ccpr: Clean up GrCCGeometry
Gets rid of the ugly template functions, rearranges a few static
methods, and adds a benchmark.
Bug: skia:
Change-Id: I442f3a581ba7faf7601ae5be0c7e07327df09496
Reviewed-on: https://skia-review.googlesource.com/122128
Reviewed-by: Brian Salomon <bsalomon@google.com>
Commit-Queue: Chris Dalton <csmartdalton@google.com>
diff --git a/src/gpu/ccpr/GrCCGeometry.cpp b/src/gpu/ccpr/GrCCGeometry.cpp
index 302cfe2..2593273 100644
--- a/src/gpu/ccpr/GrCCGeometry.cpp
+++ b/src/gpu/ccpr/GrCCGeometry.cpp
@@ -144,17 +144,16 @@
return;
}
- this->appendMonotonicQuadratics(p0, p1, p2);
+ this->appendQuadratics(p0, p1, p2);
}
-inline void GrCCGeometry::appendMonotonicQuadratics(const Sk2f& p0, const Sk2f& p1,
- const Sk2f& p2) {
+inline void GrCCGeometry::appendQuadratics(const Sk2f& p0, const Sk2f& p1, const Sk2f& p2) {
Sk2f tan0 = p1 - p0;
Sk2f tan1 = p2 - p1;
// This should almost always be this case for well-behaved curves in the real world.
if (is_convex_curve_monotonic(p0, tan0, p2, tan1)) {
- this->appendSingleMonotonicQuadratic(p0, p1, p2);
+ this->appendMonotonicQuadratic(p0, p1, p2);
return;
}
@@ -182,38 +181,68 @@
Sk2f p12 = SkNx_fma(t, tan1, p1);
Sk2f p012 = lerp(p01, p12, t);
- this->appendSingleMonotonicQuadratic(p0, p01, p012);
- this->appendSingleMonotonicQuadratic(p012, p12, p2);
+ this->appendMonotonicQuadratic(p0, p01, p012);
+ this->appendMonotonicQuadratic(p012, p12, p2);
}
-inline void GrCCGeometry::appendSingleMonotonicQuadratic(const Sk2f& p0, const Sk2f& p1,
- const Sk2f& p2) {
- SkASSERT(fPoints.back() == SkPoint::Make(p0[0], p0[1]));
-
+inline void GrCCGeometry::appendMonotonicQuadratic(const Sk2f& p0, const Sk2f& p1, const Sk2f& p2) {
// Don't send curves to the GPU if we know they are nearly flat (or just very small).
if (are_collinear(p0, p1, p2)) {
+ SkASSERT(fPoints.back() == SkPoint::Make(p0[0], p0[1]));
this->appendLine(p2);
return;
}
+ SkASSERT(fPoints.back() == SkPoint::Make(p0[0], p0[1]));
p1.store(&fPoints.push_back());
p2.store(&fPoints.push_back());
fVerbs.push_back(Verb::kMonotonicQuadraticTo);
++fCurrContourTallies.fQuadratics;
}
+static inline Sk2f first_unless_nearly_zero(const Sk2f& a, const Sk2f& b) {
+ Sk2f aa = a*a;
+ aa += SkNx_shuffle<1,0>(aa);
+ SkASSERT(aa[0] == aa[1]);
+
+ Sk2f bb = b*b;
+ bb += SkNx_shuffle<1,0>(bb);
+ SkASSERT(bb[0] == bb[1]);
+
+ return (aa > bb * SK_ScalarNearlyZero).thenElse(a, b);
+}
+
+static inline void get_cubic_tangents(const Sk2f& p0, const Sk2f& p1, const Sk2f& p2,
+ const Sk2f& p3, Sk2f* tan0, Sk2f* tan1) {
+ *tan0 = first_unless_nearly_zero(p1 - p0, p2 - p0);
+ *tan1 = first_unless_nearly_zero(p3 - p2, p3 - p1);
+}
+
+static inline bool is_cubic_nearly_quadratic(const Sk2f& p0, const Sk2f& p1, const Sk2f& p2,
+ const Sk2f& p3, const Sk2f& tan0, const Sk2f& tan1,
+ Sk2f* c) {
+ Sk2f c1 = SkNx_fma(Sk2f(1.5f), tan0, p0);
+ Sk2f c2 = SkNx_fma(Sk2f(-1.5f), tan1, p3);
+ *c = (c1 + c2) * .5f; // Hopefully optimized out if not used?
