diff options
| author |  Christopher Dalton <csmartdalton@google.com> | 2017-06-06 14:26:27 -0600 |
|---|---|---|
| committer |  Skia Commit-Bot <skia-commit-bot@chromium.org> | 2017-06-06 20:53:16 +0000 |
| commit | 7f5af0c2832e8a9682aff9521684c27e1368b6ee (patch) | |
| tree | f70fcef97e18e2d205f125eedd921893a8dc2a84 /src/pathops | |
| parent | 5355d87b0783c03a64c305bf3666a4baf2b633e7 (diff) | |
Use more stable root finding methods for cubics
Applies the quadratic formula from "Numerical Recipes in C",
Section 5.6, to the homogeneous quadratic equations that find cubic
inflection points and loop intersections. Also addresses KLM
orientation ahead of time, rather than negating K and L after the
fact.
Bug: skia:
Change-Id: Ic7e0818e2fe49b7724f9b583bae52281cfb1aea1
Reviewed-on: https://skia-review.googlesource.com/13481
Commit-Queue: Chris Dalton <csmartdalton@google.com>
Reviewed-by: Cary Clark <caryclark@google.com>
Diffstat (limited to 'src/pathops')
| -rw-r--r-- | src/pathops/SkPathOpsCubic.cpp | 18 |
1 files changed, 8 insertions, 10 deletions
diff --git a/src/pathops/SkPathOpsCubic.cpp b/src/pathops/SkPathOpsCubic.cpp index 1e74eb0afd..794e54fdfe 100644 --- a/src/pathops/SkPathOpsCubic.cpp +++ b/src/pathops/SkPathOpsCubic.cpp @@ -255,16 +255,14 @@ int SkDCubic::ComplexBreak(const SkPoint pointsPtr[4], SkScalar* t) { // 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); - SkScalar tempSqrt = SkScalarSqrt(-d[0]); - SkScalar ls = d[2] - tempSqrt; - SkScalar lt = 2.f * d[1]; - SkScalar ms = d[2] + tempSqrt; - SkScalar mt = 2.f * d[1]; - if (roughly_between(0, ls, lt) && roughly_between(0, ms, mt)) { - ls = ls / lt; - ms = ms / mt; - SkASSERT(roughly_between(0, ls, 1) && roughly_between(0, ms, 1)); - t[0] = (ls + ms) / 2; + 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; + if (roughly_between(0, td, sd) && roughly_between(0, te, se)) { + 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); } |