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Fix [#31807] Ngon triangulation error

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Notes:
*This implements a quite simple algorithm, which simply checks angles (actually, absolute cosines) of created tri and remaining face (which may be a tri, quad, or more NGon), so that both are "best" (ie avoid as much as possible too much narrow/wide corners), and also checks the new edge is OK (i.e. does not goes "out" of original face).
*Incidently, it fixes a typo in that bm_face_goodline() func!
*It's quite performant (a bit quicker than previous code, as far as I have tested it) and prevent creation of completely flat triangles as much as possible, but it's far from being a "best" solution (as it is still a "progressive" one)!
*It also introduces a new math func (in BLI_math_vector.h), cos_v3v3v3, which computes cosine (ie dot product of normalized vectors) and is roughly a quicker replacement for angle_v3v3v3, when real angles are not needed.
This commit is contained in:
Bastien Montagne
2012-06-24 16:19:19 +00:00
parent e60c2f5c3e
commit df9ca0455c
3 changed files with 127 additions and 19 deletions
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1
source/blender/blenlib/BLI_math_vector.h
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@@ -191,6 +191,7 @@ float angle_v2v2v2(const float a[2], const float b[2], const float c[2]);
float angle_normalized_v2v2(const float a[2], const float b[2]);
float angle_v3v3(const float a[3], const float b[3]);
float angle_v3v3v3(const float a[3], const float b[3], const float c[3]);
float cos_v3v3v3(const float p1[3], const float p2[3], const float p3[3]);
float angle_normalized_v3v3(const float v1[3], const float v2[3]);
float angle_on_axis_v3v3v3_v3(const float v1[3], const float v2[3], const float v3[3], const float axis[3]);
void angle_tri_v3(float angles[3], const float v1[3], const float v2[3], const float v3[3]);

13
source/blender/blenlib/intern/math_vector.c
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@@ -136,6 +136,19 @@ float angle_v3v3v3(const float v1[3], const float v2[3], const float v3[3])
return angle_normalized_v3v3(vec1, vec2);
}
/* Quicker than full angle computation */
float cos_v3v3v3(const float p1[3], const float p2[3], const float p3[3])
{
float vec1[3], vec2[3];
sub_v3_v3v3(vec1, p2, p1);
sub_v3_v3v3(vec2, p2, p3);
normalize_v3(vec1);
normalize_v3(vec2);
return dot_v3v3(vec1, vec2);
}
/* Return the shortest angle in radians between the 2 vectors */
float angle_v3v3(const float v1[3], const float v2[3])
{

132
source/blender/bmesh/intern/bmesh_polygon.c
View File

@@ -642,7 +642,7 @@ static int bm_face_goodline(float const (*projectverts)[3], BMFace *f,
//if (linecrossesf(pv1, pv2, v1, v3)) return FALSE;
if (isect_point_tri_v2(pv1, v1, v2, v3) ||
isect_point_tri_v2(pv1, v3, v2, v1))
isect_point_tri_v2(pv2, v3, v2, v1))
{
return FALSE;
}
@@ -658,18 +658,22 @@ static int bm_face_goodline(float const (*projectverts)[3], BMFace *f,
* of a polygon while tessellating.
*
* \param use_beauty Currently only applies to quads, can be extended later on.
* \param abscoss Must be allocated by caller, and at least f->len length
* (allow to avoid allocating a new one for each tri!).
*/
static BMLoop *find_ear(BMFace *f, float (*verts)[3], const int nvert, const int use_beauty)
static BMLoop *find_ear(BMFace *f, float (*verts)[3], const int nvert, const int use_beauty, float *abscoss)
{
BMLoop *bestear = NULL;
BMLoop *l_iter;
BMLoop *l_first;
const float cos_threshold = 0.9f;
if (f->len == 4) {
BMLoop *larr[4];
int i = 0;
int i = 0, i4;
float cos1, cos2;
l_iter = l_first = BM_FACE_FIRST_LOOP(f);
do {
larr[i] = l_iter;
@@ -677,17 +681,60 @@ static BMLoop *find_ear(BMFace *f, float (*verts)[3], const int nvert, const int
} while ((l_iter = l_iter->next) != l_first);
/* pick 0/1 based on best lenth */
bestear = larr[(((len_squared_v3v3(larr[0]->v->co, larr[2]->v->co) >
len_squared_v3v3(larr[1]->v->co, larr[3]->v->co))) != use_beauty)];
/* XXX Can't only rely on such test, also must check we do not get (too much) degenerated triangles!!! */
i = (((len_squared_v3v3(larr[0]->v->co, larr[2]->v->co) >
len_squared_v3v3(larr[1]->v->co, larr[3]->v->co))) != use_beauty);
i4 = (i + 3) % 4;
/* Check produced tris aren’t too flat/narrow...
