Stub for conic section max curvature
BUG=skia: R=reed@google.com Author: humper@google.com Review URL: https://codereview.chromium.org/175193003 git-svn-id: http://skia.googlecode.com/svn/trunk@13542 2bbb7eff-a529-9590-31e7-b0007b416f81
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@ -255,6 +255,15 @@ struct SkConic {
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void computeTightBounds(SkRect* bounds) const;
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void computeFastBounds(SkRect* bounds) const;
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/** Find the parameter value where the conic takes on its maximum curvature.
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*
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* @param t output scalar for max curvature. Will be unchanged if
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* max curvature outside 0..1 range.
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*
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* @return true if max curvature found inside 0..1 range, false otherwise
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*/
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bool findMaxCurvature(SkScalar* t) const;
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};
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#include "SkTemplates.h"
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@ -8,7 +8,9 @@
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#include "SkGeometry.h"
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#include "SkMatrix.h"
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bool SkXRayCrossesLine(const SkXRay& pt, const SkPoint pts[2], bool* ambiguous) {
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bool SkXRayCrossesLine(const SkXRay& pt,
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const SkPoint pts[2],
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bool* ambiguous) {
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if (ambiguous) {
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*ambiguous = false;
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}
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@ -574,8 +576,8 @@ static void flatten_double_cubic_extrema(SkScalar coords[14]) {
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}
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/** Given 4 points on a cubic bezier, chop it into 1, 2, 3 beziers such that
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the resulting beziers are monotonic in Y. This is called by the scan converter.
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Depending on what is returned, dst[] is treated as follows
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the resulting beziers are monotonic in Y. This is called by the scan
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converter. Depending on what is returned, dst[] is treated as follows:
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0 dst[0..3] is the original cubic
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1 dst[0..3] and dst[3..6] are the two new cubics
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2 dst[0..3], dst[3..6], dst[6..9] are the three new cubics
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@ -632,7 +634,10 @@ int SkFindCubicInflections(const SkPoint src[4], SkScalar tValues[]) {
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SkScalar Cx = src[3].fX + 3 * (src[1].fX - src[2].fX) - src[0].fX;
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SkScalar Cy = src[3].fY + 3 * (src[1].fY - src[2].fY) - src[0].fY;
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return SkFindUnitQuadRoots(Bx*Cy - By*Cx, Ax*Cy - Ay*Cx, Ax*By - Ay*Bx, tValues);
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return SkFindUnitQuadRoots(Bx*Cy - By*Cx,
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Ax*Cy - Ay*Cx,
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Ax*By - Ay*Bx,
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tValues);
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}
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int SkChopCubicAtInflections(const SkPoint src[], SkPoint dst[10]) {
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@ -963,7 +968,9 @@ bool SkXRayCrossesMonotonicCubic(const SkXRay& pt, const SkPoint cubic[4],
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return false;
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}
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int SkNumXRayCrossingsForCubic(const SkXRay& pt, const SkPoint cubic[4], bool* ambiguous) {
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int SkNumXRayCrossingsForCubic(const SkXRay& pt,
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const SkPoint cubic[4],
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bool* ambiguous) {
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int num_crossings = 0;
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SkPoint monotonic_cubics[10];
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int num_monotonic_cubics = SkChopCubicAtYExtrema(cubic, monotonic_cubics);
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@ -971,19 +978,25 @@ int SkNumXRayCrossingsForCubic(const SkXRay& pt, const SkPoint cubic[4], bool* a
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*ambiguous = false;
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}
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bool locally_ambiguous;
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if (SkXRayCrossesMonotonicCubic(pt, &monotonic_cubics[0], &locally_ambiguous))
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if (SkXRayCrossesMonotonicCubic(pt,
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&monotonic_cubics[0],
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&locally_ambiguous))
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++num_crossings;
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if (ambiguous) {
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*ambiguous |= locally_ambiguous;
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}
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if (num_monotonic_cubics > 0)
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if (SkXRayCrossesMonotonicCubic(pt, &monotonic_cubics[3], &locally_ambiguous))
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if (SkXRayCrossesMonotonicCubic(pt,
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&monotonic_cubics[3],
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&locally_ambiguous))
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++num_crossings;
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if (ambiguous) {
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*ambiguous |= locally_ambiguous;
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}
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if (num_monotonic_cubics > 1)
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if (SkXRayCrossesMonotonicCubic(pt, &monotonic_cubics[6], &locally_ambiguous))
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if (SkXRayCrossesMonotonicCubic(pt,
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&monotonic_cubics[6],
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&locally_ambiguous))
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++num_crossings;
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if (ambiguous) {
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*ambiguous |= locally_ambiguous;
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@ -1063,9 +1076,10 @@ static bool truncate_last_curve(const SkPoint quad[3], SkScalar x, SkScalar y,
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static const SkPoint gQuadCirclePts[kSkBuildQuadArcStorage] = {
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// The mid point of the quadratic arc approximation is half way between the two
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// control points. The float epsilon adjustment moves the on curve point out by
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// two bits, distributing the convex test error between the round rect approximation
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// and the convex cross product sign equality test.