+ return ((c1 - c2).abs() <= 1).allTrue();
+}
+
using ExcludedTerm = GrPathUtils::ExcludedTerm;
-// Calculates the padding to apply around inflection points, in homogeneous parametric coordinates.
+// Finds where to chop a non-loop around its inflection points. The resulting cubic segments will be
+// chopped such that a box of radius 'padRadius', centered at any point along the curve segment, is
+// guaranteed to not cross the tangent lines at the inflection points (a.k.a lines L & M).
//
-// More specifically, if the inflection point lies at C(t/s), then C((t +/- returnValue) / s) will
-// be the two points on the curve at which a square box with radius "padRadius" will have a corner
-// that touches the inflection point's tangent line.
+// 'chops' will be filled with 4 T values. The segments between T0..T1 and T2..T3 must be drawn with
+// flat lines instead of cubics.
//
// A serpentine cubic has two inflection points, so this method takes Sk2f and computes the padding
// for both in SIMD.
-static inline Sk2f calc_inflect_homogeneous_padding(float padRadius, const Sk2f& t, const Sk2f& s,
- const SkMatrix& CIT, ExcludedTerm skipTerm) {
+static inline void find_chops_around_inflection_points(float padRadius, const Sk2f& t,
+ const Sk2f& s, const SkMatrix& CIT,
+ ExcludedTerm skipTerm,
+ SkSTArray<4, float>* chops) {
+ SkASSERT(chops->empty());
SkASSERT(padRadius >= 0);
Sk2f Clx = s*s*s;
@@ -222,13 +251,13 @@
Sk2f Lx = CIT[0] * Clx + CIT[3] * Cly;
Sk2f Ly = CIT[1] * Clx + CIT[4] * Cly;
- float ret[2];
- Sk2f bloat = padRadius * (Lx.abs() + Ly.abs());
- (bloat * s >= 0).thenElse(bloat, -bloat).store(ret);
+ Sk2f pad = padRadius * (Lx.abs() + Ly.abs());
+ pad = (pad * s >= 0).thenElse(pad, -pad);
+ pad = Sk2f(std::cbrt(pad[0]), std::cbrt(pad[1]));
- ret[0] = cbrtf(ret[0]);
- ret[1] = cbrtf(ret[1]);
- return Sk2f::Load(ret);
+ Sk2f leftT = (t - pad) / s;
+ Sk2f rightT = (t + pad) / s;
+ Sk2f::Store2(chops->push_back_n(4), leftT, rightT);
}
static inline void swap_if_greater(float& a, float& b) {
@@ -237,22 +266,23 @@
}
}
-// Calculates all parameter values for a loop at which points a square box with radius "padRadius"
-// will have a corner that touches a tangent line from the intersection.
+// Finds where to chop a non-loop around its intersection point. The resulting cubic segments will
+// be chopped such that a box of radius 'padRadius', centered at any point along the curve segment,
+// is guaranteed to not cross the tangent lines at the intersection point (a.k.a lines L & M).
//
-// T2 must contain the lesser parameter value of the loop intersection in its first component, and
-// the greater in its second.
+// 'chops' will be filled with 0, 2, or 4 T values. The segments between T0..T1 and T2..T3 must be
+// drawn with quadratic splines instead of cubics.
//
-// roots[0] will be filled with 1 or 3 sorted parameter values, representing the padding points
-// around the first tangent. roots[1] will be filled with the padding points for the second tangent.
-static inline void calc_loop_intersect_padding_pts(float padRadius, const Sk2f& T2,
- const SkMatrix& CIT, ExcludedTerm skipTerm,
- SkSTArray<3, float, true> roots[2]) {
+// A loop intersection falls at two different T values, so this method takes Sk2f and computes the
+// padding for both in SIMD.
