skia2/docs/SkPoint_Reference.bmh

#Topic Point
#Alias Points ##
#Alias Point_Reference ##

#Struct SkPoint

#Code
#Populate
##

SkPoint holds two 32-bit floating point coordinates.

#Member SkScalar  fX
#Line # x-axis value ##
x-axis value used by both Point and Vector. May contain any value, including
infinities and NaN.
##

#Member SkScalar  fY
#Line # y-axis value ##
y-axis value used by both Point and Vector. May contain any value, including
infinities and NaN.
##

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

#Method static constexpr SkPoint Make(SkScalar x, SkScalar y)
#In Constructors
#Line # constructs from SkScalar inputs ##
#Populate

#Example
SkPoint pt1 = {45, 66};
SkPoint pt2 = SkPoint::Make(45, 66);
SkVector v1 = {45, 66};
SkVector v2 = SkPoint::Make(45, 66);
SkDebugf("all %s" "equal\n", pt1 == pt2 && pt2 == v1 && v1 == v2 ? "" : "not ");
#StdOut
all equal
##
##

#SeeAlso set() iset() SkIPoint::Make

#Method ##

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

#Subtopic Property
#Line # member values ##
##

#Method SkScalar x() const
#In Property
#Line # returns fX ##
#Populate

#Example
SkPoint pt1 = {45, 66};
SkDebugf("pt1.fX %c= pt1.x()\n", pt1.fX == pt1.x() ? '=' : '!');
#StdOut
pt1.fX == pt1.x()
##
##

#SeeAlso y() SkIPoint::x()

#Method ##

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

#Method SkScalar y() const
#In Property
#Line # returns fY ##
#Populate

#Example
SkPoint pt1 = {45, 66};
SkDebugf("pt1.fY %c= pt1.y()\n", pt1.fY == pt1.y() ? '=' : '!');
#StdOut
pt1.fY == pt1.y()
##
##

#SeeAlso x() SkIPoint::y()

#Method ##

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

#Method bool isZero() const
#In Property
#Line # returns true if both members equal zero ##
#Populate

#Example
SkPoint pt = { 0.f, -0.f};
SkDebugf("pt.fX=%c%g pt.fY=%c%g\n", std::signbit(pt.fX) ? '-' : '+', fabsf(pt.fX),
                                    std::signbit(pt.fY) ? '-' : '+', fabsf(pt.fY));
SkDebugf("pt.isZero() == %s\n", pt.isZero() ? "true" : "false");
#StdOut
pt.fX=+0 pt.fY=-0
pt.isZero() == true
##
##

#SeeAlso isFinite SkIPoint::isZero

#Method ##

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

#Subtopic Set
#Line # replaces all values ##
##

#Method void set(SkScalar x, SkScalar y)
#In Set
#Line # sets to SkScalar input ##
#Populate

#Example
SkPoint pt1, pt2 = { SK_ScalarPI, SK_ScalarSqrt2 };
pt1.set(SK_ScalarPI, SK_ScalarSqrt2);
SkDebugf("pt1 %c= pt2\n", pt1 == pt2 ? '=' : '!');
#StdOut
pt1 == pt2
##
##

#SeeAlso iset() Make

#Method ##

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

#Method void iset(int32_t x, int32_t y)
#In Set
#Line # sets to integer input ##
#Populate

#Example
SkPoint pt1, pt2 = { SK_MinS16, SK_MaxS16 };
pt1.iset(SK_MinS16, SK_MaxS16);
SkDebugf("pt1 %c= pt2\n", pt1 == pt2 ? '=' : '!');
##

#SeeAlso set Make SkIPoint::set

#Method ##

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

#Method void iset(const SkIPoint& p)
#Populate

#Example
SkIPoint iPt = { SK_MinS32, SK_MaxS32 };
SkPoint fPt;
fPt.iset(iPt);
SkDebugf("iPt: %d, %d\n", iPt.fX, iPt.fY);
SkDebugf("fPt: %g, %g\n", fPt.fX, fPt.fY);
#StdOut
iPt: -2147483647, 2147483647
fPt: -2.14748e+09, 2.14748e+09
##
##

#SeeAlso set Make SkIPoint::set

#Method ##

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

#Method void setAbs(const SkPoint& pt)
#In Set
#Line # sets sign of both members to positive ##
#Populate

