyle(SkPaint::kStroke_Style);
    for (int i = 0; i < 10; i++) {
        SkPath path;
        SkMatrix matrix;
        matrix.setRotate(36 * i, 100, 100);
        pattern.transform(matrix, &path);
        canvas->drawPath(path, paint);
    }
##

#SeeAlso addPath offset SkCanvas::concat() SkMatrix

##

# ------------------------------------------------------------------------------

#Method void transform(const SkMatrix& matrix)

Transforms Verb_Array, Point_Array, and weight by matrix.
transform may change Verbs and increase their number.
Path is replaced by transformed data.

#Param matrix  Matrix to apply to Path ##

#Example
#Height 200
    SkPath path;
    path.moveTo(100, 100);
    path.quadTo(100, 20, 20, 100);
    SkPaint paint;
    paint.setStyle(SkPaint::kStroke_Style);
    for (int i = 0; i < 10; i++) {
        SkMatrix matrix;
        matrix.setRotate(36, 100, 100);
        path.transform(matrix);
        canvas->drawPath(path, paint);
    }
##

#SeeAlso addPath offset SkCanvas::concat() SkMatrix

##

# ------------------------------------------------------------------------------

#Subtopic Last_Point
#Line # final Point in Contour ##

Path is defined cumulatively, often by adding a segment to the end of last
Contour. Last_Point of Contour is shared as first Point of added Line or Curve.
Last_Point can be read and written directly with getLastPt and setLastPt.

#Method bool getLastPt(SkPoint* lastPt) const
#In Property
#In Last_Point
#Line # returns Last_Point ##
    Returns Last_Point on Path in lastPt. Returns false if Point_Array is empty,
    storing (0, 0) if lastPt is not nullptr.

    #Param lastPt  storage for final Point in Point_Array; may be nullptr ##

    #Return  true if Point_Array contains one or more Points ##

    #Example
        SkPath path;
        path.moveTo(100, 100);
        path.quadTo(100, 20, 20, 100);
        SkMatrix matrix;
        matrix.setRotate(36, 100, 100);
        path.transform(matrix);
        SkPoint last;
        path.getLastPt(&last);
        SkDebugf("last point: %g, %g\n", last.fX, last.fY);
    #StdOut
    last point: 35.2786, 52.9772
    ##
    ##

    #SeeAlso setLastPt

##

#Method void setLastPt(SkScalar x, SkScalar y)
#In Utility
#In Last_Point
#Line # replaces Last_Point ##
    Sets Last_Point to (x, y). If Point_Array is empty, append kMove_Verb to
    Verb_Array and append (x, y) to Point_Array.

    #Param x  set x-axis value of Last_Point ##
    #Param y  set y-axis value of Last_Point ##

    #Example
    #Height 128
        SkPaint paint;
        paint.setTextSize(128);
        SkPath path;
        paint.getTextPath("@", 1, 60, 100, &path);
        path.setLastPt(20, 120);
        canvas->drawPath(path, paint);
    ##

    #SeeAlso getLastPt

##

#Method void setLastPt(const SkPoint& p)

    Sets the last point on the path. If Point_Array is empty, append kMove_Verb to
    Verb_Array and append p to Point_Array.

    #Param p  set value of Last_Point ##

    #Example
    #Height 128
        SkPaint paint;
        paint.setTextSize(128);
        SkPath path, path2;
        paint.getTextPath("A", 1, 60, 100, &path);
        paint.getTextPath("Z", 1, 60, 100, &path2);
        SkPoint pt, pt2;
        path.getLastPt(&pt);
        path2.getLastPt(&pt2);
        path.setLastPt(pt2);
        path2.setLastPt(pt);
        canvas->drawPath(path, paint);
        canvas->drawPath(path2, paint);
    ##

    #SeeAlso getLastPt

##

#Subtopic Last_Point ##

# ------------------------------------------------------------------------------

#Enum SegmentMask
#Line # returns Verb types in Path ##

#Code
    enum SegmentMask {
        kLine_SegmentMask = 1 << 0,
        kQuad_SegmentMask = 1 << 1,
        kConic_SegmentMask = 1 << 2,
        kCubic_SegmentMask = 1 << 3,
    };
##

SegmentMask constants correspond to each drawing Verb type in Path; for
instance, if Path only contains Lines, only the kLine_SegmentMask bit is set.

