Сonsider that LargeHole_DontFill is true if angle is negative

Otherwise, a wrong triangle can be generated

Signed-off-by: AndriyAndreyev <andriy.a.andreyev@gmail.com>

poly2tri/sweep/sweep.cc

@@ -262,13 +262,45 @@ void Sweep::FillAdvancingFront(SweepContext& tcx, Node& n)
 }
 
 // True if HoleAngle exceeds 90 degrees.
+// LargeHole_DontFill checks if the advancing front has a large hole.
+// A "Large hole" is a triangle formed by a sequence of points in the advancing
+// front where three neighbor points form a triangle.
+// And angle between left-top, bottom, and right-top points is more than 90 degrees.
+// The first part of the algorithm reviews only three neighbor points, e.g. named A, B, C.
+// Additional part of this logic reviews a sequence of 5 points -
+// additionally reviews one point before and one after the sequence of three (A, B, C),
+// e.g. named X and Y.
+// In this case, angles are XBC and ABY and this if angles are negative or more
+// than 90 degrees LargeHole_DontFill returns true.
+// But there is a configuration when ABC has a negative angle but XBC or ABY is less
+// than 90 degrees and positive.
+// Then function LargeHole_DontFill return false and initiates filling.
+// This filling creates a triangle ABC and adds it to the advancing front.
+// But in the case when angle ABC is negative this triangle goes inside the advancing front
+// and can intersect previously created triangles.
+// This triangle leads to making wrong advancing front and problems in triangulation in the future.
+// Looks like such a triangle should not be created.
+// The simplest way to check and fix it is to check an angle ABC.
+// If it is negative LargeHole_DontFill should return true and
+// not initiate creating the ABC triangle in the advancing front.
+// X______A         Y
+//        \        /
+//         \      /
+//          \ B  /
+//           |  /
+//           | /
+//           |/
+//           C
 bool Sweep::LargeHole_DontFill(const Node* node) const {
 
   const Node* nextNode = node->next;
   const Node* prevNode = node->prev;
   if (!AngleExceeds90Degrees(node->point, nextNode->point, prevNode->point))
           return false;
 
+  if (AngleIsNegative(node->point, nextNode->point, prevNode->point))
+          return true;
+
   // Check additional points on front.
   const Node* next2Node = nextNode->next;
   // "..Plus.." because only want angles on same side as point being added.
@@ -283,6 +315,11 @@ bool Sweep::LargeHole_DontFill(const Node* node) const {
   return true;
 }
 
+bool Sweep::AngleIsNegative(const Point* origin, const Point* pa, const Point* pb) const {
+    const double angle = Angle(origin, pa, pb);
+    return angle < 0;
+}
+
 bool Sweep::AngleExceeds90Degrees(const Point* origin, const Point* pa, const Point* pb) const {
   const double angle = Angle(origin, pa, pb);
   return ((angle > PI_div2) || (angle < -PI_div2));

poly2tri/sweep/sweep.h

@@ -172,6 +172,7 @@ class Sweep
   // Decision-making about when to Fill hole.
   // Contributed by ToolmakerSteve2
   bool LargeHole_DontFill(const Node* node) const;
+  bool AngleIsNegative(const Point* origin, const Point* pa, const Point* pb) const;
   bool AngleExceeds90Degrees(const Point* origin, const Point* pa, const Point* pb) const;
   bool AngleExceedsPlus90DegreesOrIsNegative(const Point* origin, const Point* pa, const Point* pb) const;
   double Angle(const Point* origin, const Point* pa, const Point* pb) const;