#Example
SkPoint test[] = { {0.f, -0.f}, {-1, -2},
                   { SK_ScalarInfinity, SK_ScalarNegativeInfinity },
                   { SK_ScalarNaN, -SK_ScalarNaN } };
for (const SkPoint& pt : test) {
    SkPoint absPt;
    absPt.setAbs(pt);
    SkDebugf("pt: %g, %g  abs: %g, %g\n", pt.fX, pt.fY, absPt.fX, absPt.fY);
}
#StdOut
pt: 0, -0  abs: 0, 0
pt: -1, -2  abs: 1, 2
pt: inf, -inf  abs: inf, inf
pt: nan, -nan  abs: nan, nan
##
##

#SeeAlso set Make negate

#Method ##

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

#Subtopic Offset
#Line # moves sides ##
##

#Method static void Offset(SkPoint points[], int count, const SkVector& offset)
#In Offset
#Line # translates Point array ##
#Populate

#Example
    SkPaint paint;
    paint.setAntiAlias(true);
    SkPoint points[] = { { 3, 1 }, { 4, 2 }, { 5, 1 }, { 7, 3 },
                         { 6, 4 }, { 7, 5 }, { 5, 7 },
                         { 4, 6 }, { 3, 7 }, { 1, 5 },
                         { 2, 4 }, { 1, 3 }, { 3, 1 } };
    canvas->scale(30, 15);
    paint.setStyle(SkPaint::kStroke_Style);
    canvas->drawPoints(SkCanvas::kPolygon_PointMode, SK_ARRAY_COUNT(points), points, paint);
    SkPoint::Offset(points, SK_ARRAY_COUNT(points), { 1, 9 } );
    canvas->drawPoints(SkCanvas::kPolygon_PointMode, SK_ARRAY_COUNT(points), points, paint);
##

#SeeAlso offset operator+=(const SkVector& v)

#Method ##

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

#Method static void Offset(SkPoint points[], int count, SkScalar dx, SkScalar dy)
#Populate

#Example
    SkPaint paint;
    paint.setAntiAlias(true);
    SkPoint points[] = { { 3, 1 }, { 4, 2 }, { 5, 1 }, { 7, 3 },
                         { 6, 4 }, { 7, 5 }, { 5, 7 },
                         { 4, 6 }, { 3, 7 }, { 1, 5 },
                         { 2, 4 }, { 1, 3 }, { 3, 1 } };
    canvas->scale(30, 15);
    paint.setStyle(SkPaint::kStroke_Style);
    canvas->drawPoints(SkCanvas::kPolygon_PointMode, SK_ARRAY_COUNT(points), points, paint);
    SkPoint::Offset(points, SK_ARRAY_COUNT(points), 1, 9);
    canvas->drawPoints(SkCanvas::kPolygon_PointMode, SK_ARRAY_COUNT(points), points, paint);
##

#SeeAlso offset operator+=(const SkVector& v)

#Method ##

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

#Method void offset(SkScalar dx, SkScalar dy)
#In Offset
#Line # translates Point ##
#Populate

#Example
#Height 128
    SkPaint paint;
    paint.setAntiAlias(true);
    SkPoint points[] = { { 3, 1 }, { 4, 2 }, { 5, 1 }, { 7, 3 },
                         { 6, 4 }, { 7, 5 }, { 5, 7 },
                         { 4, 6 }, { 3, 7 }, { 1, 5 },
                         { 2, 4 }, { 1, 3 }, { 3, 1 } };
    canvas->scale(30, 15);
    paint.setStyle(SkPaint::kStroke_Style);
    canvas->drawPoints(SkCanvas::kPolygon_PointMode, SK_ARRAY_COUNT(points), points, paint);
    points[1].offset(1, 1);
    paint.setColor(SK_ColorRED);
    canvas->drawPoints(SkCanvas::kPolygon_PointMode, SK_ARRAY_COUNT(points), points, paint);
##

#SeeAlso Offset operator+=(const SkVector& v)

#Method ##

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

#Method SkScalar length() const
#In Property
#Line # returns straight-line distance to origin ##
#Populate

#Example
#Height 192
    SkPaint paint;
    paint.setAntiAlias(true);
    const SkPoint points[] = { { 90, 30 }, { 120, 150 }, { 150, 30 }, { 210, 90 } };
    const SkPoint origin = {30, 140};
    for (auto point : points) {
        canvas->drawLine(origin, point, paint);
        SkAutoCanvasRestore acr(canvas, true);
        SkScalar angle = SkScalarATan2((point.fY - origin.fY), point.fX - origin.fX);
        canvas->rotate(angle * 180 / SK_ScalarPI, origin.fX, origin.fY);
        SkString length("length = ");
        length.appendScalar(point.length());
        canvas->drawString(length, origin.fX + 25, origin.fY - 4, paint);
    }
##

