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Mesh Center: improved center-of-mass calculation

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Previous method was based on face-area, giving un-even results
based on topology and gave issues with zero area faces.

This method gives matching results for concave ngons and the same geometry triangulated.
This commit is contained in:
Bill Currie 2017-05-12 11:04:03 +10:00 committed by Campbell Barton
parent 868678c85f
commit 37bc3850ce
1 changed files with 49 additions and 28 deletions
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77
source/blender/blenkernel/intern/mesh_evaluate.c
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@ -1993,36 +1993,54 @@ float BKE_mesh_calc_poly_area(
}
}
/* note, results won't be correct if polygon is non-planar */
static float mesh_calc_poly_planar_area_centroid(
/**
* Calculate the volume and volume-weighted centroid of the volume formed by the polygon and the origin.
* Results will be negative if the origin is "outside" the polygon
* (+ve normal side), but the polygon may be non-planar with no effect.
*
* Method from:
* - http://forums.cgsociety.org/archive/index.php?t-756235.html
* - http://www.globalspec.com/reference/52702/203279/4-8-the-centroid-of-a-tetrahedron
*
* \note volume is 6x actual volume, and centroid is 4x actual volume-weighted centroid
* (so division can be done once at the end)
* \note results will have bias if polygon is non-planar.
*/
static float mesh_calc_poly_volume_and_weighted_centroid(
const MPoly *mpoly, const MLoop *loopstart, const MVert *mvarray,
float r_cent[3])
{
int i;
float tri_area;
float total_area = 0.0f;
float v1[3], v2[3], v3[3], normal[3], tri_cent[3];
const float *v_pivot, *v_step1;
float total_volume = 0.0f;
BKE_mesh_calc_poly_normal(mpoly, loopstart, mvarray, normal);
copy_v3_v3(v1, mvarray[loopstart[0].v].co);
copy_v3_v3(v2, mvarray[loopstart[1].v].co);
zero_v3(r_cent);
for (i = 2; i < mpoly->totloop; i++) {
copy_v3_v3(v3, mvarray[loopstart[i].v].co);
v_pivot = mvarray[loopstart[0].v].co;
v_step1 = mvarray[loopstart[1].v].co;
tri_area = area_tri_signed_v3(v1, v2, v3, normal);
total_area += tri_area;
for (int i = 2; i < mpoly->totloop; i++) {
const float *v_step2 = mvarray[loopstart[i].v].co;
mid_v3_v3v3v3(tri_cent, v1, v2, v3);
madd_v3_v3fl(r_cent, tri_cent, tri_area);
/* Calculate the 6x volume of the tetrahedron formed by the 3 vertices
* of the triangle and the origin as the fourth vertex */
float v_cross[3];
cross_v3_v3v3(v_cross, v_pivot, v_step1);
const float tetra_volume = dot_v3v3 (v_cross, v_step2);
total_volume += tetra_volume;
copy_v3_v3(v2, v3);
/* Calculate the centroid of the tetrahedron formed by the 3 vertices
* of the triangle and the origin as the fourth vertex.
* The centroid is simply the average of the 4 vertices.
*
* Note that the vector is 4x the actual centroid so the division can be done once at the end. */
for (uint j = 0; j < 3; j++) {
r_cent[j] += tetra_volume * (v_pivot[j] + v_step1[j] + v_step2[j]);
}
v_step1 = v_step2;
}
mul_v3_fl(r_cent, 1.0f / total_area);
return total_area;
return total_volume;
}
#if 0 /* slow version of the function below */
@ -2143,25 +2161,28 @@ bool BKE_mesh_center_centroid(const Mesh *me, float r_cent[3])
{
int i = me->totpoly;
MPoly *mpoly;
float poly_area;
float total_area = 0.0f;
float poly_volume;
float total_volume = 0.0f;
float poly_cent[3];
zero_v3(r_cent);
/* calculate a weighted average of polygon centroids */
/* calculate a weighted average of polyhedron centroids */
for (mpoly = me->mpoly; i--; mpoly++) {
poly_area = mesh_calc_poly_planar_area_centroid(mpoly, me->mloop + mpoly->loopstart, me->mvert, poly_cent);
poly_volume = mesh_calc_poly_volume_and_weighted_centroid(mpoly, me->mloop + mpoly->loopstart, me->mvert, poly_cent);
madd_v3_v3fl(r_cent, poly_cent, poly_area);
total_area += poly_area;
/* poly_cent is already volume-weighted, so no need to multiply by the volume */
add_v3_v3(r_cent, poly_cent);
total_volume += poly_volume;
}
/* otherwise we get NAN for 0 polys */
if (me->totpoly) {
mul_v3_fl(r_cent, 1.0f / total_area);
if (total_volume != 0.0f) {
/* multipy by 0.25 to get the correct centroid */
/* no need to divide volume by 6 as the centroid is weighted by 6x the volume, so it all cancels out */
mul_v3_fl(r_cent, 0.25f / total_volume);
}
/* zero area faces cause this, fallback to median */
/* this can happen for non-manifold objects, fallback to median */
if (UNLIKELY(!is_finite_v3(r_cent))) {
return BKE_mesh_center_median(me, r_cent);
}