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Unified Diff: src/gpu/GrPathUtils.cpp

Issue 22900007: Add direct bezier cubic support for GPU shaders (Closed) Base URL: https://skia.googlecode.com/svn/trunk
Patch Set: Created 7 years, 4 months ago
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Index: src/gpu/GrPathUtils.cpp
diff --git a/src/gpu/GrPathUtils.cpp b/src/gpu/GrPathUtils.cpp
index 2d853883d74dd93e19304e803e6b3a1e0501d116..ca878338d343de97e680dd08289ebb3a66dfca5f 100644
--- a/src/gpu/GrPathUtils.cpp
+++ b/src/gpu/GrPathUtils.cpp
@@ -476,3 +476,332 @@ void GrPathUtils::convertCubicToQuads(const GrPoint p[4],
}
}
+
+////////////////////////////////////////////////////////////////////////////////
+
+enum CubicType {
+ kSerpentine_CubicType,
+ kCusp_CubicType,
+ kLoop_CubicType,
+ kQuadratic_CubicType,
+ kLine_CubicType,
+ kPoint_CubicType
+};
+
+// discr(I) = d0^2 * (3*d1^2 - 4*d0*d2)
+// Classification:
+// discr(I) > 0 Serpentine
+// discr(I) = 0 Cusp
+// discr(I) < 0 Loop
+// d0 = d1 = 0 Quadratic
+// d0 = d1 = d2 = 0 Line
+// p0 = p1 = p2 = p3 Point
+static CubicType classify_cubic(const SkPoint p[4], const SkScalar d[3]) {
+ if (p[0] == p[1] && p[0] == p[2] && p[0] == p[3]) {
+ return kPoint_CubicType;
+ }
+ const SkScalar discr = d[0] * d[0] * (3.f * d[1] * d[1] - 4.f * d[0] * d[2]);
+ if (discr > SK_ScalarNearlyZero) {
+ return kSerpentine_CubicType;
+ } else if (discr < -SK_ScalarNearlyZero) {
+ return kLoop_CubicType;
+ } else {
+ if (0.f == d[0] && 0.f == d[1]) {
+ return (0.f == d[2] ? kLine_CubicType : kQuadratic_CubicType);
+ } else {
+ return kCusp_CubicType;
+ }
+ }
+}
+
+// Assumes the third component of points is 1.
+// Calcs p0 . (p1 x p2)
+static SkScalar calc_dot_cross_cubic(const SkPoint& p0, const SkPoint& p1, const SkPoint& p2) {
+ const SkScalar xComp = p0.fX * (p1.fY - p2.fY);
+ const SkScalar yComp = p0.fY * (p2.fX - p1.fX);
+ const SkScalar wComp = p1.fX * p2.fY - p1.fY * p2.fX;
+ return (xComp + yComp + wComp);
+}
+
+// Solves linear system to extract klm
+// P.K = k (similarly for l, m)
+// Where P is matrix of control points
+// K is coefficients for the line K
+// k is vector of values of K evaluated at the control points
+// Solving for K, thus K = P^(-1) . k
+static void calc_cubic_klm(const SkPoint p[4], const SkScalar controlK[4],
+ const SkScalar controlL[4], const SkScalar controlM[4],
+ SkScalar k[3], SkScalar l[3], SkScalar m[3]) {
+ SkMatrix matrix;
+ matrix.setAll(p[0].fX, p[0].fY, 1.f,
+ p[1].fX, p[1].fY, 1.f,
+ p[2].fX, p[2].fY, 1.f);
+ SkMatrix inverse;
+ if (matrix.invert(&inverse)) {
+ inverse.mapHomogeneousPoints(k, controlK, 1);
+ inverse.mapHomogeneousPoints(l, controlL, 1);
+ inverse.mapHomogeneousPoints(m, controlM, 1);
+ }
+
+}
+
+static void set_serp_klm(const SkScalar d[3], SkScalar k[4], SkScalar l[4], SkScalar m[4]) {
+ SkScalar tempSqrt = SkScalarSqrt(9.f * d[1] * d[1] - 12.f * d[0] * d[2]);
+ SkScalar ls = 3.f * d[1] - tempSqrt;
+ SkScalar lt = 6.f * d[0];
+ SkScalar ms = 3.f * d[1] + tempSqrt;
+ SkScalar mt = 6.f * d[0];
+
+ k[0] = ls * ms;
+ k[1] = (3.f * ls * ms - ls * mt - lt * ms) / 3.f;
+ k[2] = (lt * (mt - 2.f * ms) + ls * (3.f * ms - 2.f * mt)) / 3.f;
+ k[3] = (lt - ls) * (mt - ms);
+
+ l[0] = ls * ls * ls;
+ const SkScalar lt_ls = lt - ls;
+ l[1] = ls * ls * lt_ls * -1.f;
+ l[2] = lt_ls * lt_ls * ls;