* Probably not the best test, but is quite efficient and should at least avoid null-area faces! */
cos1 = fabsf(cos_v3v3v3(larr[i4]->v->co, larr[i]->v->co, larr[i + 1]->v->co));
cos2 = fabsf(cos_v3v3v3(larr[i4]->v->co, larr[i + 2]->v->co, larr[i + 1]->v->co));
#if 0
printf("%d, (%f, %f), (%f, %f)\n", i, cos1, cos2,
fabsf(cos_v3v3v3(larr[i]->v->co, larr[i4]->v->co, larr[i + 2]->v->co)),
fabsf(cos_v3v3v3(larr[i]->v->co, larr[i + 1]->v->co, larr[i + 2]->v->co)));
#endif
if (cos1 < cos2)
cos1 = cos2;
if (cos1 > cos_threshold) {
if (cos1 > fabsf(cos_v3v3v3(larr[i]->v->co, larr[i4]->v->co, larr[i + 2]->v->co)) &&
cos1 > fabsf(cos_v3v3v3(larr[i]->v->co, larr[i + 1]->v->co, larr[i + 2]->v->co)))
i = !i;
}
/* Last check we do not get overlapping triangles
* (as much as possible, ther are some cases with no good solution!) */
i4 = (i + 3) % 4;
if (!bm_face_goodline((float const (*)[3])verts, f, BM_elem_index_get(larr[i4]->v), BM_elem_index_get(larr[i]->v),
BM_elem_index_get(larr[i + 1]->v), nvert))
i = !i;
/* printf("%d\n", i);*/
bestear = larr[i];
}
else {
BMVert *v1, *v2, *v3;
/* float angle, bestangle = 180.0f; */
int isear /*, i = 0 */;
float cos, tcos, bestcos = 1.0f;
float *tcoss;
int isear, i = 0, j, len;
/* Compute cos of all corners! */
l_iter = l_first = BM_FACE_FIRST_LOOP(f);
len = l_iter->f->len;
tcoss = abscoss;
do {
v1 = l_iter->prev->v;
v2 = l_iter->v;
v3 = l_iter->next->v;
*tcoss = fabsf(cos_v3v3v3(v1->co, v2->co, v3->co));
/* printf("tcoss: %f\n", *tcoss);*/
tcoss++;
} while ((l_iter = l_iter->next) != l_first);
l_iter = l_first;
tcoss = abscoss;
do {
isear = TRUE;
@@ -695,6 +742,7 @@ static BMLoop *find_ear(BMFace *f, float (*verts)[3], const int nvert, const int
v2 = l_iter->v;
v3 = l_iter->next->v;
/* We may have already internal edges... */
if (BM_edge_exists(v1, v3)) {
isear = FALSE;
}
@@ -706,7 +754,7 @@ static BMLoop *find_ear(BMFace *f, float (*verts)[3], const int nvert, const int
}
if (isear) {
#if 0
#if 0 /* Old, already commented code */
/* if this code comes back, it needs to be converted to radians */
angle = angle_v3v3v3(verts[v1->head.eflag2], verts[v2->head.eflag2], verts[v3->head.eflag2]);
if (!bestear || ABS(angle - 45.0f) < bestangle) {
@@ -717,11 +765,46 @@ static BMLoop *find_ear(BMFace *f, float (*verts)[3], const int nvert, const int
if (angle > 20 && angle < 90) break;
if (angle < 100 && i > 5) break;
i += 1;
#endif
#endif
bestear = l_iter;
break;
/* Compute highest cos (i.e. narrowest angle) of this tri. */
cos = *tcoss;
tcos = fabsf(cos_v3v3v3(v2->co, v3->co, v1->co));
if (tcos > cos)
cos = tcos;
tcos = fabsf(cos_v3v3v3(v3->co, v1->co, v2->co));
if (tcos > cos)
cos = tcos;
/* Compare to prev best (i.e. lowest) cos. */
if (cos < bestcos) {
/* We must check this tri would not leave a (too much) degenerated remaining face! */
/* For now just assume if the average of cos of all "remaining face"'s corners is below a given threshold, it’s OK. */
float avgcos = fabsf(cos_v3v3v3(v1->co, v3->co, l_iter->next->next->v->co));
const int i_limit = (i - 1 + len) % len;
avgcos += fabsf(cos_v3v3v3(l_iter->prev->prev->v->co, v1->co, v3->co));
j = (i + 2) % len;
do {
avgcos += abscoss[j];
} while ((j = (j + 1) % len) != i_limit);
avgcos /= len - 1;
/* We need a best ear in any case... */
if (avgcos < cos_threshold || (!bestear && avgcos < 1.0f)) {
/* OKI, keep this ear (corner...) as a potential best one! */
bestear = l_iter;
bestcos = cos;
}
#if 0
else
printf("Had a nice tri (higest cos of %f, current bestcos is %f), "
"but average cos of all \"remaining face\"'s corners is too high (%f)!\n",
cos, bestcos, avgcos);
#endif
}
}
tcoss++;
i++;
} while ((l_iter = l_iter->next) != l_first);
}
@@ -731,14 +814,20 @@ static BMLoop *find_ear(BMFace *f, float (*verts)[3], const int nvert, const int
/**
* \brief BMESH TRIANGULATE FACE
*
* --- Prev description (wasn’t correct, ear clipping was currently simply picking the first tri in the loop!)