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#define SK_MID_RRECT_OFFSET (SK_Scalar1 + SK_ScalarTanPIOver8 + FLT_EPSILON * 4) / 2
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// two bits, distributing the convex test error between the round rect
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// approximation and the convex cross product sign equality test.
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#define SK_MID_RRECT_OFFSET \
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(SK_Scalar1 + SK_ScalarTanPIOver8 + FLT_EPSILON * 4) / 2
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{ SK_Scalar1, 0 },
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{ SK_Scalar1, SK_ScalarTanPIOver8 },
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{ SK_MID_RRECT_OFFSET, SK_MID_RRECT_OFFSET },
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@ -1162,8 +1176,16 @@ int SkBuildQuadArc(const SkVector& uStart, const SkVector& uStop,
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return pointCount;
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}
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///////////////////////////////////////////////////////////////////////////////
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///////////////////////////////////////////////////////////////////////////////
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//
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// NURB representation for conics. Helpful explanations at:
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//
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// http://citeseerx.ist.psu.edu/viewdoc/
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// download?doi=10.1.1.44.5740&rep=rep1&type=ps
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// and
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// http://www.cs.mtu.edu/~shene/COURSES/cs3621/NOTES/spline/NURBS/RB-conics.html
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//
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// F = (A (1 - t)^2 + C t^2 + 2 B (1 - t) t w)
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// ------------------------------------------
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// ((1 - t)^2 + t^2 + 2 (1 - t) t w)
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@ -1173,12 +1195,6 @@ int SkBuildQuadArc(const SkVector& uStart, const SkVector& uStop,
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// {t^2 (2 - 2 w), t (-2 + 2 w), 1}
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//
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// Take the parametric specification for the conic (either X or Y) and return
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// in coeff[] the coefficients for the simple quadratic polynomial
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// coeff[0] for t^2
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// coeff[1] for t
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// coeff[2] for constant term
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//
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static SkScalar conic_eval_pos(const SkScalar src[], SkScalar w, SkScalar t) {
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SkASSERT(src);
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SkASSERT(t >= 0 && t <= SK_Scalar1);
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@ -1210,7 +1226,9 @@ static SkScalar conic_eval_pos(const SkScalar src[], SkScalar w, SkScalar t) {
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// coeff[1] for t^1
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// coeff[2] for t^0
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//
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static void conic_deriv_coeff(const SkScalar src[], SkScalar w, SkScalar coeff[3]) {
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static void conic_deriv_coeff(const SkScalar src[],
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SkScalar w,
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SkScalar coeff[3]) {
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const SkScalar P20 = src[4] - src[0];
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const SkScalar P10 = src[2] - src[0];
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const SkScalar wP10 = w * P10;
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@ -1300,7 +1318,8 @@ void SkConic::chopAt(SkScalar t, SkConic dst[2]) const {
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// or
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// w1 /= sqrt(w0*w2)
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//
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// However, in our case, we know that for dst[0], w0 == 1, and for dst[1], w2 == 1
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// However, in our case, we know that for dst[0]:
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// w0 == 1, and for dst[1], w2 == 1
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//
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SkScalar root = SkScalarSqrt(tmp2[1].fZ);
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dst[0].fW = tmp2[0].fZ / root;
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@ -1442,3 +1461,8 @@ void SkConic::computeTightBounds(SkRect* bounds) const {
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void SkConic::computeFastBounds(SkRect* bounds) const {
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bounds->set(fPts, 3);
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}
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bool SkConic::findMaxCurvature(SkScalar* t) const {
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// TODO: Implement me
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return false;
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}
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