Improve cubic KLM accuracy
Moves cubic root finding logic out of GrPathUtils and
PathOpsCubicIntersectionTest, and unifies it in SkGeometry.
"Normalizes" the homogeneous parameter values of the roots, rather
than the cubic inflection function. Does this normalization by
twiddling the exponents instead of division (which causes a loss of
precision).
Abandons the built-in derivatives in GrCubicEffect. These don't have
high enough precision on many mobile gpus. Instead we pass the KLM
matrix to the vertex shader via uniform, where we can use it to set up
new linear functionals from which the fragment shader can calculate
the gradient of the implicit function.
Bug: skia:4410
Change-Id: Ibd64e999520adc8cdef7803a492d3699995aef5a
Reviewed-on: https://skia-review.googlesource.com/19017
Reviewed-by: Greg Daniel <egdaniel@google.com>
Commit-Queue: Chris Dalton <csmartdalton@google.com>
diff --git a/src/pathops/SkPathOpsCubic.cpp b/src/pathops/SkPathOpsCubic.cpp
index 794e54f..d7b905c 100644
--- a/src/pathops/SkPathOpsCubic.cpp
+++ b/src/pathops/SkPathOpsCubic.cpp
@@ -248,20 +248,13 @@
if (cubic.monotonicInX() && cubic.monotonicInY()) {
return 0;
}
- SkScalar d[4];
- SkCubicType cubicType = SkClassifyCubic(pointsPtr, d);
+ SkScalar tt[2], ss[2];
+ SkCubicType cubicType = SkClassifyCubic(pointsPtr, tt, ss);
switch (cubicType) {
case SkCubicType::kLoop: {
- // crib code from gpu path utils that finds t values where loop self-intersects
- // use it to find mid of t values which should be a friendly place to chop
- SkASSERT(d[0] < 0);
- const SkScalar q = d[2] + SkScalarCopySign(SkScalarSqrt(-d[0]), d[2]);
- const SkScalar td = q;
- const SkScalar sd = 2 * d[1];
- const SkScalar te = 2 * (d[2] * d[2] - d[3] * d[1]);
- const SkScalar se = d[1] * q;
+ const SkScalar &td = tt[0], &te = tt[1], &sd = ss[0], &se = ss[1];
if (roughly_between(0, td, sd) && roughly_between(0, te, se)) {
- SkASSERT(roughly_between(0, td / sd, 1) && roughly_between(0, te / se, 1));
+ SkASSERT(roughly_between(0, td/sd, 1) && roughly_between(0, te/se, 1));
t[0] = (td * se + te * sd) / (2 * sd * se);
SkASSERT(roughly_between(0, *t, 1));
return (int) (t[0] > 0 && t[0] < 1);
@@ -270,7 +263,7 @@
// fall through if no t value found
case SkCubicType::kSerpentine:
case SkCubicType::kLocalCusp:
- case SkCubicType::kInfiniteCusp: {
+ case SkCubicType::kCuspAtInfinity: {
double inflectionTs[2];
int infTCount = cubic.findInflections(inflectionTs);
double maxCurvature[3];