+static inline void find_chops_around_loop_intersection(float padRadius, const Sk2f& t,
+ const Sk2f& s, const SkMatrix& CIT,
+ ExcludedTerm skipTerm,
+ SkSTArray<4, float>* chops) {
+ SkASSERT(chops->empty());
SkASSERT(padRadius >= 0);
- SkASSERT(T2[0] <= T2[1]);
- SkASSERT(roots[0].empty());
- SkASSERT(roots[1].empty());
+ Sk2f T2 = t/s;
Sk2f T1 = SkNx_shuffle<1,0>(T2);
Sk2f Cl = (ExcludedTerm::kLinearTerm == skipTerm) ? T2*-2 - T1 : T2*T2 + T2*T1*2;
Sk2f Lx = Cl * CIT[3] + CIT[0];
@@ -286,47 +316,197 @@
for (int i = 0; i < 2; ++i) {
if (1 == numRoots[i]) {
+ // When there is only one root, line L chops from root..1, line M chops from 0..root.
+ if (1 == i) {
+ chops->push_back(0);
+ }
float A = cbrtf(R[i]);
float B = A != 0 ? QQ[i]/A : 0;
- roots[i].push_back(A + B + D[i]);
+ chops->push_back(A + B + D[i]);
+ if (0 == i) {
+ chops->push_back(1);
+ }
continue;
}
static constexpr float k2PiOver3 = 2 * SK_ScalarPI / 3;
float theta = std::acos(cosTheta3[i]) * (1.f/3);
- roots[i].push_back(P[i] * std::cos(theta) + D[i]);
- roots[i].push_back(P[i] * std::cos(theta + k2PiOver3) + D[i]);
- roots[i].push_back(P[i] * std::cos(theta - k2PiOver3) + D[i]);
+ float roots[3] = {P[i] * std::cos(theta) + D[i],
+ P[i] * std::cos(theta + k2PiOver3) + D[i],
+ P[i] * std::cos(theta - k2PiOver3) + D[i]};
// Sort the three roots.
- swap_if_greater(roots[i][0], roots[i][1]);
- swap_if_greater(roots[i][1], roots[i][2]);
- swap_if_greater(roots[i][0], roots[i][1]);
+ swap_if_greater(roots[0], roots[1]);
+ swap_if_greater(roots[1], roots[2]);
+ swap_if_greater(roots[0], roots[1]);
+
+ // Line L chops around the first 2 roots, line M chops around the second 2.
+ chops->push_back_n(2, &roots[i]);
}
}
-static inline Sk2f first_unless_nearly_zero(const Sk2f& a, const Sk2f& b) {
- Sk2f aa = a*a;
- aa += SkNx_shuffle<1,0>(aa);
- SkASSERT(aa[0] == aa[1]);
+void GrCCGeometry::cubicTo(const SkPoint P[4], float inflectPad, float loopIntersectPad) {
+ SkASSERT(fBuildingContour);
+ SkASSERT(P[0] == fPoints.back());
- Sk2f bb = b*b;
- bb += SkNx_shuffle<1,0>(bb);
- SkASSERT(bb[0] == bb[1]);
+ // Don't crunch on the curve or inflate geometry if it is nearly flat (or just very small).
+ // Flat curves can break the math below.
+ if (are_collinear(P)) {
+ this->lineTo(P[3]);
+ return;
+ }
- return (aa > bb * SK_ScalarNearlyZero).thenElse(a, b);
+ Sk2f p0 = Sk2f::Load(P);
+ Sk2f p1 = Sk2f::Load(P+1);
+ Sk2f p2 = Sk2f::Load(P+2);
+ Sk2f p3 = Sk2f::Load(P+3);
+
+ // Also detect near-quadratics ahead of time.
+ Sk2f tan0, tan1, c;
+ get_cubic_tangents(p0, p1, p2, p3, &tan0, &tan1);
+ if (is_cubic_nearly_quadratic(p0, p1, p2, p3, tan0, tan1, &c)) {
+ this->appendQuadratics(p0, c, p3);
+ return;
+ }
+
+ double tt[2], ss[2], D[4];
+ fCurrCubicType = SkClassifyCubic(P, tt, ss, D);
+ SkASSERT(!SkCubicIsDegenerate(fCurrCubicType));
+ Sk2f t = Sk2f(static_cast<float>(tt[0]), static_cast<float>(tt[1]));
+ Sk2f s = Sk2f(static_cast<float>(ss[0]), static_cast<float>(ss[1]));
+
+ SkMatrix CIT;
+ ExcludedTerm skipTerm = GrPathUtils::calcCubicInverseTransposePowerBasisMatrix(P, &CIT);
+ SkASSERT(ExcludedTerm::kNonInvertible != skipTerm); // Should have been caught above.
