diff options
Diffstat (limited to 'core/math/triangulate.cpp')
| -rw-r--r-- | core/math/triangulate.cpp | 42 |
1 files changed, 34 insertions, 8 deletions
diff --git a/core/math/triangulate.cpp b/core/math/triangulate.cpp index 5bae74ac7e..563ba7268f 100644 --- a/core/math/triangulate.cpp +++ b/core/math/triangulate.cpp @@ -51,7 +51,8 @@ real_t Triangulate::get_area(const Vector<Vector2> &contour) { bool Triangulate::is_inside_triangle(real_t Ax, real_t Ay, real_t Bx, real_t By, real_t Cx, real_t Cy, - real_t Px, real_t Py) + real_t Px, real_t Py, + bool include_edges) { real_t ax, ay, bx, by, cx, cy, apx, apy, bpx, bpy, cpx, cpy; @@ -74,10 +75,14 @@ bool Triangulate::is_inside_triangle(real_t Ax, real_t Ay, cCROSSap = cx * apy - cy * apx; bCROSScp = bx * cpy - by * cpx; - return ((aCROSSbp > 0.0) && (bCROSScp > 0.0) && (cCROSSap > 0.0)); + if (include_edges) { + return ((aCROSSbp > 0.0) && (bCROSScp > 0.0) && (cCROSSap > 0.0)); + } else { + return ((aCROSSbp >= 0.0) && (bCROSScp >= 0.0) && (cCROSSap >= 0.0)); + } }; -bool Triangulate::snip(const Vector<Vector2> &p_contour, int u, int v, int w, int n, const Vector<int> &V) { +bool Triangulate::snip(const Vector<Vector2> &p_contour, int u, int v, int w, int n, const Vector<int> &V, bool relaxed) { int p; real_t Ax, Ay, Bx, By, Cx, Cy, Px, Py; const Vector2 *contour = &p_contour[0]; @@ -91,13 +96,20 @@ bool Triangulate::snip(const Vector<Vector2> &p_contour, int u, int v, int w, in Cx = contour[V[w]].x; Cy = contour[V[w]].y; - if (CMP_EPSILON > (((Bx - Ax) * (Cy - Ay)) - ((By - Ay) * (Cx - Ax)))) return false; + // It can happen that the triangulation ends up with three aligned vertices to deal with. + // In this scenario, making the check below strict may reject the possibility of + // forming a last triangle with these aligned vertices, preventing the triangulatiom + // from completing. + // To avoid that we allow zero-area triangles if all else failed. + float threshold = relaxed ? -CMP_EPSILON : CMP_EPSILON; + + if (threshold > (((Bx - Ax) * (Cy - Ay)) - ((By - Ay) * (Cx - Ax)))) return false; for (p = 0; p < n; p++) { if ((p == u) || (p == v) || (p == w)) continue; Px = contour[V[p]].x; Py = contour[V[p]].y; - if (is_inside_triangle(Ax, Ay, Bx, By, Cx, Cy, Px, Py)) return false; + if (is_inside_triangle(Ax, Ay, Bx, By, Cx, Cy, Px, Py, relaxed)) return false; } return true; @@ -121,6 +133,8 @@ bool Triangulate::triangulate(const Vector<Vector2> &contour, Vector<int> &resul for (int v = 0; v < n; v++) V[v] = (n - 1) - v; + bool relaxed = false; + int nv = n; /* remove nv-2 Vertices, creating 1 triangle every time */ @@ -129,8 +143,20 @@ bool Triangulate::triangulate(const Vector<Vector2> &contour, Vector<int> &resul for (int v = nv - 1; nv > 2;) { /* if we loop, it is probably a non-simple polygon */ if (0 >= (count--)) { - //** Triangulate: ERROR - probable bad polygon! - return false; + if (relaxed) { + //** Triangulate: ERROR - probable bad polygon! + return false; + } else { + // There may be aligned vertices that the strict + // checks prevent from triangulating. In this situation + // we are better off adding flat triangles than + // failing, so we relax the checks and try one last + // round. + // Only relaxing the constraints as a last resort avoids + // degenerate triangles when they aren't necessary. + count = 2 * nv; + relaxed = true; + } } /* three consecutive vertices in current polygon, <u,v,w> */ @@ -141,7 +167,7 @@ bool Triangulate::triangulate(const Vector<Vector2> &contour, Vector<int> &resul int w = v + 1; if (nv <= w) w = 0; /* next */ - if (snip(contour, u, v, w, nv, V)) { + if (snip(contour, u, v, w, nv, V, relaxed)) { int a, b, c, s, t; /* true names of the vertices */ |