fix zero-length tangent

src/core/SkGeometry.cpp

Index: src/core/SkGeometry.cpp
diff --git a/src/core/SkGeometry.cpp b/src/core/SkGeometry.cpp
index 6afd9d7ffb0ed1478b6afd0062a76ce93f2db02a..4f820795a002b5d947f226de706b388f66a79c00 100644
--- a/src/core/SkGeometry.cpp
+++ b/src/core/SkGeometry.cpp
@@ -130,13 +130,6 @@ static SkScalar eval_quad(const SkScalar src[], SkScalar t) {
 #endif
 }
 
-static SkScalar eval_quad_derivative(const SkScalar src[], SkScalar t) {
-    SkScalar A = src[4] - 2 * src[2] + src[0];
-    SkScalar B = src[2] - src[0];
-
-    return 2 * SkScalarMulAdd(A, t, B);
-}
-
 void SkQuadToCoeff(const SkPoint pts[3], SkPoint coeff[3]) {
     Sk2s p0 = from_point(pts[0]);
     Sk2s p1 = from_point(pts[1]);
@@ -157,8 +150,7 @@ void SkEvalQuadAt(const SkPoint src[3], SkScalar t, SkPoint* pt, SkVector* tange
         pt->set(eval_quad(&src[0].fX, t), eval_quad(&src[0].fY, t));
     }
     if (tangent) {
-        tangent->set(eval_quad_derivative(&src[0].fX, t),
-                     eval_quad_derivative(&src[0].fY, t));
+        *tangent = SkEvalQuadTangentAt(src, t);
     }
 }
 
@@ -179,6 +171,12 @@ SkPoint SkEvalQuadAt(const SkPoint src[3], SkScalar t) {
 }
 
 SkVector SkEvalQuadTangentAt(const SkPoint src[3], SkScalar t) {
+    // The derivative equation is 2(b - a +(a - 2b +c)t). This returns a
+    // zero tangent vector when t is 0 or 1, and the control point is equal
+    // to the end point. In this case, use the quad end points to compute the tangent.
+    if ((t == 0 && src[0] == src[1]) || (t == 1 && src[1] == src[2])) {
+        return src[2] - src[0];
+    }
     SkASSERT(src);
     SkASSERT(t >= 0 && t <= SK_Scalar1);
 
@@ -398,8 +396,22 @@ void SkEvalCubicAt(const SkPoint src[4], SkScalar t, SkPoint* loc,
         loc->set(eval_cubic(&src[0].fX, t), eval_cubic(&src[0].fY, t));
     }
     if (tangent) {
-        tangent->set(eval_cubic_derivative(&src[0].fX, t),
-                     eval_cubic_derivative(&src[0].fY, t));
+        // The derivative equation returns a zero tangent vector when t is 0 or 1, and the
+        // adjacent control point is equal to the end point. In this case, use the
+        // next control point or the end points to compute the tangent.
+        if ((t == 0 && src[0] == src[1]) || (t == 1 && src[2] == src[3])) {
+            if (t == 0) {
+                *tangent = src[2] - src[0];
+            } else {
+                *tangent = src[3] - src[1];
+            }
+            if (!tangent->fX && !tangent->fY) {
+                *tangent = src[3] - src[0];
+            }
+        } else {
+            tangent->set(eval_cubic_derivative(&src[0].fX, t),
+                         eval_cubic_derivative(&src[0].fY, t));
+        }
     }
     if (curvature) {
         curvature->set(eval_cubic_2ndDerivative(&src[0].fX, t),
@@ -1176,12 +1188,6 @@ static void conic_deriv_coeff(const SkScalar src[],
     coeff[2] = wP10;
 }
 
-static SkScalar conic_eval_tan(const SkScalar coord[], SkScalar w, SkScalar t) {
-    SkScalar coeff[3];
-    conic_deriv_coeff(coord, w, coeff);
-    return t * (t * coeff[0] + coeff[1]) + coeff[2];
-}
-
 static bool conic_find_extrema(const SkScalar src[], SkScalar w, SkScalar* t) {
     SkScalar coeff[3];
     conic_deriv_coeff(src, w, coeff);
@@ -1232,8 +1238,7 @@ void SkConic::evalAt(SkScalar t, SkPoint* pt, SkVector* tangent) const {
                 conic_eval_pos(&fPts[0].fY, fW, t));
     }
     if (tangent) {
-        tangent->set(conic_eval_tan(&fPts[0].fX, fW, t),
-                     conic_eval_tan(&fPts[0].fY, fW, t));
+        *tangent = evalTangentAt(t);
     }
 }
 
@@ -1291,6 +1296,12 @@ SkPoint SkConic::evalAt(SkScalar t) const {
 }
 
 SkVector SkConic::evalTangentAt(SkScalar t) const {
+    // The derivative equation returns a zero tangent vector when t is 0 or 1,
+    // and the control point is equal to the end point.
+    // In this case, use the conic endpoints to compute the tangent.
+    if ((t == 0 && fPts[0] == fPts[1]) || (t == 1 && fPts[1] == fPts[2])) {
+        return fPts[2] - fPts[0];
+    }
     Sk2s p0 = from_point(fPts[0]);
     Sk2s p1 = from_point(fPts[1]);
     Sk2s p2 = from_point(fPts[2]);