#Bug 6785
#Const kLine_SegmentMask 1
#Line # contains one or more Lines ##
Set if Verb_Array contains kLine_Verb.
##
#Const kQuad_SegmentMask 2
#Line # contains one or more Quads ##
Set if Verb_Array contains kQuad_Verb. Note that conicTo may add a Quad.
##
#Const kConic_SegmentMask 4
#Line # contains one or more Conics ##
Set if Verb_Array contains kConic_Verb.
##
#Const kCubic_SegmentMask 8
#Line # contains one or more Cubics ##
Set if Verb_Array contains kCubic_Verb.
##

#Example
#Description
When conicTo has a weight of one, Quad is added to Path.
##
    SkPath path;
    path.conicTo(10, 10, 20, 30, 1);
    SkDebugf("Path kConic_SegmentMask is %s\n", path.getSegmentMasks() &
          SkPath::kConic_SegmentMask ? "set" : "clear");
    SkDebugf("Path kQuad_SegmentMask is %s\n", path.getSegmentMasks() &
          SkPath::kQuad_SegmentMask ? "set" : "clear");
#StdOut
Path kConic_SegmentMask is clear
Path kQuad_SegmentMask is set
##
##

#SeeAlso getSegmentMasks Verb

##

# ------------------------------------------------------------------------------

#Method uint32_t getSegmentMasks() const
#In Utility
#In Property
#Line # returns types in Verb_Array ##
Returns a mask, where each set bit corresponds to a SegmentMask constant
if Path contains one or more Verbs of that type.
Returns zero if Path contains no Lines, or Curves: Quads, Conics, or Cubics.

getSegmentMasks() returns a cached result; it is very fast.

#Return  SegmentMask bits or zero ##

#Example
SkPath path;
path.quadTo(20, 30, 40, 50);
path.close();
const char* masks[] = { "line", "quad", "conic", "cubic" };
int index = 0;
for (auto mask : { SkPath::kLine_SegmentMask, SkPath::kQuad_SegmentMask,
        SkPath::kConic_SegmentMask, SkPath::kCubic_SegmentMask } ) {
    if (mask & path.getSegmentMasks()) {
       SkDebugf("mask %s set\n", masks[index]);
    }
    ++index;
}
#StdOut
mask quad set
##
##

#SeeAlso getSegmentMasks Verb

##

# ------------------------------------------------------------------------------

#Method bool contains(SkScalar x, SkScalar y) const
#In Property
#Line # returns if Point is in fill area ##
Returns true if the point (x, y) is contained by Path, taking into
account FillType.

#Table
#Legend
# FillType                 # contains() returns true if Point is enclosed by ##
##
# kWinding_FillType        # a non-zero sum of Contour Directions. ##
# kEvenOdd_FillType        # an odd number of Contours.            ##
# kInverseWinding_FillType # a zero sum of Contour Directions.     ##
# kInverseEvenOdd_FillType # and even number of Contours.          ##
##

#Param x  x-axis value of containment test ##
#Param y  y-axis value of containment test ##

#Return  true if Point is in Path ##

#Example
SkPath path;
SkPaint paint;
paint.setTextSize(256);
paint.getTextPath("&", 1, 30, 220, &path);
for (int y = 2; y < 256; y += 9) {
   for (int x = 2; x < 256; x += 9) {
       int coverage = 0;
       for (int iy = -4; iy <= 4; iy += 2) {
           for (int ix = -4; ix <= 4; ix += 2) {
               coverage += path.contains(x + ix, y + iy);
           }
       }
       paint.setColor(SkColorSetARGB(0x5f, 0xff * coverage / 25, 0, 0xff * (25 - coverage) / 25));
       canvas->drawCircle(x, y, 8, paint);
   }
}
##

#SeeAlso conservativelyContainsRect Fill_Type Op

##

# ------------------------------------------------------------------------------

#Method void dump(SkWStream* stream, bool forceClose, bool dumpAsHex) const
#In Utility
#Line # sends text representation to stream ##
Writes text representation of Path to stream. If stream is nullptr, writes to
standard output. Set forceClose to true to get edges used to fill Path.
Set dumpAsHex true to generate exact binary representations
of floating point numbers used in Point_Array and Conic_Weights.

#Param stream      writable WStream receiving Path text representation; may be nullptr ##
#Param forceClose  true if missing kClose_Verb is output ##
#Param dumpAsHex   true if SkScalar values are written as hexadecimal ##

#Example
   SkPath path;
   path.quadTo(20, 30, 40, 50);
   for (bool forceClose : { false, true } ) {
       for (bool dumpAsHex : { false, true } ) {
           path.dump(nullptr, forceClose, dumpAsHex);
           SkDebugf("\n");
       }
   }
#StdOut
path.setFillType(SkPath::kWinding_FillType);
path.moveTo(0, 0);
path.quadTo(20, 30, 40, 50);

path.setFillType(SkPath::kWinding_FillType);
path.moveTo(SkBits2Float(0x00000000), SkBits2Float(0x00000000));  // 0, 0
path.quadTo(SkBits2Float(0x41a00000), SkBits2Float(0x41f00000), SkBits2Float(0x42200000), SkBits2Float(0x42480000));  // 20, 30, 40, 50

path.setFillType(SkPath::kWinding_FillType);
path.moveTo(0, 0);
path.quadTo(20, 30, 40, 50);
path.lineTo(0, 0);
path.close();

path.setFillType(SkPath::kWinding_FillType);
path.moveTo(SkBits2Float(0x00000000), SkBits2Float(0x00000000));  // 0, 0
path.quadTo(SkBits2Float(0x41a00000), SkBits2Float(0x41f00000), SkBits2Float(0x42200000), SkBits2Float(0x42480000));  // 20, 30, 40, 50
path.lineTo(SkBits2Float(0x00000000), SkBits2Float(0x00000000));  // 0, 0
path.close();
##
##