#SeeAlso distanceToOrigin Length setLength Distance

#Method ##

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

#Method SkScalar distanceToOrigin() const
#In Property
#Line # returns straight-line distance to origin ##
#Populate

#Example
#Height 192
    SkPaint paint;
    paint.setAntiAlias(true);
    const SkPoint points[] = { { 60, -110 }, { 90, 10 }, { 120, -110 }, { 180, -50 } };
    const SkPoint origin = {0, 0};
    canvas->translate(30, 140);
    for (auto point : points) {
        canvas->drawLine(origin, point, paint);
        SkAutoCanvasRestore acr(canvas, true);
        SkScalar angle = SkScalarATan2((point.fY - origin.fY), point.fX - origin.fX);
        canvas->rotate(angle * 180 / SK_ScalarPI, origin.fX, origin.fY);
        SkString distance("distance = ");
        distance.appendScalar(point.distanceToOrigin());
        canvas->drawString(distance, origin.fX + 25, origin.fY - 4, paint);
    }
##

#SeeAlso length Length setLength Distance

#Method ##

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

#Method bool normalize()
#In Set
#Line # sets length to one, preserving direction ##
#Populate

#Example
    SkPaint paint;
    paint.setAntiAlias(true);
    const SkPoint lines[][2] = { {{  30, 110 }, { 190,  30 }},
                                 {{ 120, 140 }, {  30, 220 }}};
    for (auto line : lines) {
        canvas->drawLine(line[0], line[1], paint);
        SkVector vector = line[1] - line[0];
        if (vector.normalize()) {
            SkVector rotate90 = { -vector.fY, vector.fX };
            rotate90 *= 10.f;
            canvas->drawLine(line[0] - rotate90, line[0] + rotate90, paint);
            canvas->drawLine(line[1] - rotate90, line[1] + rotate90, paint);
        }
    }
##

#SeeAlso Normalize setLength length Length

#Method ##

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

#Method bool setNormalize(SkScalar x, SkScalar y)
#In Set
#Line # sets length to one, in direction of (x, y) ##
#Populate

#Example
    SkPaint paint;
    paint.setAntiAlias(true);
    const SkPoint points[] = { { 60, -110 }, { 90, 10 }, { 120, -110 }, { 180, -50 } };
    const SkPoint origin = {0, 0};
    canvas->translate(30, 140);
    for (auto point : points) {
        paint.setStrokeWidth(1);
        paint.setColor(SK_ColorBLACK);
        canvas->drawLine(origin, point, paint);
        SkVector normal;
        normal.setNormalize(point.fX, point.fY);
        normal *= 100;
        paint.setStrokeWidth(10);
        paint.setColor(0x3f4512bf);
        canvas->drawLine(origin, normal, paint);
    }
##

#SeeAlso normalize setLength

#Method ##

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

#Method bool setLength(SkScalar length)
#In Set
#Line # sets straight-line distance to origin ##
#Populate

#Example
#Height 160
    SkPaint paint;
    paint.setAntiAlias(true);
    const SkPoint points[] = { { 60, -110 }, { 90, 10 }, { 120, -110 }, { 180, -50 } };
    const SkPoint origin = {0, 0};
    canvas->translate(30, 140);
    for (auto point : points) {
        paint.setStrokeWidth(1);
        paint.setColor(SK_ColorBLACK);
        canvas->drawLine(origin, point, paint);
        SkVector normal = point;
        normal.setLength(100);
        paint.setStrokeWidth(10);
        paint.setColor(0x3f45bf12);
        canvas->drawLine(origin, normal, paint);
    }
##

#SeeAlso length Length setNormalize setAbs

#Method ##

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

#Method bool setLength(SkScalar x, SkScalar y, SkScalar length)
#Populate

#Example
#Height 160
    SkPaint paint;
    paint.setAntiAlias(true);
    const SkPoint points[] = { { 60, -110 }, { 90, 10 }, { 120, -110 }, { 180, -50 } };
    const SkPoint origin = {0, 0};
    canvas->translate(30, 140);
    for (auto point : points) {
        paint.setStrokeWidth(1);
        paint.setColor(SK_ColorBLACK);
        canvas->drawLine(origin, point, paint);
        SkVector normal;
        normal.setLength(point.fX, point.fY, 100);
        paint.setStrokeWidth(10);
        paint.setColor(0x3fbf4512);
        canvas->drawLine(origin, normal, paint);
    }
##

