Fix SkPath::arcTo when sweepAngle is tiny and radius is big

src/core/SkPath.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 <cmath>
 #include "SkBuffer.h"
 #include "SkCubicClipper.h"
@@ skipping 1272 matching lines @@
     if (arc_is_lone_point(oval, startAngle, sweepAngle, &lonePt)) {
         forceMoveTo ? this->moveTo(lonePt) : this->lineTo(lonePt);
         return;
     }
 
     SkVector startV, stopV;
     SkRotationDirection dir;
     angles_to_unit_vectors(startAngle, sweepAngle, &startV, &stopV, &dir);
 
     SkPoint singlePt;
+
+    // At this point, we know that the arc is not a lone point, but startV == stopV
+    // indicates that the sweepAngle is too small such that angles_to_unit_vectors
+    // cannot handle it.
+    if (startV == stopV) {
+        SkScalar endAngle = SkDegreesToRadians(startAngle + sweepAngle);
+        SkScalar radiusX = oval.width() / 2;
+        SkScalar radiusY = oval.height() / 2;
+        singlePt.set(oval.centerX() + radiusX * cosf(endAngle),
+            oval.centerY() + radiusY * sinf(endAngle));

[caryclark, 2016/10/05 14:08:11]

SkScalarSinCos() is preferable

[xidachen, 2016/10/05 14:24:32]

While I do agree that SkScalarSinCos() is preferable, it doesn't work here. The
fundamental problem of the bug is that sinf(sweepAngle) is very very small, it
is smaller than *SkScalarNearlyZero*, so when we call SkScalarSinCos() we end up
having sin = 0 and cos = 1, that causes the bug. Because when the radius is
huge, e.g., 100000, even if sin(sweepAngle) = 0.0001, we should still draw a
line. Unfortunately 0.0001 is smaller than *SkScalarNearlyZero*.

The *SkScalarNearlyZero* threshould is actually the reason why we got startV ==
stopV in the function angles_to_unit_vectors().

[caryclark, 2016/10/05 14:47:03]

A comment in the code to this effect would be helpful here.

How about sk_float_sin and sk_float_cos?

[xidachen, 2016/10/05 16:33:51]

comment added.

sk_float_sin and sk_float_cos works fine. I have changed to those two.

+        forceMoveTo ? this->moveTo(singlePt) : this->lineTo(singlePt);

[caryclark, 2016/10/05 14:08:11]

Does your example GM trigger both sides of this expression?

[xidachen, 2016/10/05 14:24:32]

No, it only triggers lineTo. This line is basically copied from line 1317 below.

[caryclark, 2016/10/05 14:47:03]

It would be great if was possible to verify that the new code path works

[xidachen, 2016/10/05 16:33:51]

I believe SkPath::addArc calls arcTo with forceMoveTo == true. So I added a call
to addArc in the gm/addarc, and we can see that when forceMoveTo is true, it
doesn't draw a line. I hope that does correspond to what you asked.

+        return;
+    }
+
     SkConic conics[SkConic::kMaxConicsForArc];
     int count = build_arc_conics(oval, startV, stopV, dir, conics, &singlePt);
     if (count) {
         this->incReserve(count * 2 + 1);
         const SkPoint& pt = conics[0].fPts[0];
         forceMoveTo ? this->moveTo(pt) : this->lineTo(pt);
         for (int i = 0; i < count; ++i) {
             this->conicTo(conics[i].fPts[1], conics[i].fPts[2], conics[i].fW);
         }
     } else {
@@ skipping 2070 matching lines @@
         path->arcTo(oval, startAngle, 180.f, false);
         startAngle += 180.f;
         forceMoveTo = false;
         sweepAngle -= 360.f;
     }
     path->arcTo(oval, startAngle, sweepAngle, forceMoveTo);
     if (useCenter) {
         path->close();
     }
 }