#SeeAlso dumpHex SkRect::dump() SkRRect::dump() SkPathMeasure::dump()

##

# ------------------------------------------------------------------------------

#Method void dump() const

Writes text representation of Path to standard output. The representation may be
directly compiled as C++ code. Floating point values are written
with limited precision; it may not be possible to reconstruct original Path
from output.

#Example
SkPath path, copy;
path.lineTo(6.f / 7, 2.f / 3);
path.dump();
copy.setFillType(SkPath::kWinding_FillType);
copy.moveTo(0, 0);
copy.lineTo(0.857143f, 0.666667f);
SkDebugf("path is " "%s" "equal to copy\n", path == copy ? "" : "not ");
#StdOut
path.setFillType(SkPath::kWinding_FillType);
path.moveTo(0, 0);
path.lineTo(0.857143f, 0.666667f);
path is not equal to copy
##
##

#SeeAlso dumpHex SkRect::dump() SkRRect::dump() SkPathMeasure::dump() writeToMemory

##

# ------------------------------------------------------------------------------

#Method void dumpHex() const
#In Utility
#Line # sends text representation using hexadecimal to standard output ##
Writes text representation of Path to standard output. The representation may be
directly compiled as C++ code. Floating point values are written
in hexadecimal to preserve their exact bit pattern. The output reconstructs the
original Path.

Use instead of dump() when submitting
#A bug reports against Skia # https://bug.skia.org ##
.

#Example
SkPath path, copy;
path.lineTo(6.f / 7, 2.f / 3);
path.dumpHex();
copy.setFillType(SkPath::kWinding_FillType);
copy.moveTo(SkBits2Float(0x00000000), SkBits2Float(0x00000000));  // 0, 0
copy.lineTo(SkBits2Float(0x3f5b6db7), SkBits2Float(0x3f2aaaab));  // 0.857143f, 0.666667f
SkDebugf("path is " "%s" "equal to copy\n", path == copy ? "" : "not ");
#StdOut
path.setFillType(SkPath::kWinding_FillType);
path.moveTo(SkBits2Float(0x00000000), SkBits2Float(0x00000000));  // 0, 0
path.lineTo(SkBits2Float(0x3f5b6db7), SkBits2Float(0x3f2aaaab));  // 0.857143f, 0.666667f
path is equal to copy
##
##

#SeeAlso dump SkRect::dumpHex SkRRect::dumpHex writeToMemory

##

# ------------------------------------------------------------------------------

#Method size_t writeToMemory(void* buffer) const
#In Utility
#Line # copies data to buffer ##
Writes Path to buffer, returning the number of bytes written.
Pass nullptr to obtain the storage size.

Writes Fill_Type, Verb_Array, Point_Array, Conic_Weight, and
additionally writes computed information like Convexity and bounds.

Use only be used in concert with readFromMemory;
the format used for Path in memory is not guaranteed.

#Param buffer  storage for Path; may be nullptr ##

#Return  size of storage required for Path; always a multiple of 4 ##

#Example
void draw(SkCanvas* canvas) {
    SkPath path, copy;
    path.lineTo(6.f / 7, 2.f / 3);
    size_t size = path.writeToMemory(nullptr);
    SkTDArray<char> storage;
    storage.setCount(size);
    path.writeToMemory(storage.begin());
    copy.readFromMemory(storage.begin(), size);
    SkDebugf("path is " "%s" "equal to copy\n", path == copy ? "" : "not ");
}
#StdOut
path is equal to copy
##
##

#SeeAlso serialize readFromMemory dump dumpHex

##

#Method sk_sp<SkData> serialize() const
#In Utility
#Line # copies data to buffer ##
Writes Path to buffer, returning the buffer written to, wrapped in Data.

serialize() writes Fill_Type, Verb_Array, Point_Array, Conic_Weight, and
additionally writes computed information like Convexity and bounds.

serialize() should only be used in concert with readFromMemory.
The format used for Path in memory is not guaranteed.