#SeeAlso length Length setNormalize setAbs

#Method ##

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

#Method void scale(SkScalar scale, SkPoint* dst) const
#In Offset
#In Operators
#Line # multiplies Point by scale factor ##
#Populate

#Example
    SkPaint paint;
    paint.setAntiAlias(true);
    SkPoint point = {40, -15}, scaled;
    SkPoint origin = {30, 110};
    for (auto scale : {1, 2, 3, 5}) {
        paint.setStrokeWidth(scale * 5);
        paint.setARGB(0x7f, 0x9f, 0xbf, 0x33 * scale);
        point.scale(scale, &scaled);
        canvas->drawLine(origin, origin + scaled, paint);
    }
##

#SeeAlso operator*(SkScalar scale)_const operator*=(SkScalar scale) setLength

#Method ##

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

#Method void scale(SkScalar value)
#Populate

#Example
    SkPaint paint;
    paint.setAntiAlias(true);
    SkPoint point = {40, -15};
    SkPoint origin = {30, 110};
    for (auto scale : {1, 2, 3, 5}) {
        paint.setStrokeWidth(scale * 5);
        paint.setARGB(0x7f, 0x9f, 0xbf, 0x33 * scale);
        point.scale(scale);
        canvas->drawLine(origin, origin + point, paint);
    }
##

#SeeAlso operator*(SkScalar scale)_const operator*=(SkScalar scale) setLength

#Method ##

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

#Method void negate()
#In Operators
#Line # reverses the sign of both members ##
#Populate

#Example
SkPoint test[] = { {0.f, -0.f}, {-1, -2},
                   { SK_ScalarInfinity, SK_ScalarNegativeInfinity },
                   { SK_ScalarNaN, -SK_ScalarNaN } };
for (const SkPoint& pt : test) {
    SkPoint negPt = pt;
    negPt.negate();
    SkDebugf("pt: %g, %g  negate: %g, %g\n", pt.fX, pt.fY, negPt.fX, negPt.fY);
}
#StdOut
pt: 0, -0  negate: -0, 0
pt: -1, -2  negate: 1, 2
pt: inf, -inf  negate: -inf, inf
pt: nan, -nan  negate: -nan, nan
##
##

#SeeAlso operator-()_const setAbs

#Method ##

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

#Method SkPoint operator-()_const

#Line # reverses sign of Point ##
#Populate

#Example
SkPoint test[] = { {0.f, -0.f}, {-1, -2},
                   { SK_ScalarInfinity, SK_ScalarNegativeInfinity },
                   { SK_ScalarNaN, -SK_ScalarNaN } };
for (const SkPoint& pt : test) {
    SkPoint negPt = -pt;
    SkDebugf("pt: %g, %g  negate: %g, %g\n", pt.fX, pt.fY, negPt.fX, negPt.fY);
}
#StdOut
pt: 0, -0  negate: -0, 0
pt: -1, -2  negate: 1, 2
pt: inf, -inf  negate: -inf, inf
pt: nan, -nan  negate: -nan, nan
##
##

#SeeAlso negate operator-(const SkPoint& a, const SkPoint& b) operator-=(const SkVector& v) SkIPoint::operator-()_const

#Method ##

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

#Method void operator+=(const SkVector& v)

#Line # adds Vector to Point ##
Adds Vector v to Point. Sets Point to: #Formula # (fX + v.fX, fY + v.fY) ##.

#Param v  Vector to add ##

#Example
#Height 128
    SkPaint paint;
    paint.setAntiAlias(true);
    SkPoint points[] = { { 3, 1 }, { 4, 2 }, { 5, 1 }, { 7, 3 },
                         { 6, 4 }, { 7, 5 }, { 5, 7 },
                         { 4, 6 }, { 3, 7 }, { 1, 5 },
                         { 2, 4 }, { 1, 3 }, { 3, 1 } };
    canvas->scale(30, 15);
    paint.setStyle(SkPaint::kStroke_Style);
    canvas->drawPoints(SkCanvas::kPolygon_PointMode, SK_ARRAY_COUNT(points), points, paint);
    points[1] += {1, 1};
    points[2] += {-1, -1};
    paint.setColor(SK_ColorRED);
    canvas->drawPoints(SkCanvas::kPolygon_PointMode, SK_ARRAY_COUNT(points), points, paint);
##

#SeeAlso offset() operator+(const SkPoint& a, const SkVector& b) SkIPoint::operator+=(const SkIVector& v)

#Method ##

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

#Method void operator-=(const SkVector& v)

#Line # subtracts Vector from Point ##
Subtracts Vector v from Point. Sets Point to: #Formula # (fX - v.fX, fY - v.fY) ##.

