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Allow degenerate triangles in polygon triangulation when necessary.

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This commit is contained in:
Nicolas Silva 2018-02-28 22:46:56 -05:00
parent 8df449100a
commit e73266a51c
2 changed files with 37 additions and 10 deletions
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42
core/math/triangulate.cpp
View file

@ -51,7 +51,8 @@ real_t Triangulate::get_area(const Vector<Vector2> &contour) {
bool Triangulate::is_inside_triangle(real_t Ax, real_t Ay, bool Triangulate::is_inside_triangle(real_t Ax, real_t Ay,
real_t Bx, real_t By, real_t Bx, real_t By,
real_t Cx, real_t Cy, 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; 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; cCROSSap = cx * apy - cy * apx;
bCROSScp = bx * cpy - by * cpx; 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; int p;
real_t Ax, Ay, Bx, By, Cx, Cy, Px, Py; real_t Ax, Ay, Bx, By, Cx, Cy, Px, Py;
const Vector2 *contour = &p_contour[0]; 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; Cx = contour[V[w]].x;
Cy = contour[V[w]].y; 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++) { for (p = 0; p < n; p++) {
if ((p == u) || (p == v) || (p == w)) continue; if ((p == u) || (p == v) || (p == w)) continue;
Px = contour[V[p]].x; Px = contour[V[p]].x;
Py = contour[V[p]].y; 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; return true;
@ -121,6 +133,8 @@ bool Triangulate::triangulate(const Vector<Vector2> &contour, Vector<int> &resul
for (int v = 0; v < n; v++) for (int v = 0; v < n; v++)
V[v] = (n - 1) - v; V[v] = (n - 1) - v;
bool relaxed = false;
int nv = n; int nv = n;
/* remove nv-2 Vertices, creating 1 triangle every time */ /* 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;) { for (int v = nv - 1; nv > 2;) {
/* if we loop, it is probably a non-simple polygon */ /* if we loop, it is probably a non-simple polygon */
if (0 >= (count--)) { if (0 >= (count--)) {
//** Triangulate: ERROR - probable bad polygon! if (relaxed) {
return false; //** 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> */ /* 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; int w = v + 1;
if (nv <= w) w = 0; /* next */ 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; int a, b, c, s, t;
/* true names of the vertices */ /* true names of the vertices */

5
core/math/triangulate.h
View file

@ -51,10 +51,11 @@ public:
static bool is_inside_triangle(real_t Ax, real_t Ay, static bool is_inside_triangle(real_t Ax, real_t Ay,
real_t Bx, real_t By, real_t Bx, real_t By,
real_t Cx, real_t Cy, real_t Cx, real_t Cy,
real_t Px, real_t Py); real_t Px, real_t Py,
bool include_edges);
private: private:
static bool snip(const Vector<Vector2> &p_contour, int u, int v, int w, int n, const Vector<int> &V); static bool snip(const Vector<Vector2> &p_contour, int u, int v, int w, int n, const Vector<int> &V, bool relaxed);
}; };
#endif #endif