Add some new PolyUtils tests.

Also:
* clean up PolyUtils checks to be correct and consistent.
* fix some bugs discovered by the unit tests.

Bug: skia:
Change-Id: I1a8e07d13cb44fecc67344154dc1002f3f910f5d
Reviewed-on: https://skia-review.googlesource.com/138592
Reviewed-by: Robert Phillips <robertphillips@google.com>
Reviewed-by: Greg Daniel <egdaniel@google.com>
Commit-Queue: Jim Van Verth <jvanverth@google.com>
diff --git a/src/utils/SkPolyUtils.cpp b/src/utils/SkPolyUtils.cpp
index ea9d649..e323f21 100755
--- a/src/utils/SkPolyUtils.cpp
+++ b/src/utils/SkPolyUtils.cpp
@@ -35,13 +35,20 @@
     return 0;
 }
 
-// returns 1 for ccw, -1 for cw and 0 if degenerate
-static int get_winding(const SkPoint* polygonVerts, int polygonSize) {
+// Returns 1 for cw, -1 for ccw and 0 if zero signed area (either degenerate or self-intersecting)
+int SkGetPolygonWinding(const SkPoint* polygonVerts, int polygonSize) {
+    if (polygonSize < 3) {
+        return 0;
+    }
+
     // compute area and use sign to determine winding
     SkScalar quadArea = 0;
-    for (int curr = 0; curr < polygonSize; ++curr) {
+    SkVector v0 = polygonVerts[1] - polygonVerts[0];
+    for (int curr = 1; curr < polygonSize - 1; ++curr) {
         int next = (curr + 1) % polygonSize;
-        quadArea += polygonVerts[curr].cross(polygonVerts[next]);
+        SkVector v1 = polygonVerts[next] - polygonVerts[0];
+        quadArea += v0.cross(v1);
+        v0 = v1;
     }
     if (SkScalarNearlyZero(quadArea)) {
         return 0;
@@ -111,6 +118,15 @@
     return true;
 }
 
+// compute fraction of d along v
+static inline SkScalar compute_param(const SkVector& v, const SkVector& d) {
+    if (SkScalarNearlyZero(v.fX)) {
+        return d.fY / v.fY;
+    } else {
+        return d.fX / v.fX;
+    }
+}
+
 // Compute the intersection 'p' between segments s0 and s1, if any.
 // 's' is the parametric value for the intersection along 's0' & 't' is the same for 's1'.
 // Returns false if there is no intersection.
@@ -132,36 +148,60 @@
 
     SkVector v0 = s0.fP1 - s0.fP0;
     SkVector v1 = s1.fP1 - s1.fP0;
-    // We should have culled coincident points before this
-    SkASSERT(!SkPointPriv::EqualsWithinTolerance(s0.fP0, s0.fP1));
-    SkASSERT(!SkPointPriv::EqualsWithinTolerance(s1.fP0, s1.fP1));
-
     SkVector d = s1.fP0 - s0.fP0;
     SkScalar perpDot = v0.cross(v1);
     SkScalar localS, localT;
     if (SkScalarNearlyZero(perpDot)) {
         // segments are parallel, but not collinear
-        if (!SkScalarNearlyZero(d.dot(d), SK_ScalarNearlyZero*SK_ScalarNearlyZero)) {
+        if (!SkScalarNearlyZero(d.cross(v0)) || !SkScalarNearlyZero(d.cross(v1))) {
             return false;
         }
 
-        // project segment1's endpoints onto segment0
-        localS = d.fX / v0.fX;
-        localT = 0;
-        if (localS < 0 || localS > SK_Scalar1) {
-            // the first endpoint doesn't lie on segment0, try the other one
-            SkScalar oldLocalS = localS;
-            localS = (s1.fP1.fX - s0.fP0.fX) / v0.fX;
-            localT = SK_Scalar1;
-            if (localS < 0 || localS > SK_Scalar1) {
-                // it's possible that segment1's interval surrounds segment0
-                // this is false if the params have the same signs, and in that case no collision
-                if (localS*oldLocalS > 0) {
+        // Check for degenerate segments
+        if (!SkPointPriv::CanNormalize(v0.fX, v0.fY)) {
+            // Both are degenerate
+            if (!SkPointPriv::CanNormalize(v1.fX, v1.fY)) {
+                // Check if they're the same point
+                if (!SkPointPriv::CanNormalize(d.fX, d.fY)) {
+                    *p = s0.fP0;
+                    *s = 0;
+                    *t = 0;
+                    return true;
+                } else {
                     return false;
                 }
-                // otherwise project segment0's endpoint onto segment1 instead
-                localS = 0;
-                localT = -d.fX / v1.fX;
+            }
+            // Otherwise project onto segment1
+            localT = compute_param(v1, -d);
+            if (localT < 0 || localT > SK_Scalar1) {
+                return false;
+            }
+            localS = 0;
+        } else {
+            // Project segment1's endpoints onto segment0
+            localS = compute_param(v0, d);
+            localT = 0;
+            if (localS < 0 || localS > SK_Scalar1) {
+                // The first endpoint doesn't lie on segment0
+                // If segment1 is degenerate, then there's no collision
+                if (!SkPointPriv::CanNormalize(v1.fX, v1.fY)) {
+                    return false;
+                }
+
+                // Otherwise try the other one
+                SkScalar oldLocalS = localS;
+                localS = compute_param(v0, s1.fP1 - s0.fP0);
+                localT = SK_Scalar1;
+                if (localS < 0 || localS > SK_Scalar1) {
+                    // it's possible that segment1's interval surrounds segment0
+                    // this is false if params have the same signs, and in that case no collision
+                    if (localS*oldLocalS > 0) {
+                        return false;
+                    }
+                    // otherwise project segment0's endpoint onto segment1 instead
+                    localS = 0;
+                    localT = compute_param(v1, -d);
+                }
             }
         }
     } else {
@@ -175,8 +215,7 @@
         }
     }
 