+ SkASSERT(0 == CIT[6]);
+ SkASSERT(0 == CIT[7]);
+ SkASSERT(1 == CIT[8]);
+
+ SkSTArray<4, float> chops;
+ if (SkCubicType::kLoop != fCurrCubicType) {
+ find_chops_around_inflection_points(inflectPad, t, s, CIT, skipTerm, &chops);
+ } else {
+ find_chops_around_loop_intersection(loopIntersectPad, t, s, CIT, skipTerm, &chops);
+ }
+ if (chops[1] >= chops[2]) {
+ // This just the means the KLM roots are so close that their paddings overlap. We will
+ // approximate the entire middle section, but still have it chopped midway. For loops this
+ // chop guarantees the append code only sees convex segments. Otherwise, it means we are (at
+ // least almost) a cusp and the chop makes sure we get a sharp point.
+ Sk2f ts = t * SkNx_shuffle<1,0>(s);
+ chops[1] = chops[2] = (ts[0] + ts[1]) / (2*s[0]*s[1]);
+ }
+
+#ifdef SK_DEBUG
+ for (int i = 1; i < chops.count(); ++i) {
+ SkASSERT(chops[i] >= chops[i - 1]);
+ }
+#endif
+ this->appendCubics(AppendCubicMode::kLiteral, p0, p1, p2, p3, chops.begin(), chops.count());
}
-static inline bool is_cubic_nearly_quadratic(const Sk2f& p0, const Sk2f& p1, const Sk2f& p2,
- const Sk2f& p3, Sk2f& tan0, Sk2f& tan1, Sk2f& c) {
- tan0 = first_unless_nearly_zero(p1 - p0, p2 - p0);
- tan1 = first_unless_nearly_zero(p3 - p2, p3 - p1);
+static inline void chop_cubic(const Sk2f& p0, const Sk2f& p1, const Sk2f& p2, const Sk2f& p3,
+ float T, Sk2f* ab, Sk2f* abc, Sk2f* abcd, Sk2f* bcd, Sk2f* cd) {
+ Sk2f TT = T;
+ *ab = lerp(p0, p1, TT);
+ Sk2f bc = lerp(p1, p2, TT);
+ *cd = lerp(p2, p3, TT);
+ *abc = lerp(*ab, bc, TT);
+ *bcd = lerp(bc, *cd, TT);
+ *abcd = lerp(*abc, *bcd, TT);
+}
- Sk2f c1 = SkNx_fma(Sk2f(1.5f), tan0, p0);
- Sk2f c2 = SkNx_fma(Sk2f(-1.5f), tan1, p3);
- c = (c1 + c2) * .5f; // Hopefully optimized out if not used?
+void GrCCGeometry::appendCubics(AppendCubicMode mode, const Sk2f& p0, const Sk2f& p1,
+ const Sk2f& p2, const Sk2f& p3, const float chops[], int numChops,
+ float localT0, float localT1) {
+ if (numChops) {
+ SkASSERT(numChops > 0);
+ int midChopIdx = numChops/2;
+ float T = chops[midChopIdx];
+ // Chops alternate between literal and approximate mode.
+ AppendCubicMode rightMode = (AppendCubicMode)((bool)mode ^ (midChopIdx & 1) ^ 1);
- return ((c1 - c2).abs() <= 1).allTrue();
+ if (T <= localT0) {
+ // T is outside 0..1. Append the right side only.
+ this->appendCubics(rightMode, p0, p1, p2, p3, &chops[midChopIdx + 1],
+ numChops - midChopIdx - 1, localT0, localT1);
+ return;
+ }
+
+ if (T >= localT1) {
+ // T is outside 0..1. Append the left side only.