#Param v  Vector to subtract ##

#Example
#Height 128
    SkPaint paint;
    paint.setAntiAlias(true);
    SkPoint points[] = { { 3, 1 }, { 4, 2 }, { 5, 1 }, { 7, 3 },
                         { 6, 4 }, { 7, 5 }, { 5, 7 },
                         { 4, 6 }, { 3, 7 }, { 1, 5 },
                         { 2, 4 }, { 1, 3 }, { 3, 1 } };
    canvas->scale(30, 15);
    paint.setStyle(SkPaint::kStroke_Style);
    canvas->drawPoints(SkCanvas::kPolygon_PointMode, SK_ARRAY_COUNT(points), points, paint);
    points[1] -= {1, 1};
    points[2] -= {-1, -1};
    paint.setColor(SK_ColorRED);
    canvas->drawPoints(SkCanvas::kPolygon_PointMode, SK_ARRAY_COUNT(points), points, paint);
##

#SeeAlso offset() operator-(const SkPoint& a, const SkPoint& b) SkIPoint::operator-=(const SkIVector& v)

#Method ##

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

#Method SkPoint operator*(SkScalar scale)_const

#Line # returns Point multiplied by scale ##
#Populate

#Example
#Height 128
    SkPaint paint;
    paint.setAntiAlias(true);
    SkPoint points[] = { { 3, 1 }, { 4, 2 }, { 5, 1 }, { 7, 3 },
                         { 6, 4 }, { 7, 5 }, { 5, 7 },
                         { 4, 6 }, { 3, 7 }, { 1, 5 },
                         { 2, 4 }, { 1, 3 }, { 3, 1 } };
    canvas->scale(15, 10);
    paint.setStyle(SkPaint::kStroke_Style);
    canvas->drawPoints(SkCanvas::kPolygon_PointMode, SK_ARRAY_COUNT(points), points, paint);
    for (auto& point : points) {
        point = point * 1.5f;
    }
    paint.setColor(SK_ColorRED);
    canvas->drawPoints(SkCanvas::kPolygon_PointMode, SK_ARRAY_COUNT(points), points, paint);
##

#SeeAlso operator*=(SkScalar scale) scale() setLength setNormalize

#Method ##

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

#Method SkPoint& operator*=(SkScalar scale)

#Line # multiplies Point by scale factor ##
Multiplies Point by scale. Sets Point to: #Formula # (fX * scale, fY * scale) ##.

#Param scale  Scalar to multiply by ##

#Return reference to Point ##

#Example
#Height 128
    SkPaint paint;
    paint.setAntiAlias(true);
    SkPoint points[] = { { 3, 1 }, { 4, 2 }, { 5, 1 }, { 7, 3 },
                         { 6, 4 }, { 7, 5 }, { 5, 7 },
                         { 4, 6 }, { 3, 7 }, { 1, 5 },
                         { 2, 4 }, { 1, 3 }, { 3, 1 } };
    canvas->scale(15, 10);
    paint.setStyle(SkPaint::kStroke_Style);
    canvas->drawPoints(SkCanvas::kPolygon_PointMode, SK_ARRAY_COUNT(points), points, paint);
    for (auto& point : points) {
        point *= 2;
    }
    paint.setColor(SK_ColorRED);
    canvas->drawPoints(SkCanvas::kPolygon_PointMode, SK_ARRAY_COUNT(points), points, paint);
##

#SeeAlso operator*(SkScalar scale)_const scale() setLength setNormalize

#Method ##

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

#Method bool isFinite() const
#In Property
#Line # returns true if no member is infinite or NaN ##
#Populate

#Example
SkPoint test[] = { {0, -0.f}, {-1, -2}, {SK_ScalarInfinity, 1}, {SK_ScalarNaN, -1} };
for (const SkPoint& pt : test) {
    SkDebugf("pt: %g, %g  finite: %s\n", pt.fX, pt.fY, pt.isFinite() ? "true" : "false");
}
#StdOut
pt: 0, -0  finite: true
pt: -1, -2  finite: true
pt: inf, 1  finite: false
pt: nan, -1  finite: false
##
##