-    v0 *= localS;
-    *p = s0.fP0 + v0;
+    *p = s0.fP0 + v0*localS;
     *s = localS;
     *t = localT;
 
@@ -207,25 +246,49 @@
     return localS;
 }
 
-static bool is_convex(const SkTDArray<SkPoint>& poly) {
-    if (poly.count() <= 3) {
-        return true;
+bool SkIsConvexPolygon(const SkPoint* polygonVerts, int polygonSize) {
+    if (polygonSize < 3) {
+        return false;
     }
 
-    SkVector v0 = poly[0] - poly[poly.count() - 1];
-    SkVector v1 = poly[1] - poly[poly.count() - 1];
-    SkScalar winding = v0.cross(v1);
+    SkScalar lastArea = 0;
+    SkScalar lastPerpDot = 0;
 
-    for (int i = 0; i < poly.count() - 1; ++i) {
-        int j = i + 1;
-        int k = (i + 2) % poly.count();
-
-        SkVector v0 = poly[j] - poly[i];
-        SkVector v1 = poly[k] - poly[i];
+    int prevIndex = polygonSize - 1;
+    int currIndex = 0;
+    int nextIndex = 1;
+    SkPoint origin = polygonVerts[0];
+    SkVector v0 = polygonVerts[currIndex] - polygonVerts[prevIndex];
+    SkVector v1 = polygonVerts[nextIndex] - polygonVerts[currIndex];
+    SkVector w0 = polygonVerts[currIndex] - origin;
+    SkVector w1 = polygonVerts[nextIndex] - origin;
+    for (int i = 0; i < polygonSize; ++i) {
+        // Check that winding direction is always the same (otherwise we have a reflex vertex)
         SkScalar perpDot = v0.cross(v1);
-        if (winding*perpDot < 0) {
+        if (lastPerpDot*perpDot < 0) {
             return false;
         }
+        if (0 != perpDot) {
+            lastPerpDot = perpDot;
+        }
+
+        // If the signed area ever flips it's concave
+        // TODO: see if we can verify convexity only with signed area
+        SkScalar quadArea = w0.cross(w1);
+        if (quadArea*lastArea < 0) {
+            return false;
+        }
+        if (0 != quadArea) {
+            lastArea = quadArea;
+        }
+
+        prevIndex = currIndex;
+        currIndex = nextIndex;
+        nextIndex = (currIndex + 1) % polygonSize;
+        v0 = v1;
+        v1 = polygonVerts[nextIndex] - polygonVerts[currIndex];
+        w0 = w1;
+        w1 = polygonVerts[nextIndex] - origin;
     }
 
     return true;
@@ -281,7 +344,7 @@
     }
 
     // get winding direction
-    int winding = get_winding(inputPolygonVerts, inputPolygonSize);
+    int winding = SkGetPolygonWinding(inputPolygonVerts, inputPolygonSize);
     if (0 == winding) {
         return false;
     }
@@ -395,7 +458,7 @@
         insetPolygon->pop();
     }
 
-    return (insetPolygon->count() >= 3 && is_convex(*insetPolygon));
+    return SkIsConvexPolygon(insetPolygon->begin(), insetPolygon->count());
 }
 
 ///////////////////////////////////////////////////////////////////////////////////////////
@@ -416,6 +479,8 @@
     *n = steps;
 }
 
+///////////////////////////////////////////////////////////////////////////////////////////
+
 // tolerant less-than comparison
 static inline bool nearly_lt(SkScalar a, SkScalar b, SkScalar tolerance = SK_ScalarNearlyZero) {
     return a < b - tolerance;
@@ -626,7 +691,7 @@
     }
 
     // get winding direction
-    int winding = get_winding(inputPolygonVerts, inputPolygonSize);
+    int winding = SkGetPolygonWinding(inputPolygonVerts, inputPolygonSize);
     if (0 == winding) {
         return false;
     }
@@ -787,7 +852,7 @@
     }
 
     // check winding of offset polygon (it should be same as the original polygon)
-    SkScalar offsetWinding = get_winding(offsetPolygon->begin(), offsetPolygon->count());
+    SkScalar offsetWinding = SkGetPolygonWinding(offsetPolygon->begin(), offsetPolygon->count());
 
     return (winding*offsetWinding > 0 &&
             SkIsSimplePolygon(offsetPolygon->begin(), offsetPolygon->count()));
@@ -891,7 +956,7 @@
     // get winding direction
     // TODO: we do this for all the polygon routines -- might be better to have the client
     // compute it and pass it in
-    int winding = get_winding(polygonVerts, polygonSize);
+    int winding = SkGetPolygonWinding(polygonVerts, polygonSize);
     if (0 == winding) {
         return false;
     }