+ this->appendCubics(mode, p0, p1, p2, p3, chops, midChopIdx, localT0, localT1);
+ return;
+ }
+
+ float localT = (T - localT0) / (localT1 - localT0);
+ Sk2f p01, p02, pT, p11, p12;
+ chop_cubic(p0, p1, p2, p3, localT, &p01, &p02, &pT, &p11, &p12);
+ this->appendCubics(mode, p0, p01, p02, pT, chops, midChopIdx, localT0, T);
+ this->appendCubics(rightMode, pT, p11, p12, p3, &chops[midChopIdx + 1],
+ numChops - midChopIdx - 1, T, localT1);
+ return;
+ }
+
+ this->appendCubics(mode, p0, p1, p2, p3);
+}
+
+void GrCCGeometry::appendCubics(AppendCubicMode mode, const Sk2f& p0, const Sk2f& p1,
+ const Sk2f& p2, const Sk2f& p3, int maxSubdivisions) {
+ if ((p0 == p3).allTrue()) {
+ return;
+ }
+
+ if (SkCubicType::kLoop != fCurrCubicType) {
+ // Serpentines and cusps are always monotonic after chopping around inflection points.
+ SkASSERT(!SkCubicIsDegenerate(fCurrCubicType));
+
+ if (AppendCubicMode::kApproximate == mode) {
+ // This section passes through an inflection point, so we can get away with a flat line.
+ // This can cause some curves to feel slightly more flat when inspected rigorously back
+ // and forth against another renderer, but for now this seems acceptable given the
+ // simplicity.
+ SkASSERT(fPoints.back() == SkPoint::Make(p0[0], p0[1]));
+ this->appendLine(p3);
+ return;
+ }
+ } else {
+ Sk2f tan0, tan1;
+ get_cubic_tangents(p0, p1, p2, p3, &tan0, &tan1);
+
+ if (maxSubdivisions && !is_convex_curve_monotonic(p0, tan0, p3, tan1)) {
+ this->chopAndAppendCubicAtMidTangent(mode, p0, p1, p2, p3, tan0, tan1,
+ maxSubdivisions - 1);
+ return;
+ }
+
+ if (AppendCubicMode::kApproximate == mode) {
+ Sk2f c;
+ if (!is_cubic_nearly_quadratic(p0, p1, p2, p3, tan0, tan1, &c) && maxSubdivisions) {
+ this->chopAndAppendCubicAtMidTangent(mode, p0, p1, p2, p3, tan0, tan1,
+ maxSubdivisions - 1);
+ return;
+ }
+
+ this->appendMonotonicQuadratic(p0, c, p3);
+ return;
+ }
+ }
+
+ // Don't send curves to the GPU if we know they are nearly flat (or just very small).
+ // Since the cubic segment is known to be convex at this point, our flatness check is simple.
+ if (are_collinear(p0, (p1 + p2) * .5f, p3)) {
+ SkASSERT(fPoints.back() == SkPoint::Make(p0[0], p0[1]));
+ this->appendLine(p3);
+ return;
+ }
+
+ SkASSERT(fPoints.back() == SkPoint::Make(p0[0], p0[1]));
+ p1.store(&fPoints.push_back());
+ p2.store(&fPoints.push_back());
+ p3.store(&fPoints.push_back());
+ fVerbs.push_back(Verb::kMonotonicCubicTo);
+ ++fCurrContourTallies.fCubics;
}
// Given a convex curve segment with the following order-2 tangent function:
@@ -377,177 +557,11 @@
return std::abs(q*q - r) < std::abs(a*c - r) ? q/a : c/q;
}
-void GrCCGeometry::cubicTo(const SkPoint P[4], float inflectPad, float loopIntersectPad) {
- SkASSERT(fBuildingContour);
- SkASSERT(P[0] == fPoints.back());
-
- // Don't crunch on the curve or inflate geometry if it is nearly flat (or just very small).
- // Flat curves can break the math below.
- if (are_collinear(P)) {
- this->lineTo(P[3]);
- return;
- }
-
- Sk2f p0 = Sk2f::Load(P);
- Sk2f p1 = Sk2f::Load(P+1);
- Sk2f p2 = Sk2f::Load(P+2);
- Sk2f p3 = Sk2f::Load(P+3);
-
- // Also detect near-quadratics ahead of time.