#Return  Path data wrapped in Data buffer ##

#Example
void draw(SkCanvas* canvas) {
    SkPath path, copy;
    path.lineTo(6.f / 7, 2.f / 3);
    sk_sp<SkData> data = path.serialize();
    copy.readFromMemory(data->data(), data->size());
    SkDebugf("path is " "%s" "equal to copy\n", path == copy ? "" : "not ");
}
#StdOut
path is equal to copy
##
##

#SeeAlso writeToMemory readFromMemory dump dumpHex
##

# ------------------------------------------------------------------------------

#Method size_t readFromMemory(const void* buffer, size_t length)
#In Utility
#Line # initializes from buffer ##
Initializes Path from buffer of size length. Returns zero if the buffer is
data is inconsistent, or the length is too small.

Reads Fill_Type, Verb_Array, Point_Array, Conic_Weight, and
additionally reads computed information like Convexity and bounds.

Used only in concert with writeToMemory;
the format used for Path in memory is not guaranteed.

#Param buffer  storage for Path ##
#Param length  buffer size in bytes; must be multiple of 4 ##

#Return  number of bytes read, or zero on failure ##

#Example
void draw(SkCanvas* canvas) {
    SkPath path, copy;
    path.lineTo(6.f / 7, 2.f / 3);
    size_t size = path.writeToMemory(nullptr);
    SkTDArray<char> storage;
    storage.setCount(size);
    path.writeToMemory(storage.begin());
    size_t wrongSize = size - 4;
    size_t bytesRead = copy.readFromMemory(storage.begin(), wrongSize);
    SkDebugf("length = %u; returned by readFromMemory = %u\n", wrongSize, bytesRead);
    size_t largerSize = size + 4;
    bytesRead = copy.readFromMemory(storage.begin(), largerSize);
    SkDebugf("length = %u; returned by readFromMemory = %u\n", largerSize, bytesRead);
}
#StdOut
length = 32; returned by readFromMemory = 0
length = 40; returned by readFromMemory = 36
##
##

#SeeAlso writeToMemory

##

# ------------------------------------------------------------------------------
#Subtopic Generation_ID
#Alias Generation_IDs ##
#Line # value reflecting contents change ##
Generation_ID provides a quick way to check if Verb_Array, Point_Array, or
Conic_Weight has changed. Generation_ID is not a hash; identical Paths will
not necessarily have matching Generation_IDs.

Empty Paths have a Generation_ID of one.

#Method uint32_t getGenerationID() const

#In Generation_ID
#Line # returns unique ID ##
Returns a non-zero, globally unique value. A different value is returned
if Verb_Array, Point_Array, or Conic_Weight changes.

Setting Fill_Type does not change Generation_ID.

Each time the path is modified, a different Generation_ID will be returned.

#Bug 1762
Fill_Type does affect Generation_ID on Android framework.

#Return  non-zero, globally unique value ##

#Example
SkPath path;
SkDebugf("empty genID = %u\n", path.getGenerationID());
path.lineTo(1, 2);
SkDebugf("1st lineTo genID = %u\n", path.getGenerationID());
path.rewind();
SkDebugf("empty genID = %u\n", path.getGenerationID());
path.lineTo(1, 2);
SkDebugf("2nd lineTo genID = %u\n", path.getGenerationID());
#StdOut
empty genID = 1
1st lineTo genID = 2
empty genID = 1
2nd lineTo genID = 3
##
##

#SeeAlso operator==(const SkPath& a, const SkPath& b)

##

#Subtopic ##

# ------------------------------------------------------------------------------

#Method bool isValid() const
#In Property
#In Utility
#Line # returns if data is internally consistent ##
    Returns if Path data is consistent. Corrupt Path data is detected if
    internal values are out of range or internal storage does not match
    array dimensions.

    #Return  true if Path data is consistent ##

    #NoExample
    ##

##

#Method bool pathRefIsValid() const
#Deprecated soon
##

# ------------------------------------------------------------------------------

#Class Iter
#Line # data iterator ##

#Code
#Populate
##

Iterates through Verb_Array, and associated Point_Array and Conic_Weight.
Provides options to treat open Contours as closed, and to ignore
degenerate data.

#Example
#Height 128
#Description
Ignoring the actual Verbs and replacing them with Quads rounds the
path of the glyph.
##
void draw(SkCanvas* canvas) {
    SkPaint paint;
    paint.setAntiAlias(true);
    paint.setTextSize(256);
    SkPath asterisk, path;
    paint.getTextPath("*", 1, 50, 192, &asterisk);
    SkPath::Iter iter(asterisk, true);
    SkPoint start[4], pts[4];
    iter.next(start);  // skip moveTo
    iter.next(start);  // first quadTo
    path.moveTo((start[0] + start[1]) * 0.5f);
    while (SkPath::kClose_Verb != iter.next(pts)) {
        path.quadTo(pts[0], (pts[0] + pts[1]) * 0.5f);
    }
    path.quadTo(start[0], (start[0] + start[1]) * 0.5f);
    canvas->drawPath(path, paint);
}
##

#SeeAlso RawIter

#Method Iter()
#Line # constructs Path iterator ##
Initializes Iter with an empty Path. next() on Iter returns kDone_Verb.
Call setPath to initialize Iter at a later time.