+ l[3] = -1.f * lt_ls * lt_ls * lt_ls;
+
+ m[0] = ms * ms * ms;
+ const SkScalar mt_ms = mt - ms;
+ m[1] = ms * ms * mt_ms * -1.f;
+ m[2] = mt_ms * mt_ms * ms;
+ m[3] = -1.f * mt_ms * mt_ms * mt_ms;
+
+ // If d0 < 0 we need to flip the orientation of our curve
+ // This is done by negating the k and l values
+ // We want negative distance values to be on the inside
+ if ( d[0] > 0) {
+ for (int i = 0; i < 4; ++i) {
+ k[i] = -k[i];
+ l[i] = -l[i];
+ }
+ }
+}
+
+static void set_loop_klm(const SkScalar d[3], SkScalar k[4], SkScalar l[4], SkScalar m[4]) {
+ SkScalar tempSqrt = SkScalarSqrt(4.f * d[0] * d[2] - 3.f * d[1] * d[1]);
+ SkScalar ls = d[1] - tempSqrt;
+ SkScalar lt = 2.f * d[0];
+ SkScalar ms = d[1] + tempSqrt;
+ SkScalar mt = 2.f * d[0];
+
+ k[0] = ls * ms;
+ k[1] = (3.f * ls*ms - ls * mt - lt * ms) / 3.f;
+ k[2] = (lt * (mt - 2.f * ms) + ls * (3.f * ms - 2.f * mt)) / 3.f;
+ k[3] = (lt - ls) * (mt - ms);
+
+ l[0] = ls * ls * ms;
+ l[1] = (ls * (ls * (mt - 3.f * ms) + 2.f * lt * ms))/-3.f;
+ l[2] = ((lt - ls) * (ls * (2.f * mt - 3.f * ms) + lt * ms))/3.f;
+ l[3] = -1.f * (lt - ls) * (lt - ls) * (mt - ms);
+
+ m[0] = ls * ms * ms;
+ m[1] = (ms * (ls * (2.f * mt - 3.f * ms) + lt * ms))/-3.f;
+ m[2] = ((mt - ms) * (ls * (mt - 3.f * ms) + 2.f * lt * ms))/3.f;
+ m[3] = -1.f * (lt - ls) * (mt - ms) * (mt - ms);
+
+
+ // If (d0 < 0 && sign(k1) > 0) || (d0 > 0 && sign(k1) < 0),
+ // we need to flip the orientation of our curve.
+ // This is done by negating the k and l values
+ if ( (d[0] < 0 && k[1] < 0) || (d[0] > 0 && k[1] > 0)) {
+ for (int i = 0; i < 4; ++i) {
+ k[i] = -k[i];
+ l[i] = -l[i];
+ }
+ }
+}
+
+static void set_cusp_klm(const SkScalar d[3], SkScalar k[4], SkScalar l[4], SkScalar m[4]) {
+ const SkScalar ls = d[2];
+ const SkScalar lt = 3.f * d[1];
+
+ k[0] = ls;
+ k[1] = ls - lt / 3.f;
+ k[2] = ls - 2.f * lt / 3.f;
+ k[3] = ls - lt;
+
+ l[0] = ls * ls * ls;
+ const SkScalar ls_lt = ls - lt;
+ l[1] = ls * ls * ls_lt;
+ l[2] = ls_lt * ls_lt * ls;
+ l[3] = ls_lt * ls_lt * ls_lt;
+
+ m[0] = 1.f;
+ m[1] = 1.f;
+ m[2] = 1.f;
+ m[3] = 1.f;
+}
+
+// For the case when a cubic is actually a quadratic
+// M =
+// 0 0 0
+// 1/3 0 1/3
+// 2/3 1/3 2/3
+// 1 1 1
+static void set_quadratic_klm(const SkScalar d[3], SkScalar k[4], SkScalar l[4], SkScalar m[4]) {
+ k[0] = 0.f;
+ k[1] = 1.f/3.f;
+ k[2] = 2.f/3.f;
+ k[3] = 1.f;
+
+ l[0] = 0.f;
+ l[1] = 0.f;
+ l[2] = 1.f/3.f;
+ l[3] = 1.f;
+
+ m[0] = 0.f;
+ m[1] = 1.f/3.f;
+ m[2] = 2.f/3.f;
+ m[3] = 1.f;
+
+ // If d2 < 0 we need to flip the orientation of our curve
+ // This is done by negating the k and l values
+ if ( d[2] > 0) {
+ for (int i = 0; i < 4; ++i) {
+ k[i] = -k[i];
+ l[i] = -l[i];
+ }
+ }
+}
+
+// Calc coefficients of I(s,t) where roots of I are inflection points of curve
+// I(s,t) = t*(3*d0*s^2 - 3*d1*s*t + d2*t^2)
+// d0 = a1 - 2*a2+3*a3
+// d1 = -a2 + 3*a3
+// d2 = 3*a3
+// a1 = p0 . (p3 x p2)
+// a2 = p1 . (p0 x p3)
+// a3 = p2 . (p1 x p0)
+// Places the values of d1, d2, d3 in array d passed in
+static void calc_cubic_inflection_func(const SkPoint p[4], SkScalar d[3]) {
+ SkScalar a1 = calc_dot_cross_cubic(p[0], p[3], p[2]);
+ SkScalar a2 = calc_dot_cross_cubic(p[1], p[0], p[3]);
+ SkScalar a3 = calc_dot_cross_cubic(p[2], p[1], p[0]);
+
+ // need to scale a's or values in later calculations will grow to high