- Sk2f tan0, tan1, c;
- if (is_cubic_nearly_quadratic(p0, p1, p2, p3, tan0, tan1, c)) {
- this->appendMonotonicQuadratics(p0, c, p3);
- return;
- }
-
- double tt[2], ss[2];
- fCurrCubicType = SkClassifyCubic(P, tt, ss);
- SkASSERT(!SkCubicIsDegenerate(fCurrCubicType)); // Should have been caught above.
-
- SkMatrix CIT;
- ExcludedTerm skipTerm = GrPathUtils::calcCubicInverseTransposePowerBasisMatrix(P, &CIT);
- SkASSERT(ExcludedTerm::kNonInvertible != skipTerm); // Should have been caught above.
- SkASSERT(0 == CIT[6]);
- SkASSERT(0 == CIT[7]);
- SkASSERT(1 == CIT[8]);
-
- // Each cubic has five different sections (not always inside t=[0..1]):
- //
- // 1. The section before the first inflection or loop intersection point, with padding.
- // 2. The section that passes through the first inflection/intersection (aka the K,L
- // intersection point or T=tt[0]/ss[0]).
- // 3. The section between the two inflections/intersections, with padding.
- // 4. The section that passes through the second inflection/intersection (aka the K,M
- // intersection point or T=tt[1]/ss[1]).
- // 5. The section after the second inflection/intersection, with padding.
- //
- // Sections 1,3,5 can be rendered directly using the CCPR cubic shader.
- //
- // Sections 2 & 4 must be approximated. For loop intersections we render them with
- // quadratic(s), and when passing through an inflection point we use a plain old flat line.
- //
- // We find T0..T3 below to be the dividing points between these five sections.
- float T0, T1, T2, T3;
- if (SkCubicType::kLoop != fCurrCubicType) {
- Sk2f t = Sk2f(static_cast<float>(tt[0]), static_cast<float>(tt[1]));
- Sk2f s = Sk2f(static_cast<float>(ss[0]), static_cast<float>(ss[1]));
- Sk2f pad = calc_inflect_homogeneous_padding(inflectPad, t, s, CIT, skipTerm);
-
- float T[2];
- ((t - pad) / s).store(T);
- T0 = T[0];
- T2 = T[1];
-
- ((t + pad) / s).store(T);
- T1 = T[0];
- T3 = T[1];
- } else {
- const float T[2] = {static_cast<float>(tt[0]/ss[0]), static_cast<float>(tt[1]/ss[1])};
- SkSTArray<3, float, true> roots[2];
- calc_loop_intersect_padding_pts(loopIntersectPad, Sk2f::Load(T), CIT, skipTerm, roots);
- T0 = roots[0].front();
- if (1 == roots[0].count() || 1 == roots[1].count()) {
- // The loop is tighter than our desired padding. Collapse the middle section to a point
- // somewhere in the middle-ish of the loop and Sections 2 & 4 will approximate the the
- // whole thing with quadratics.
- T1 = T2 = (T[0] + T[1]) * .5f;
- } else {
- T1 = roots[0][1];
- T2 = roots[1][1];
- }
- T3 = roots[1].back();
- }
-
- // Guarantee that T0..T3 are monotonic.
- if (T0 > T3) {
- // This is not a mathematically valid scenario. The only reason it would happen is if
- // padding is very small and we have encountered FP rounding error.
- T0 = T1 = T2 = T3 = (T0 + T3) / 2;
- } else if (T1 > T2) {
- // This just means padding before the middle section overlaps the padding after it. We
- // collapse the middle section to a single point that splits the difference between the
- // overlap in padding.
- T1 = T2 = (T1 + T2) / 2;
- }
- // Clamp T1 & T2 inside T0..T3. The only reason this would be necessary is if we have
- // encountered FP rounding error.
- T1 = std::max(T0, std::min(T1, T3));
- T2 = std::max(T0, std::min(T2, T3));
-
- // Next we chop the cubic up at all T0..T3 inside 0..1 and store the resulting segments.
- if (T1 >= 1) {
- // Only sections 1 & 2 can be in 0..1.
- this->chopCubic<&GrCCGeometry::appendMonotonicCubics,
- &GrCCGeometry::appendCubicApproximation>(p0, p1, p2, p3, T0);
- return;
- }
-
- if (T2 <= 0) {
- // Only sections 4 & 5 can be in 0..1.