#Return  Iter of empty Path ##

#Example
void draw(SkCanvas* canvas) {
    SkPath::Iter iter;
    SkPoint points[4];
    SkDebugf("iter is " "%s" "done\n", SkPath::kDone_Verb == iter.next(points) ? "" : "not ");
    SkPath path;
    iter.setPath(path, false);
    SkDebugf("iter is " "%s" "done\n", SkPath::kDone_Verb == iter.next(points) ? "" : "not ");
}
#StdOut
iter is done
iter is done
##
##

#SeeAlso setPath

##

#Method Iter(const SkPath& path, bool forceClose)
#Line # constructs Path iterator ##

Sets Iter to return elements of Verb_Array, Point_Array, and Conic_Weight in path.
If forceClose is true, Iter will add kLine_Verb and kClose_Verb after each
open Contour. path is not altered.

#Param path  Path to iterate ##
#Param forceClose true if open Contours generate kClose_Verb ##

#Return Iter of path ##

#Example
void draw(SkCanvas* canvas) {
    auto debugster = [](const char* prefix, SkPath::Iter& iter) -> void {
        SkDebugf("%s:\n", prefix);
        const char* verbStr[] =  { "Move", "Line", "Quad", "Conic", "Cubic", "Close", "Done" };
        const int pointCount[] = {     1 ,     2 ,     3 ,      3 ,      4 ,      1 ,     0  };
        SkPath::Verb verb;
        do {
           SkPoint points[4];
           verb = iter.next(points);
           SkDebugf("k%s_Verb ", verbStr[(int) verb]);
           for (int i = 0; i < pointCount[(int) verb]; ++i) {
                SkDebugf("{%g, %g}, ", points[i].fX, points[i].fY);
           }
           if (SkPath::kConic_Verb == verb) {
               SkDebugf("weight = %g", iter.conicWeight());
           }
           SkDebugf("\n");
        } while (SkPath::kDone_Verb != verb);
        SkDebugf("\n");
    };

    SkPath path;
    path.quadTo(10, 20, 30, 40);
    SkPath::Iter openIter(path, false);
    debugster("open", openIter);
    SkPath::Iter closedIter(path, true);
    debugster("closed", closedIter);
}
#StdOut
open:
kMove_Verb {0, 0},
kQuad_Verb {0, 0}, {10, 20}, {30, 40},
kDone_Verb

closed:
kMove_Verb {0, 0},
kQuad_Verb {0, 0}, {10, 20}, {30, 40},
kLine_Verb {30, 40}, {0, 0},
kClose_Verb {0, 0},
kDone_Verb
##
##

#SeeAlso setPath

##

#Method void setPath(const SkPath& path, bool forceClose)
#Line # resets Iter to Path ##
Sets Iter to return elements of Verb_Array, Point_Array, and Conic_Weight in path.
If forceClose is true, Iter will add kLine_Verb and kClose_Verb after each
open Contour. path is not altered.

#Param path  Path to iterate ##
#Param forceClose true if open Contours generate kClose_Verb ##

#Example
void draw(SkCanvas* canvas) {
    auto debugster = [](const char* prefix, SkPath::Iter& iter) -> void {
        SkDebugf("%s:\n", prefix);
        const char* verbStr[] =  { "Move", "Line", "Quad", "Conic", "Cubic", "Close", "Done" };
        const int pointCount[] = {     1 ,     2 ,     3 ,      3 ,      4 ,      1 ,     0  };
        SkPath::Verb verb;
        do {
           SkPoint points[4];
           verb = iter.next(points);
           SkDebugf("k%s_Verb ", verbStr[(int) verb]);
           for (int i = 0; i < pointCount[(int) verb]; ++i) {
                SkDebugf("{%g, %g}, ", points[i].fX, points[i].fY);
           }
           if (SkPath::kConic_Verb == verb) {
               SkDebugf("weight = %g", iter.conicWeight());
           }
           SkDebugf("\n");
        } while (SkPath::kDone_Verb != verb);
        SkDebugf("\n");
    };

    SkPath path;
    path.quadTo(10, 20, 30, 40);
    SkPath::Iter iter(path, false);
    debugster("quad open", iter);
    SkPath path2;
    path2.conicTo(1, 2, 3, 4, .5f);
    iter.setPath(path2, true);
    debugster("conic closed", iter);
}
#StdOut
quad open:
kMove_Verb {0, 0},
kQuad_Verb {0, 0}, {10, 20}, {30, 40},
kDone_Verb

conic closed:
kMove_Verb {0, 0},
kConic_Verb {0, 0}, {1, 2}, {3, 4}, weight = 0.5
kLine_Verb {3, 4}, {0, 0},
kClose_Verb {0, 0},
kDone_Verb
##
##

#SeeAlso Iter(const SkPath& path, bool forceClose)

##

#Method Verb next(SkPoint pts[4], bool doConsumeDegenerates = true, bool exact = false)
#Line # returns next Verb ##

Returns next Verb in Verb_Array, and advances Iter.
When Verb_Array is exhausted, returns kDone_Verb.