#SeeAlso SkRect::isFinite SkPath::isFinite

#Method ##

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

#Method bool equals(SkScalar x, SkScalar y) const
#In Operators
#Line # returns true if Points are equal ##
#Populate

#Example
SkPoint test[] = { {0, -0.f}, {-1, -2}, {SK_ScalarInfinity, 1}, {SK_ScalarNaN, -1} };
for (const SkPoint& pt : test) {
    SkDebugf("pt: %g, %g  %c= pt\n", pt.fX, pt.fY, pt.equals(pt.fX, pt.fY) ? '=' : '!');
}
#StdOut
pt: 0, -0  == pt
pt: -1, -2  == pt
pt: inf, 1  == pt
pt: nan, -1  != pt
##
##

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

#Method ##

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

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

#Line # returns true if Point are equal ##
#Populate

#Example
SkPoint test[] = { {0, -0.f}, {-1, -2}, {SK_ScalarInfinity, 1}, {SK_ScalarNaN, -1} };
for (const SkPoint& pt : test) {
    SkDebugf("pt: %g, %g  %c= pt\n", pt.fX, pt.fY, pt == pt ? '=' : '!');
}
#StdOut
pt: 0, -0  == pt
pt: -1, -2  == pt
pt: inf, 1  == pt
pt: nan, -1  != pt
##
##

#SeeAlso equals() operator!=(const SkPoint& a, const SkPoint& b)

#Method ##

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

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

#Line # returns true if Point are unequal ##
#Populate

#Example
SkPoint test[] = { {0, -0.f}, {-1, -2}, {SK_ScalarInfinity, 1}, {SK_ScalarNaN, -1} };
for (const SkPoint& pt : test) {
    SkDebugf("pt: %g, %g  %c= pt\n", pt.fX, pt.fY, pt != pt ? '!' : '=');
}
#StdOut
pt: 0, -0  == pt
pt: -1, -2  == pt
pt: inf, 1  == pt
pt: nan, -1  != pt
##
##

#SeeAlso operator==(const SkPoint& a, const SkPoint& b) equals()

#Method ##

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

#Method SkVector operator-(const SkPoint& a, const SkPoint& b)

#Line # returns Vector between Points ##
Returns Vector from b to a, computed as #Formula # (a.fX - b.fX, a.fY - b.fY) ##.

Can also be used to subtract Vector from Point, returning Point.
Can also be used to subtract Vector from Vector, returning Vector.

#Param a  Point to subtract from ##
#Param b  Point to subtract ##

#Return Vector from b to a ##

#Example
    SkPaint paint;
    paint.setAntiAlias(true);
    SkPoint points[] = { { 3, 1 }, { 4, 2 }, { 5, 1 }, { 7, 3 },
                         { 6, 4 }, { 7, 5 }, { 5, 7 },
                         { 4, 6 }, { 3, 7 }, { 1, 5 },
                         { 2, 4 }, { 1, 3 }, { 3, 1 } };
    canvas->scale(30, 15);
    paint.setStyle(SkPaint::kStroke_Style);
    canvas->drawPoints(SkCanvas::kPolygon_PointMode, SK_ARRAY_COUNT(points), points, paint);
    points[1] += points[0] - points[2];
    points[2] -= points[3] - points[5];
    paint.setColor(SK_ColorRED);
    canvas->drawPoints(SkCanvas::kPolygon_PointMode, SK_ARRAY_COUNT(points), points, paint);
##

#SeeAlso operator-=(const SkVector& v) offset()

#Method ##

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

#Method SkPoint operator+(const SkPoint& a, const SkVector& b)

#Line # returns Point offset by Vector ##
Returns Point resulting from Point a offset by Vector b, computed as:
#Formula # (a.fX + b.fX, a.fY + b.fY) ##.

Can also be used to offset Point b by Vector a, returning Point.
Can also be used to add Vector to Vector, returning Vector.