* Triangulates a face using a simple 'ear clipping' algorithm that tries to
* favor non-skinny triangles (angles less than 90 degrees).
*
* If the triangulator has bits left over (or cannot triangulate at all)
* it uses a simple fan triangulation,
* --- End of prev description
*
* Currently tries to repeatedly find the best triangle (i.e. the most "open" one), provided it does not
* produces a "remaining" face with too much wide/narrow angles
* (using cos (i.e. dot product of normalized vectors) of angles).
*
* newfaces, if non-null, must be an array of BMFace pointers,
* with a length equal to f->len. it will be filled with the new
* with a length equal to f->len. It will be filled with the new
* triangles, and will be NULL-terminated.
*
* \note newedgeflag sets a flag layer flag, obviously not the header flag.
@@ -748,10 +837,11 @@ void BM_face_triangulate(BMesh *bm, BMFace *f, float (*projectverts)[3],
const short use_beauty)
{
int i, done, nvert, nf_i = 0;
BMLoop *newl, *nextloop;
BMLoop *newl;
BMLoop *l_iter;
BMLoop *l_first;
/* BMVert *v; */ /* UNUSED */
float *abscoss = NULL;
BLI_array_fixedstack_declare(abscoss, 16, f->len, "BM_face_triangulate: temp absolute cosines of face corners");
/* copy vertex coordinates to vertspace arra */
i = 0;
@@ -764,14 +854,14 @@ void BM_face_triangulate(BMesh *bm, BMFace *f, float (*projectverts)[3],
bm->elem_index_dirty |= BM_VERT; /* see above */
///bmesh_face_normal_update(bm, f, f->no, projectverts);
/* bmesh_face_normal_update(bm, f, f->no, projectverts); */
calc_poly_normal(f->no, projectverts, f->len);
poly_rotate_plane(f->no, projectverts, i);
nvert = f->len;
//calc_poly_plane(projectverts, i);
/* calc_poly_plane(projectverts, i); */
for (i = 0; i < nvert; i++) {
projectverts[i][2] = 0.0f;
}
@@ -779,10 +869,10 @@ void BM_face_triangulate(BMesh *bm, BMFace *f, float (*projectverts)[3],
done = FALSE;
while (!done && f->len > 3) {
done = TRUE;
l_iter = find_ear(f, projectverts, nvert, use_beauty);
l_iter = find_ear(f, projectverts, nvert, use_beauty, abscoss);
if (l_iter) {
done = FALSE;
/* v = l->v; */ /* UNUSED */
/* printf("Subdividing face...\n");*/
f = BM_face_split(bm, l_iter->f, l_iter->prev->v,
l_iter->next->v,
&newl, NULL, TRUE);
@@ -812,6 +902,7 @@ void BM_face_triangulate(BMesh *bm, BMFace *f, float (*projectverts)[3],
}
}
#if 0 /* XXX find_ear should now always return a corner, so no more need for this piece of code... */
if (f->len > 3) {
l_iter = BM_FACE_FIRST_LOOP(f);
while (l_iter->f->len > 3) {
@@ -833,7 +924,10 @@ void BM_face_triangulate(BMesh *bm, BMFace *f, float (*projectverts)[3],
l_iter = nextloop;
}
}
#endif
BLI_array_fixedstack_free(abscoss);
/* NULL-terminate */
if (newfaces) newfaces[nf_i] = NULL;
}