Zero to four Points are stored in pts, depending on the returned Verb.

If doConsumeDegenerates is true, skip consecutive kMove_Verb entries, returning
only the last in the series; and skip very small Lines, Quads, and Conics; and
skip kClose_Verb following kMove_Verb.
if doConsumeDegenerates is true and exact is true, only skip Lines, Quads, and
Conics with zero lengths.

    #Param  pts storage for Point data describing returned Verb ##
    #Param doConsumeDegenerates if true, skip degenerate Verbs ##
    #Param exact skip zero length curves ##

    #Return next Verb from Verb_Array  ##

#Example
#Description
skip degenerate skips the first in a kMove_Verb pair, the kMove_Verb
followed by the kClose_Verb, the zero length Line and the very small Line.

skip degenerate if exact skips the same as skip degenerate, but shows
the very small Line.

skip none shows all of the Verbs and Points in Path.
##
void draw(SkCanvas* canvas) {
    auto debugster = [](const char* prefix, const SkPath& path, bool degen, bool exact) -> void {
        SkPath::Iter iter(path, false);
        SkDebugf("%s:\n", prefix);
        const char* verbStr[] =  { "Move", "Line", "Quad", "Conic", "Cubic", "Close", "Done" };
        const int pointCount[] = {     1 ,     2 ,     3 ,      3 ,      4 ,      1 ,     0  };
        SkPath::Verb verb;
        do {
           SkPoint points[4];
           verb = iter.next(points, degen, exact);
           SkDebugf("k%s_Verb ", verbStr[(int) verb]);
           for (int i = 0; i < pointCount[(int) verb]; ++i) {
                SkDebugf("{%1.8g, %1.8g}, ", points[i].fX, points[i].fY);
           }
           SkDebugf("\n");
        } while (SkPath::kDone_Verb != verb);
        SkDebugf("\n");
    };

    SkPath path;
    path.moveTo(10, 10);
    path.moveTo(20, 20);
    path.quadTo(10, 20, 30, 40);
    path.moveTo(1, 1);
    path.close();
    path.moveTo(30, 30);
    path.lineTo(30, 30);
    path.moveTo(30, 30);
    path.lineTo(30.00001f, 30);
    debugster("skip degenerate", path, true, false);
    debugster("skip degenerate if exact", path, true, true);
    debugster("skip none", path, false, false);
}
#StdOut
skip degenerate:
kMove_Verb {20, 20},
kQuad_Verb {20, 20}, {10, 20}, {30, 40},
kDone_Verb

skip degenerate if exact:
kMove_Verb {20, 20},
kQuad_Verb {20, 20}, {10, 20}, {30, 40},
kMove_Verb {30, 30},
kLine_Verb {30, 30}, {30.00001, 30},
kDone_Verb

skip none:
kMove_Verb {10, 10},
kMove_Verb {20, 20},
kQuad_Verb {20, 20}, {10, 20}, {30, 40},
kMove_Verb {1, 1},
kClose_Verb {1, 1},
kMove_Verb {30, 30},
kLine_Verb {30, 30}, {30, 30},
kMove_Verb {30, 30},
kLine_Verb {30, 30}, {30.00001, 30},
kDone_Verb
##
##

#SeeAlso Verb IsLineDegenerate IsCubicDegenerate IsQuadDegenerate

##

#Method SkScalar conicWeight() const
#Line # returns Conic_Weight ##
    Returns Conic_Weight if next() returned kConic_Verb.

    If next() has not been called, or next() did not return kConic_Verb,
    result is undefined.