- this->chopCubic<&GrCCGeometry::appendCubicApproximation,
- &GrCCGeometry::appendMonotonicCubics>(p0, p1, p2, p3, T3);
- return;
- }
-
- Sk2f midp0, midp1; // These hold the first two bezier points of the middle section, if needed.
-
- if (T1 > 0) {
- Sk2f T1T1 = Sk2f(T1);
- Sk2f ab1 = lerp(p0, p1, T1T1);
- Sk2f bc1 = lerp(p1, p2, T1T1);
- Sk2f cd1 = lerp(p2, p3, T1T1);
- Sk2f abc1 = lerp(ab1, bc1, T1T1);
- Sk2f bcd1 = lerp(bc1, cd1, T1T1);
- Sk2f abcd1 = lerp(abc1, bcd1, T1T1);
-
- // Sections 1 & 2.
- this->chopCubic<&GrCCGeometry::appendMonotonicCubics,
- &GrCCGeometry::appendCubicApproximation>(p0, ab1, abc1, abcd1, T0/T1);
-
- if (T2 >= 1) {
- // The rest of the curve is Section 3 (middle section).
- this->appendMonotonicCubics(abcd1, bcd1, cd1, p3);
- return;
- }
-
- // Now calculate the first two bezier points of the middle section. The final two will come
- // from when we chop the other side, as that is numerically more stable.
- midp0 = abcd1;
- midp1 = lerp(abcd1, bcd1, Sk2f((T2 - T1) / (1 - T1)));
- } else if (T2 >= 1) {
- // The entire cubic is Section 3 (middle section).
- this->appendMonotonicCubics(p0, p1, p2, p3);
- return;
- }
-
- SkASSERT(T2 > 0 && T2 < 1);
-
- Sk2f T2T2 = Sk2f(T2);
- Sk2f ab2 = lerp(p0, p1, T2T2);
- Sk2f bc2 = lerp(p1, p2, T2T2);
- Sk2f cd2 = lerp(p2, p3, T2T2);
- Sk2f abc2 = lerp(ab2, bc2, T2T2);
- Sk2f bcd2 = lerp(bc2, cd2, T2T2);
- Sk2f abcd2 = lerp(abc2, bcd2, T2T2);
-
- if (T1 <= 0) {
- // The curve begins at Section 3 (middle section).
- this->appendMonotonicCubics(p0, ab2, abc2, abcd2);
- } else if (T2 > T1) {
- // Section 3 (middle section).
- Sk2f midp2 = lerp(abc2, abcd2, Sk2f(T1/T2));
- this->appendMonotonicCubics(midp0, midp1, midp2, abcd2);
- }
-
- // Sections 4 & 5.
- this->chopCubic<&GrCCGeometry::appendCubicApproximation,
- &GrCCGeometry::appendMonotonicCubics>(abcd2, bcd2, cd2, p3, (T3-T2) / (1-T2));
-}
-
-template<GrCCGeometry::AppendCubicFn AppendLeftRight>
-inline void GrCCGeometry::chopCubicAtMidTangent(const Sk2f& p0, const Sk2f& p1, const Sk2f& p2,
- const Sk2f& p3, const Sk2f& tan0,
- const Sk2f& tan1, int maxFutureSubdivisions) {
+inline void GrCCGeometry::chopAndAppendCubicAtMidTangent(AppendCubicMode mode, const Sk2f& p0,
+ const Sk2f& p1, const Sk2f& p2,
+ const Sk2f& p3, const Sk2f& tan0,
+ const Sk2f& tan1,
+ int maxFutureSubdivisions) {
float midT = find_midtangent(tan0, tan1, 3, p3 + (p1 - p2)*3 - p0,
6, p0 - p1*2 + p2,
3, p1 - p0);
@@ -559,97 +573,10 @@
return;
}
- this->chopCubic<AppendLeftRight, AppendLeftRight>(p0, p1, p2, p3, midT, maxFutureSubdivisions);
-}
-
-template<GrCCGeometry::AppendCubicFn AppendLeft, GrCCGeometry::AppendCubicFn AppendRight>
-inline void GrCCGeometry::chopCubic(const Sk2f& p0, const Sk2f& p1, const Sk2f& p2,
- const Sk2f& p3, float T, int maxFutureSubdivisions) {
- if (T >= 1) {
- (this->*AppendLeft)(p0, p1, p2, p3, maxFutureSubdivisions);