+ SkScalar max = SkScalarAbs(a1);
+ max = SkMaxScalar(max, SkScalarAbs(a2));
+ max = SkMaxScalar(max, SkScalarAbs(a3));
+ max = 1.f/max;
+ a1 = a1 * max;
+ a2 = a2 * max;
+ a3 = a3 * max;
+
+ d[2] = 3.f * a3;
+ d[1] = d[2] - a2;
+ d[0] = d[1] - a2 + a1;
+}
+
+int GrPathUtils::chopCubicAtLoopIntersection(const SkPoint src[4], SkPoint dst[10], SkScalar klm[9],
+ SkScalar klm_rev[3]) {
+ // Variable to store the two parametric values at the loop double point
+ SkScalar smallS = 0.f;
+ SkScalar largeS = 0.f;
+
+ SkScalar d[3];
+ calc_cubic_inflection_func(src, d);
+
+ CubicType cType = classify_cubic(src, d);
+
+ int chop_count = 0;
+ if (kLoop_CubicType == cType) {
+ SkScalar tempSqrt = SkScalarSqrt(4.f * d[0] * d[2] - 3.f * d[1] * d[1]);
+ SkScalar ls = d[1] - tempSqrt;
+ SkScalar lt = 2.f * d[0];
+ SkScalar ms = d[1] + tempSqrt;
+ SkScalar mt = 2.f * d[0];
+ ls = ls / lt;
+ ms = ms / mt;
+ // need to have t values sorted since this is what is expected by SkChopCubicAt
+ if (ls <= ms) {
+ smallS = ls;
+ largeS = ms;
+ } else {
+ smallS = ms;
+ largeS = ls;
+ }
+
+ SkScalar chop_ts[2];
+ if (smallS > 0.f && smallS < 1.f) {
+ chop_ts[chop_count++] = smallS;
+ }
+ if (largeS > 0.f && largeS < 1.f) {
+ chop_ts[chop_count++] = largeS;
+ }
+ if(dst) {
+ SkChopCubicAt(src, dst, chop_ts, chop_count);
+ }
+ } else {
+ if (dst) {
+ memcpy(dst, src, sizeof(SkPoint) * 4);
+ }
+ }
+
+ if (klm && klm_rev) {
+ // Set klm_rev to to match the sub_section of cubic that needs to have its orientation
+ // flipped. This will always be the section that is the "loop"
+ if (2 == chop_count) {
+ klm_rev[0] = 1.f;
+ klm_rev[1] = -1.f;
+ klm_rev[2] = 1.f;
+ } else if (1 == chop_count) {
+ if (smallS < 0.f) {
+ klm_rev[0] = -1.f;
+ klm_rev[1] = 1.f;
+ } else {
+ klm_rev[0] = 1.f;
+ klm_rev[1] = -1.f;
+ }
+ } else {
+ if (smallS < 0.f && largeS > 1.f) {
+ klm_rev[0] = -1.f;
+ } else {
+ klm_rev[0] = 1.f;
+ }
+ }
+ SkScalar controlK[4];
+ SkScalar controlL[4];
+ SkScalar controlM[4];
+
+ if (kSerpentine_CubicType == cType || (kCusp_CubicType == cType && 0.f != d[0])) {
+ set_serp_klm(d, controlK, controlL, controlM);
+ } else if (kLoop_CubicType == cType) {
+ set_loop_klm(d, controlK, controlL, controlM);
+ } else if (kCusp_CubicType == cType) {
+ SkASSERT(0.f == d[0]);
+ set_cusp_klm(d, controlK, controlL, controlM);
+ } else if (kQuadratic_CubicType == cType) {
+ set_quadratic_klm(d, controlK, controlL, controlM);
+ }
+
+ calc_cubic_klm(src, controlK, controlL, controlM, klm, &klm[3], &klm[6]);
+ }
+ return chop_count + 1;
+}
+
+void GrPathUtils::getCubicKLM(const SkPoint p[4], SkScalar klm[9]) {
+ SkScalar d[3];
+ calc_cubic_inflection_func(p, d);
+
+ CubicType cType = classify_cubic(p, d);
+
+ SkScalar controlK[4];
+ SkScalar controlL[4];
+ SkScalar controlM[4];
+
+ if (kSerpentine_CubicType == cType || (kCusp_CubicType == cType && 0.f != d[0])) {
+ set_serp_klm(d, controlK, controlL, controlM);
+ } else if (kLoop_CubicType == cType) {
+ set_loop_klm(d, controlK, controlL, controlM);
+ } else if (kCusp_CubicType == cType) {
+ SkASSERT(0.f == d[0]);
+ set_cusp_klm(d, controlK, controlL, controlM);
+ } else if (kQuadratic_CubicType == cType) {
+ set_quadratic_klm(d, controlK, controlL, controlM);
+ }
+
+ calc_cubic_klm(p, controlK, controlL, controlM, klm, &klm[3], &klm[6]);
+}
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