    #Return  Conic_Weight for Conic Points returned by next() ##

    #Example
    void draw(SkCanvas* canvas) {
       SkPath path;
       path.conicTo(1, 2, 3, 4, .5f);
       SkPath::Iter iter(path, false);
       SkPoint p[4];
       SkDebugf("first verb is " "%s" "move\n", SkPath::kMove_Verb == iter.next(p) ? "" : "not ");
       SkDebugf("next verb is " "%s" "conic\n", SkPath::kConic_Verb == iter.next(p) ? "" : "not ");
       SkDebugf("conic points: {%g,%g}, {%g,%g}, {%g,%g}\n", p[0].fX, p[0].fY, p[1].fX, p[1].fY,
                    p[2].fX, p[2].fY);
       SkDebugf("conic weight: %g\n", iter.conicWeight());
    }
    #StdOut
first verb is move
next verb is conic
conic points: {0,0}, {1,2}, {3,4}
conic weight: 0.5
    ##
    ##

    #SeeAlso Conic_Weight

##

#Method bool isCloseLine() const
#Line # returns if Line was generated by kClose_Verb ##
    Returns true if last kLine_Verb returned by next() was generated
    by kClose_Verb. When true, the end point returned by next() is
    also the start point of Contour.

    If next() has not been called, or next() did not return kLine_Verb,
    result is undefined.

    #Return  true if last kLine_Verb was generated by kClose_Verb ##

    #Example
void draw(SkCanvas* canvas) {
   SkPath path;
   path.moveTo(6, 7);
   path.conicTo(1, 2, 3, 4, .5f);
   path.close();
   SkPath::Iter iter(path, false);
   SkPoint p[4];
   SkDebugf("1st verb is " "%s" "move\n", SkPath::kMove_Verb == iter.next(p) ? "" : "not ");
   SkDebugf("moveTo point: {%g,%g}\n", p[0].fX, p[0].fY);
   SkDebugf("2nd verb is " "%s" "conic\n", SkPath::kConic_Verb == iter.next(p) ? "" : "not ");
   SkDebugf("3rd verb is " "%s" "line\n", SkPath::kLine_Verb == iter.next(p) ? "" : "not ");
   SkDebugf("line points: {%g,%g}, {%g,%g}\n", p[0].fX, p[0].fY, p[1].fX, p[1].fY);
   SkDebugf("line " "%s" "generated by close\n", iter.isCloseLine() ? "" : "not ");
   SkDebugf("4th verb is " "%s" "close\n", SkPath::kClose_Verb == iter.next(p) ? "" : "not ");
}
    #StdOut
1st verb is move
moveTo point: {6,7}
2nd verb is conic
3rd verb is line
line points: {3,4}, {6,7}
line generated by close
4th verb is close
    ##
    ##

    #SeeAlso close()
##

#Method bool isClosedContour() const
#Line # returns if Contour has kClose_Verb ##
Returns true if subsequent calls to next() return kClose_Verb before returning
kMove_Verb. if true, Contour Iter is processing may end with kClose_Verb, or
Iter may have been initialized with force close set to true.

#Return true if Contour is closed ##

#Example
void draw(SkCanvas* canvas) {
   for (bool forceClose : { false, true } ) {
       SkPath path;
       path.conicTo(1, 2, 3, 4, .5f);
       SkPath::Iter iter(path, forceClose);
       SkDebugf("without close(), forceClose is %s: isClosedContour returns %s\n",
           forceClose ? "true " : "false", iter.isClosedContour() ? "true" : "false");
       path.close();
       iter.setPath(path, forceClose);
       SkDebugf("with close(),    forceClose is %s: isClosedContour returns %s\n",
           forceClose ? "true " : "false", iter.isClosedContour() ? "true" : "false");
    }
}
#StdOut
without close(), forceClose is false: isClosedContour returns false
with close(),    forceClose is false: isClosedContour returns true
without close(), forceClose is true : isClosedContour returns true
with close(),    forceClose is true : isClosedContour returns true
##
##

#SeeAlso Iter(const SkPath& path, bool forceClose)

##

#Class Iter ##

#Class RawIter
#Line # raw data iterator ##

#Code
#Populate
##

Iterates through Verb_Array, and associated Point_Array and Conic_Weight.
Verb_Array, Point_Array, and Conic_Weight are returned unaltered.


    #Method RawIter()
    #Line # constructs empty Path iterator ##

        Initializes RawIter with an empty Path. next() on RawIter returns kDone_Verb.
        Call setPath to initialize SkPath::Iter at a later time.

        #Return RawIter of empty Path ##

        #NoExample
        ##
    ##

    #Method RawIter(const SkPath& path)
    #Line # constructs with Path to iterate over ##


        Sets RawIter to return elements of Verb_Array, Point_Array, and Conic_Weight in path.

        #Param path  Path to iterate ##

        #Return RawIter of path ##

        #NoExample
        ##
    ##

    #Method void setPath(const SkPath& path)
    #Line # sets Path to iterate over ##

        Sets SkPath::Iter to return elements of Verb_Array, Point_Array, and Conic_Weight in path.

        #Param path  Path to iterate ##

        #NoExample
        ##
   ##

    #Method Verb next(SkPoint pts[4])
    #Line # returns next Verb and associated Points ##
        Returns next Verb in Verb_Array, and advances RawIter.
        When Verb_Array is exhausted, returns kDone_Verb.
        Zero to four Points are stored in pts, depending on the returned Verb.