- return;
- }
-
- if (T <= 0) {
- (this->*AppendRight)(p0, p1, p2, p3, maxFutureSubdivisions);
- return;
- }
-
- Sk2f TT = T;
- Sk2f ab = lerp(p0, p1, TT);
- Sk2f bc = lerp(p1, p2, TT);
- Sk2f cd = lerp(p2, p3, TT);
- Sk2f abc = lerp(ab, bc, TT);
- Sk2f bcd = lerp(bc, cd, TT);
- Sk2f abcd = lerp(abc, bcd, TT);
- (this->*AppendLeft)(p0, ab, abc, abcd, maxFutureSubdivisions);
- (this->*AppendRight)(abcd, bcd, cd, p3, maxFutureSubdivisions);
-}
-
-void GrCCGeometry::appendMonotonicCubics(const Sk2f& p0, const Sk2f& p1, const Sk2f& p2,
- const Sk2f& p3, int maxSubdivisions) {
- SkASSERT(maxSubdivisions >= 0);
- if ((p0 == p3).allTrue()) {
- return;
- }
-
- if (maxSubdivisions) {
- Sk2f tan0 = first_unless_nearly_zero(p1 - p0, p2 - p0);
- Sk2f tan1 = first_unless_nearly_zero(p3 - p2, p3 - p1);
-
- if (!is_convex_curve_monotonic(p0, tan0, p3, tan1)) {
- this->chopCubicAtMidTangent<&GrCCGeometry::appendMonotonicCubics>(p0, p1, p2, p3,
- tan0, tan1,
- maxSubdivisions - 1);
- return;
- }
- }
-
- SkASSERT(fPoints.back() == SkPoint::Make(p0[0], p0[1]));
-
- // Don't send curves to the GPU if we know they are nearly flat (or just very small).
- // Since the cubic segment is known to be convex at this point, our flatness check is simple.
- if (are_collinear(p0, (p1 + p2) * .5f, p3)) {
- this->appendLine(p3);
- return;
- }
-
- p1.store(&fPoints.push_back());
- p2.store(&fPoints.push_back());
- p3.store(&fPoints.push_back());
- fVerbs.push_back(Verb::kMonotonicCubicTo);
- ++fCurrContourTallies.fCubics;
-}
-
-void GrCCGeometry::appendCubicApproximation(const Sk2f& p0, const Sk2f& p1, const Sk2f& p2,
- const Sk2f& p3, int maxSubdivisions) {
- SkASSERT(maxSubdivisions >= 0);
- if ((p0 == p3).allTrue()) {
- return;
- }
-
- if (SkCubicType::kLoop != fCurrCubicType && SkCubicType::kQuadratic != fCurrCubicType) {
- // This section passes through an inflection point, so we can get away with a flat line.
- // This can cause some curves to feel slightly more flat when inspected rigorously back and
- // forth against another renderer, but for now this seems acceptable given the simplicity.
- SkASSERT(fPoints.back() == SkPoint::Make(p0[0], p0[1]));
- this->appendLine(p3);
- return;
- }
-
- Sk2f tan0, tan1, c;
- if (!is_cubic_nearly_quadratic(p0, p1, p2, p3, tan0, tan1, c) && maxSubdivisions) {
- this->chopCubicAtMidTangent<&GrCCGeometry::appendCubicApproximation>(p0, p1, p2, p3,
- tan0, tan1,
- maxSubdivisions - 1);
- return;
- }
-
- if (maxSubdivisions) {
- this->appendMonotonicQuadratics(p0, c, p3);
- } else {
- this->appendSingleMonotonicQuadratic(p0, c, p3);
- }
+ Sk2f p01, p02, pT, p11, p12;
+ chop_cubic(p0, p1, p2, p3, midT, &p01, &p02, &pT, &p11, &p12);
+ this->appendCubics(mode, p0, p01, p02, pT, maxFutureSubdivisions);
+ this->appendCubics(mode, pT, p11, p12, p3, maxFutureSubdivisions);
}
void GrCCGeometry::conicTo(const SkPoint P[3], float w) {