#Param a  Point or Vector to add to ##
#Param b  Point or Vector to add ##

#Return Point equal to a offset by b ##

#Example
    SkPaint paint;
    paint.setAntiAlias(true);
    SkPoint points[] = { { 3, 1 }, { 4, 2 }, { 5, 1 }, { 7, 3 },
                         { 6, 4 }, { 7, 5 }, { 5, 7 },
                         { 4, 6 }, { 3, 7 }, { 1, 5 },
                         { 2, 4 }, { 1, 3 }, { 3, 1 } };
    canvas->scale(30, 15);
    paint.setStyle(SkPaint::kStroke_Style);
    canvas->drawPoints(SkCanvas::kPolygon_PointMode, SK_ARRAY_COUNT(points), points, paint);
    SkVector mod = {1, 1};
    for (auto& point : points) {
        point = point + mod;
        mod.fX *= 1.1f;
        mod.fY += .2f;
    }
    paint.setColor(SK_ColorRED);
    canvas->drawPoints(SkCanvas::kPolygon_PointMode, SK_ARRAY_COUNT(points), points, paint);
##

#SeeAlso operator+=(const SkVector& v) offset()

#Method ##

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

#Method static SkScalar Length(SkScalar x, SkScalar y)
#In Property
#Line # returns straight-line distance to origin ##
#Populate

#Example
#Height 192
    SkPaint paint;
    paint.setAntiAlias(true);
    const SkPoint points[] = { { 90, 30 }, { 120, 150 }, { 150, 30 }, { 210, 90 } };
    const SkPoint origin = {30, 140};
    for (auto point : points) {
        canvas->drawLine(origin, point, paint);
        SkAutoCanvasRestore acr(canvas, true);
        SkScalar angle = SkScalarATan2((point.fY - origin.fY), point.fX - origin.fX);
        canvas->rotate(angle * 180 / SK_ScalarPI, origin.fX, origin.fY);
        SkString length("length = ");
        length.appendScalar(SkPoint::Length(point.fX, point.fY));
        canvas->drawString(length, origin.fX + 25, origin.fY - 4, paint);
    }
##

#SeeAlso length() Distance setLength

#Method ##

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

#Method static SkScalar Normalize(SkVector* vec)
#In Offset
#Line # sets length to one, and returns prior length ##
#Populate

#Example
    SkPaint paint;
    paint.setAntiAlias(true);
    const SkPoint lines[][2] = { {{  30, 110 }, { 190,  30 }},
                                 {{  30, 220 }, { 120, 140 }}};
    for (auto line : lines) {
        canvas->drawLine(line[0], line[1], paint);
        SkVector vector = line[1] - line[0];
        SkScalar priorLength = SkPoint::Normalize(&vector);
        SkVector rotate90 = { -vector.fY, vector.fX };
        rotate90 *= 10.f;
        canvas->drawLine(line[0] - rotate90, line[0] + rotate90, paint);
        canvas->drawLine(line[1] - rotate90, line[1] + rotate90, paint);
        SkString length("length = ");
        length.appendScalar(priorLength);
        canvas->drawString(length, line[0].fX + 25, line[0].fY - 4, paint);
    }
##

#SeeAlso normalize() setLength Length

#Method ##

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

#Method static SkScalar Distance(const SkPoint& a, const SkPoint& b)
#In Property
#Line # returns straight-line distance between points ##
#Populate

#Example
#Height 192
    SkPaint paint;
    paint.setAntiAlias(true);
    const SkPoint lines[][2] = {{{-10, -10}, {90, 30}}, {{0, 0}, {150, 30}}, {{10, 25}, {120, 150}}};
    const SkPoint origin = {30, 160};
    for (auto line : lines) {
        SkPoint a = origin + line[0];
        const SkPoint& b = line[1];
        canvas->drawLine(a, b, paint);
        SkAutoCanvasRestore acr(canvas, true);
        SkScalar angle = SkScalarATan2((b.fY - a.fY), b.fX - a.fX);
        canvas->rotate(angle * 180 / SK_ScalarPI, a.fX, a.fY);
        SkString distance("distance = ");
        distance.appendScalar(SkPoint::Distance(a, b));
        canvas->drawString(distance, a.fX + 25, a.fY - 4, paint);
    }
##

#SeeAlso length() setLength

#Method ##

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

#Method static SkScalar DotProduct(const SkVector& a, const SkVector& b)
#In Operators
#Line # returns dot product ##
#Populate

