Allow degenerate triangles in polygon triangulation when necessary.
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8df449100a
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2 changed files with 37 additions and 10 deletions
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@ -51,7 +51,8 @@ real_t Triangulate::get_area(const Vector<Vector2> &contour) {
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bool Triangulate::is_inside_triangle(real_t Ax, real_t Ay,
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real_t Bx, real_t By,
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real_t Cx, real_t Cy,
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real_t Px, real_t Py)
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real_t Px, real_t Py,
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bool include_edges)
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{
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real_t ax, ay, bx, by, cx, cy, apx, apy, bpx, bpy, cpx, cpy;
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@ -74,10 +75,14 @@ bool Triangulate::is_inside_triangle(real_t Ax, real_t Ay,
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cCROSSap = cx * apy - cy * apx;
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bCROSScp = bx * cpy - by * cpx;
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return ((aCROSSbp > 0.0) && (bCROSScp > 0.0) && (cCROSSap > 0.0));
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if (include_edges) {
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return ((aCROSSbp > 0.0) && (bCROSScp > 0.0) && (cCROSSap > 0.0));
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} else {
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return ((aCROSSbp >= 0.0) && (bCROSScp >= 0.0) && (cCROSSap >= 0.0));
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}
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};
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bool Triangulate::snip(const Vector<Vector2> &p_contour, int u, int v, int w, int n, const Vector<int> &V) {
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bool Triangulate::snip(const Vector<Vector2> &p_contour, int u, int v, int w, int n, const Vector<int> &V, bool relaxed) {
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int p;
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real_t Ax, Ay, Bx, By, Cx, Cy, Px, Py;
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const Vector2 *contour = &p_contour[0];
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@ -91,13 +96,20 @@ bool Triangulate::snip(const Vector<Vector2> &p_contour, int u, int v, int w, in
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Cx = contour[V[w]].x;
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Cy = contour[V[w]].y;
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if (CMP_EPSILON > (((Bx - Ax) * (Cy - Ay)) - ((By - Ay) * (Cx - Ax)))) return false;
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// It can happen that the triangulation ends up with three aligned vertices to deal with.
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// In this scenario, making the check below strict may reject the possibility of
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// forming a last triangle with these aligned vertices, preventing the triangulatiom
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// from completing.
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// To avoid that we allow zero-area triangles if all else failed.
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float threshold = relaxed ? -CMP_EPSILON : CMP_EPSILON;
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if (threshold > (((Bx - Ax) * (Cy - Ay)) - ((By - Ay) * (Cx - Ax)))) return false;
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for (p = 0; p < n; p++) {
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if ((p == u) || (p == v) || (p == w)) continue;
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Px = contour[V[p]].x;
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Py = contour[V[p]].y;
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if (is_inside_triangle(Ax, Ay, Bx, By, Cx, Cy, Px, Py)) return false;
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if (is_inside_triangle(Ax, Ay, Bx, By, Cx, Cy, Px, Py, relaxed)) return false;
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}
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return true;
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@ -121,6 +133,8 @@ bool Triangulate::triangulate(const Vector<Vector2> &contour, Vector<int> &resul
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for (int v = 0; v < n; v++)
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V[v] = (n - 1) - v;
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bool relaxed = false;
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int nv = n;
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/* remove nv-2 Vertices, creating 1 triangle every time */
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@ -129,8 +143,20 @@ bool Triangulate::triangulate(const Vector<Vector2> &contour, Vector<int> &resul
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for (int v = nv - 1; nv > 2;) {
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/* if we loop, it is probably a non-simple polygon */
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if (0 >= (count--)) {
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//** Triangulate: ERROR - probable bad polygon!
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return false;
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if (relaxed) {
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//** Triangulate: ERROR - probable bad polygon!
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return false;
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} else {
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// There may be aligned vertices that the strict
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// checks prevent from triangulating. In this situation
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// we are better off adding flat triangles than
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// failing, so we relax the checks and try one last
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// round.
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// Only relaxing the constraints as a last resort avoids
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// degenerate triangles when they aren't necessary.
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count = 2 * nv;
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relaxed = true;
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}
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}
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/* three consecutive vertices in current polygon, <u,v,w> */
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@ -141,7 +167,7 @@ bool Triangulate::triangulate(const Vector<Vector2> &contour, Vector<int> &resul
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int w = v + 1;
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if (nv <= w) w = 0; /* next */
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if (snip(contour, u, v, w, nv, V)) {
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if (snip(contour, u, v, w, nv, V, relaxed)) {
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int a, b, c, s, t;
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/* true names of the vertices */
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@ -51,10 +51,11 @@ public:
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static bool is_inside_triangle(real_t Ax, real_t Ay,
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real_t Bx, real_t By,
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real_t Cx, real_t Cy,
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real_t Px, real_t Py);
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real_t Px, real_t Py,
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bool include_edges);
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private:
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static bool snip(const Vector<Vector2> &p_contour, int u, int v, int w, int n, const Vector<int> &V);
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static bool snip(const Vector<Vector2> &p_contour, int u, int v, int w, int n, const Vector<int> &V, bool relaxed);
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};
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#endif
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