diff --git a/src/gpu/ops/GrAAConvexPathRenderer.cpp b/src/gpu/ops/GrAAConvexPathRenderer.cpp
index 5944aef..5021aa7 100644
--- a/src/gpu/ops/GrAAConvexPathRenderer.cpp
+++ b/src/gpu/ops/GrAAConvexPathRenderer.cpp
@@ -289,42 +289,50 @@
 
     for (;;) {
         SkPoint pts[4];
-        SkPath::Verb verb = iter.next(pts, true, true);
+        SkPath::Verb verb = iter.next(pts);
         switch (verb) {
             case SkPath::kMove_Verb:
                 m.mapPoints(pts, 1);
                 update_degenerate_test(&degenerateData, pts[0]);
                 break;
             case SkPath::kLine_Verb: {
-                m.mapPoints(&pts[1], 1);
-                update_degenerate_test(&degenerateData, pts[1]);
-                add_line_to_segment(pts[1], segments);
+                if (!SkPathPriv::AllPointsEq(pts, 2)) {
+                    m.mapPoints(&pts[1], 1);
+                    update_degenerate_test(&degenerateData, pts[1]);
+                    add_line_to_segment(pts[1], segments);
+                }
                 break;
             }
             case SkPath::kQuad_Verb:
-                m.mapPoints(pts, 3);
-                update_degenerate_test(&degenerateData, pts[1]);
-                update_degenerate_test(&degenerateData, pts[2]);
-                add_quad_segment(pts, segments);
+                if (!SkPathPriv::AllPointsEq(pts, 3)) {
+                    m.mapPoints(pts, 3);
+                    update_degenerate_test(&degenerateData, pts[1]);
+                    update_degenerate_test(&degenerateData, pts[2]);
+                    add_quad_segment(pts, segments);
+                }
                 break;
             case SkPath::kConic_Verb: {
-                m.mapPoints(pts, 3);
-                SkScalar weight = iter.conicWeight();
-                SkAutoConicToQuads converter;
-                const SkPoint* quadPts = converter.computeQuads(pts, weight, 0.25f);
-                for (int i = 0; i < converter.countQuads(); ++i) {
-                    update_degenerate_test(&degenerateData, quadPts[2*i + 1]);
-                    update_degenerate_test(&degenerateData, quadPts[2*i + 2]);
-                    add_quad_segment(quadPts + 2*i, segments);
+                if (!SkPathPriv::AllPointsEq(pts, 3)) {
+                    m.mapPoints(pts, 3);
+                    SkScalar weight = iter.conicWeight();
+                    SkAutoConicToQuads converter;
+                    const SkPoint* quadPts = converter.computeQuads(pts, weight, 0.25f);
+                    for (int i = 0; i < converter.countQuads(); ++i) {
+                        update_degenerate_test(&degenerateData, quadPts[2*i + 1]);
+                        update_degenerate_test(&degenerateData, quadPts[2*i + 2]);
+                        add_quad_segment(quadPts + 2*i, segments);
+                    }
                 }
                 break;
             }
             case SkPath::kCubic_Verb: {
-                m.mapPoints(pts, 4);
-                update_degenerate_test(&degenerateData, pts[1]);
-                update_degenerate_test(&degenerateData, pts[2]);
-                update_degenerate_test(&degenerateData, pts[3]);
-                add_cubic_segments(pts, dir, segments);
+                if (!SkPathPriv::AllPointsEq(pts, 4)) {
+                    m.mapPoints(pts, 4);
+                    update_degenerate_test(&degenerateData, pts[1]);
+                    update_degenerate_test(&degenerateData, pts[2]);
+                    update_degenerate_test(&degenerateData, pts[3]);
+                    add_cubic_segments(pts, dir, segments);
+                }
                 break;
             }
             case SkPath::kDone_Verb:
diff --git a/src/gpu/ops/GrAAConvexTessellator.cpp b/src/gpu/ops/GrAAConvexTessellator.cpp
index 5e545d4..0e753a1 100644
--- a/src/gpu/ops/GrAAConvexTessellator.cpp
+++ b/src/gpu/ops/GrAAConvexTessellator.cpp
@@ -394,19 +394,27 @@
     SkPath::Iter iter(path, true);
     SkPoint pts[4];
     SkPath::Verb verb;
-    while ((verb = iter.next(pts, true, true)) != SkPath::kDone_Verb) {
+    while ((verb = iter.next(pts)) != SkPath::kDone_Verb) {
         switch (verb) {
             case SkPath::kLine_Verb:
-                this->lineTo(m, pts[1], kSharp_CurveState);
+                if (!SkPathPriv::AllPointsEq(pts, 2)) {
+                    this->lineTo(m, pts[1], kSharp_CurveState);
+                }
                 break;
             case SkPath::kQuad_Verb:
-                this->quadTo(m, pts);
+                if (!SkPathPriv::AllPointsEq(pts, 3)) {
+                    this->quadTo(m, pts);
+                }
                 break;
             case SkPath::kCubic_Verb:
-                this->cubicTo(m, pts);
+                if (!SkPathPriv::AllPointsEq(pts, 4)) {
+                    this->cubicTo(m, pts);
+                }
                 break;
             case SkPath::kConic_Verb:
-                this->conicTo(m, pts, iter.conicWeight());
+                if (!SkPathPriv::AllPointsEq(pts, 3)) {
+                    this->conicTo(m, pts, iter.conicWeight());
+                }
                 break;
             case SkPath::kMove_Verb:
             case SkPath::kClose_Verb:
diff --git a/src/gpu/ops/GrAAHairLinePathRenderer.cpp b/src/gpu/ops/GrAAHairLinePathRenderer.cpp
index 6b054f8..748946b 100644
--- a/src/gpu/ops/GrAAHairLinePathRenderer.cpp
+++ b/src/gpu/ops/GrAAHairLinePathRenderer.cpp
@@ -312,7 +312,7 @@
 
     for (;;) {
         SkPoint pathPts[4];
-        SkPath::Verb verb = iter.next(pathPts, false);
+        SkPath::Verb verb = iter.next(pathPts);
         switch (verb) {
             case SkPath::kConic_Verb:
                 if (convertConicsToQuads) {
diff --git a/src/gpu/ops/GrDefaultPathRenderer.cpp b/src/gpu/ops/GrDefaultPathRenderer.cpp
index 2c4db58..f31e7e9 100644
--- a/src/gpu/ops/GrDefaultPathRenderer.cpp
+++ b/src/gpu/ops/GrDefaultPathRenderer.cpp
@@ -151,7 +151,7 @@
 
         bool done = false;
         while (!done) {
-            SkPath::Verb verb = iter.next(pts, false);
+            SkPath::Verb verb = iter.next(pts);
             switch (verb) {
                 case SkPath::kMove_Verb:
                     this->moveTo(pts[0]);
@@ -183,7 +183,7 @@
         SkPath::Verb verb;
 
         SkPoint pts[4];
-        while ((verb = iter.next(pts, false)) != SkPath::kDone_Verb) {
+        while ((verb = iter.next(pts)) != SkPath::kDone_Verb) {
             if (SkPath::kMove_Verb == verb && !first) {
                 return true;
             }