        #Param  pts storage for Point data describing returned Verb ##

        #Return next Verb from Verb_Array  ##

        #Example
        void draw(SkCanvas* canvas) {
            SkPath path;
            path.moveTo(50, 60);
            path.quadTo(10, 20, 30, 40);
            path.close();
            path.lineTo(30, 30);
            path.conicTo(1, 2, 3, 4, .5f);
            path.cubicTo(-1, -2, -3, -4, -5, -6);
            SkPath::RawIter iter(path);
            const char* verbStr[] =  { "Move", "Line", "Quad", "Conic", "Cubic", "Close", "Done" };
            const int pointCount[] = {     1 ,     2 ,     3 ,      3 ,      4 ,      1 ,     0  };
            SkPath::Verb verb;
            do {
                SkPoint points[4];
                verb = iter.next(points);
                SkDebugf("k%s_Verb ", verbStr[(int) verb]);
                for (int i = 0; i < pointCount[(int) verb]; ++i) {
                    SkDebugf("{%1.8g, %1.8g}, ", points[i].fX, points[i].fY);
                }
                if (SkPath::kConic_Verb == verb) {
                    SkDebugf("weight = %g", iter.conicWeight());
                }
                SkDebugf("\n");
            } while (SkPath::kDone_Verb != verb);
        }
    #StdOut
        kMove_Verb {50, 60},
        kQuad_Verb {50, 60}, {10, 20}, {30, 40},
        kClose_Verb {50, 60},
        kMove_Verb {50, 60},
        kLine_Verb {50, 60}, {30, 30},
        kConic_Verb {30, 30}, {1, 2}, {3, 4}, weight = 0.5
        kCubic_Verb {3, 4}, {-1, -2}, {-3, -4}, {-5, -6},
        kDone_Verb
    ##
    ##

    #SeeAlso peek()

    ##

    #Method Verb peek() const
    #Line # returns next Verb ##
        Returns next Verb, but does not advance RawIter.

        #Return next Verb from Verb_Array  ##

        #Example
            SkPath path;
            path.quadTo(10, 20, 30, 40);
            path.conicTo(1, 2, 3, 4, .5f);
            path.cubicTo(1, 2, 3, 4, .5, 6);
            SkPath::RawIter iter(path);
            SkPath::Verb verb, peek = iter.peek();
            const char* verbStr[] =  { "Move", "Line", "Quad", "Conic", "Cubic", "Close", "Done" };
            do {
                SkPoint points[4];
                verb = iter.next(points);
                SkDebugf("peek %s %c= verb %s\n", verbStr[peek], peek == verb ? '=' : '!', verbStr[verb]);
                peek = iter.peek();
            } while (SkPath::kDone_Verb != verb);
            SkDebugf("peek %s %c= verb %s\n", verbStr[peek], peek == verb ? '=' : '!', verbStr[verb]);
            #StdOut
                #Volatile
                peek Move == verb Move
                peek Quad == verb Quad
                peek Conic == verb Conic
                peek Cubic == verb Cubic
                peek Done == verb Done
                peek Done == verb Done
            ##
        ##

        #Bug 6832
        StdOut is not really volatile, it just produces the wrong result.
        A simple fix changes the output of hairlines and needs to be
        investigated to see if the change is correct or not.
        see change 21340 (abandoned for now)

        #SeeAlso next

    ##

    #Method SkScalar conicWeight() const
    #Line # returns Conic_Weight ##

        Returns Conic_Weight if next() returned kConic_Verb.

        If next() has not been called, or next() did not return kConic_Verb,
        result is undefined.

        #Return  Conic_Weight for Conic Points returned by next() ##

    #Example
    void draw(SkCanvas* canvas) {
       SkPath path;
       path.conicTo(1, 2, 3, 4, .5f);
       SkPath::RawIter iter(path);
       SkPoint p[4];
       SkDebugf("first verb is " "%s" "move\n", SkPath::kMove_Verb == iter.next(p) ? "" : "not ");
       SkDebugf("next verb is " "%s" "conic\n", SkPath::kConic_Verb == iter.next(p) ? "" : "not ");
       SkDebugf("conic points: {%g,%g}, {%g,%g}, {%g,%g}\n", p[0].fX, p[0].fY, p[1].fX, p[1].fY,
                    p[2].fX, p[2].fY);
       SkDebugf("conic weight: %g\n", iter.conicWeight());
    }
    #StdOut
        first verb is move
        next verb is conic
        conic points: {0,0}, {1,2}, {3,4}
        conic weight: 0.5
    ##
    ##

    #SeeAlso Conic_Weight

    ##

#Class RawIter ##

#Class SkPath ##

#Topic Path ##