#Example
    SkPaint paint;
    paint.setAntiAlias(true);
    SkVector vectors[][2] = {{{50, 2}, {-14, 20}}, {{0, 50}, {-50, 0}}, {{-20, 25}, {25, -20}},
                             {{-20, -24}, {-24, -20}}};
    SkPoint center[] = {{32, 32}, {160, 32}, {32, 160}, {160, 160}};
    paint.setStrokeWidth(2);
    for (size_t i = 0; i < 4; ++i) {
        canvas->drawLine(center[i], center[i] + vectors[i][0], paint);
        canvas->drawLine(center[i], center[i] + vectors[i][1], paint);
        SkString str;
        str.printf("dot = %g", SkPoint::DotProduct(vectors[i][0], vectors[i][1]));
        canvas->drawString(str, center[i].fX, center[i].fY, paint);
    }
##

#SeeAlso dot CrossProduct

#Method ##

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

#Method static SkScalar CrossProduct(const SkVector& a, const SkVector& b)
#In Operators
#Line # returns cross product ##
#Populate

#Example
    SkPaint paint;
    paint.setAntiAlias(true);
    SkVector vectors[][2] = {{{50, 2}, {-14, 20}}, {{0, 50}, {-50, 0}}, {{-20, 25}, {25, -20}},
                             {{-20, -24}, {-24, -20}}};
    SkPoint center[] = {{32, 32}, {160, 32}, {32, 160}, {160, 160}};
    paint.setStrokeWidth(2);
    for (size_t i = 0; i < 4; ++i) {
        paint.setColor(SK_ColorRED);
        canvas->drawLine(center[i], center[i] + vectors[i][0], paint);
        paint.setColor(SK_ColorBLUE);
        canvas->drawLine(center[i], center[i] + vectors[i][1], paint);
        SkString str;
        SkScalar cross = SkPoint::CrossProduct(vectors[i][1], vectors[i][0]);
        str.printf("cross = %g", cross);
        paint.setColor(cross >= 0 ? SK_ColorRED : SK_ColorBLUE);
        canvas->drawString(str, center[i].fX, center[i].fY, paint);
    }
##

#SeeAlso cross DotProduct

#Method ##

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

#Method SkScalar cross(const SkVector& vec) const
#In Operators
#Line # returns cross product ##
#Populate

#Example
    SkPaint paint;
    paint.setAntiAlias(true);
    SkVector vectors[][2] = {{{50, 2}, {-14, 20}}, {{0, 50}, {-50, 0}}, {{-20, 25}, {25, -20}},
                             {{-20, -24}, {-24, -20}}};
    SkPoint center[] = {{32, 32}, {160, 32}, {32, 160}, {160, 160}};
    paint.setStrokeWidth(2);
    for (size_t i = 0; i < 4; ++i) {
        paint.setColor(SK_ColorRED);
        canvas->drawLine(center[i], center[i] + vectors[i][0], paint);
        paint.setColor(SK_ColorBLUE);
        canvas->drawLine(center[i], center[i] + vectors[i][1], paint);
        SkString str;
        SkScalar cross = vectors[i][0].cross(vectors[i][1]);
        str.printf("cross = %g", cross);
        paint.setColor(cross >= 0 ? SK_ColorRED : SK_ColorBLUE);
        canvas->drawString(str, center[i].fX, center[i].fY, paint);
    }
##

#SeeAlso CrossProduct dot

#Method ##

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

#Method SkScalar dot(const SkVector& vec) const
#In Operators
#Line # returns dot product ##
#Populate

#Example
    SkPaint paint;
    paint.setAntiAlias(true);
    SkVector vectors[][2] = {{{50, 2}, {-14, 20}}, {{0, 50}, {-50, 0}}, {{-20, 25}, {25, -20}},
                             {{-20, -24}, {-24, -20}}};
    SkPoint center[] = {{32, 32}, {160, 32}, {32, 160}, {160, 160}};
    paint.setStrokeWidth(2);
    for (size_t i = 0; i < 4; ++i) {
        canvas->drawLine(center[i], center[i] + vectors[i][0], paint);
        canvas->drawLine(center[i], center[i] + vectors[i][1], paint);
        SkString str;
        str.printf("dot = %g", vectors[i][0].dot(vectors[i][1]));
        canvas->drawString(str, center[i].fX, center[i].fY, paint);
    }
##

#SeeAlso DotProduct cross

#Method ##

#Struct SkPoint ##


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

#Subtopic Vector
#Line # alias for Point ##
    #Alias Vector ##
    #Alias Vectors ##
    #Typedef SkPoint SkVector
    #Line # alias for Point ##
    #Code
    typedef SkPoint SkVector;
    ##
    SkVector provides an alternative name for SkPoint. SkVector and SkPoint can
    be used interchangeably for all purposes.
    #Typedef ##
##

#Topic Point ##