avoid generating degenerate conic from arc

src/core/SkGeometry.cpp

 /*
  * Copyright 2006 The Android Open Source Project
  *
  * Use of this source code is governed by a BSD-style license that can be
  * found in the LICENSE file.
  */
 
 #include "SkGeometry.h"
 #include "SkMatrix.h"
 #include "SkNx.h"
@@ skipping 1333 matching lines @@
 
     if (dot < 1) {
         SkVector offCurve = { lastQ.x() + x, lastQ.y() + y };
         // compute the bisector vector, and then rescale to be the off-curve point.
         // we compute its length from cos(theta/2) = length / 1, using half-angle identity we get
         // length = sqrt(2 / (1 + cos(theta)). We already have cos() when to computed the dot.
         // This is nice, since our computed weight is cos(theta/2) as well!
         //
         const SkScalar cosThetaOver2 = SkScalarSqrt((1 + dot) / 2);
         offCurve.setLength(SkScalarInvert(cosThetaOver2));
-        dst[conicCount].set(lastQ, offCurve, finalP, cosThetaOver2);
-        conicCount += 1;
+        if (!lastQ.equalsWithinTolerance(offCurve)) {
+            dst[conicCount].set(lastQ, offCurve, finalP, cosThetaOver2);
+            conicCount += 1;
+        } 

[Mark Kilgard, 2016/08/26 17:13:07]

I don't like this epsilon handling here.  It's just going to shift the issue.

The method looks much as I expected it to look.  It divides large arcs into 90
degree quadrants.

Can you instead figure out how many even segments to divide the arc into?

This approach has two advantages:
1) more stable, no epsilon change
2) each conic's w value will be identical

Example:  If the angle is 200 degrees, notice that ceil(200/90) is 3 (2.222
rounds up to 3) then 200/3 = 66.66.  Now you can do the sqrt((1+dot)/2) math to
determine a single w where dot is cos of 66.66 degrees.

Make sense?  I think this can be a simpler overall algorithm than what you have
here.

Keep in mind if somebody had a abnormally large miter limit and used a miter
join, they might still be able to get zinged join geometry.

     }
 
     // now handle counter-clockwise and the initial unitStart rotation
     SkMatrix    matrix;
     matrix.setSinCos(uStart.fY, uStart.fX);
     if (dir == kCCW_SkRotationDirection) {
         matrix.preScale(SK_Scalar1, -SK_Scalar1);
     }
     if (userMatrix) {
         matrix.postConcat(*userMatrix);
     }
     for (int i = 0; i < conicCount; ++i) {
         matrix.mapPoints(dst[i].fPts, 3);
     }
     return conicCount;
 }