Web Animations: Allow timing inputs outside the range [0, 1]

Source/platform/animation/UnitBezier.h

Index: Source/platform/animation/UnitBezier.h
diff --git a/Source/platform/animation/UnitBezier.h b/Source/platform/animation/UnitBezier.h
index b2d4ed361a41b1a9c46f53478841a04b1238ccbf..879d4362d3a43b22b70441668065b3a0d203049f 100644
--- a/Source/platform/animation/UnitBezier.h
+++ b/Source/platform/animation/UnitBezier.h
@@ -43,6 +43,36 @@ struct UnitBezier {
         cy = 3.0 * p1y;
         by = 3.0 * (p2y - p1y) - cy;
         ay = 1.0 - cy - by;
+
+        // End-point gradients are used to calculate timing function results
+        // outside the range [0, 1].
+        //
+        // There are three possibilities for the gradient at each end:
+        // (1) the closest control point is not horizontally coincident with regard to

[alancutter (OOO until 2018), 2014/04/16 04:50:42]

Change to "adjacent control point"?
Closest sounds like you're talking terms of proximity in space when you mean
proximity in the sequence.
This should say "with the end point", this is what the code appears to do.

[shans, 2014/04/17 06:04:18]

I don't think these edits make this prose any better.

+        //     (0, 0) or (1, 1). In this case the line between the end point and
+        //     the control point is tangent to the bezier at the end point.
+        // (2) the closest control point is coincident with the end point. In

[alancutter (OOO until 2018), 2014/04/16 04:50:42]

Add "and the far control point is not horizontally coincident with the end
point", the code appears to also check this condition as well.

I suppose this would technically add another condition to cover where the
adjacent control point is coincident with the end point and the far control
point is horizontally coincident but vertically distinct that should fall under
case 3.

[shans, 2014/04/17 06:04:18]

Likewise.

+        //     this case the line between the end point and the far control
+        //     point is tangent to the bezier at the end point.
+        // (3) the closest control point is horizontally coincident with the end
+        //     point, but vertically distinct. In this case the gradient at the
+        //     end point is Infinite. However, this causes issues when
+        //     interpolating. As a result, we break down to a simple case of
+        //     0 gradient under these conditions.
+
+        if (p1x > 0)
+            m_startGradient = p1y / p1x;
+        else if (!p1y && p2x > 0)
+            m_startGradient = p2y / p2x;
+        else
+            m_startGradient = 0;
+
+        if (p2x < 1)
+            m_endGradient = (p2y - 1) / (p2x - 1);
+        else if (p2x == 1 && p1x < 1)
+            m_endGradient = (p1y - 1) / (p1x - 1);
+        else
+            m_endGradient = 0;
     }
 
     double sampleCurveX(double t)
@@ -110,9 +140,9 @@ struct UnitBezier {
     double solve(double x, double epsilon)
     {
         if (x < 0.0)
-            return 0.0;
+            return 0.0 + m_startGradient * x;
         if (x > 1.0)
-            return 1.0;
+            return 1.0 + m_endGradient * (x - 1.0);
         return sampleCurveY(solveCurveX(x, epsilon));
     }
 
@@ -124,6 +154,9 @@ private:
     double ay;
     double by;
     double cy;
+
+    double m_startGradient;
+    double m_endGradient;
 };
 
 } // namespace WebCore