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Math Lib: improve area calculation

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- area_quad_v3 now works correctly with concave quads.
- add area_squared_*** functions, to use when comparing to avoid a sqrt().
This commit is contained in:
Campbell Barton 2015-01-13 19:01:40 +11:00
parent 00ef77c1a2
commit 3debcc8b51
5 changed files with 70 additions and 46 deletions
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7
source/blender/blenkernel/intern/mesh_evaluate.c
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@ -896,13 +896,6 @@ float BKE_mesh_calc_poly_area(MPoly *mpoly, MLoop *loopstart,
mvarray[loopstart[2].v].co
);
}
else if (mpoly->totloop == 4) {
return area_quad_v3(mvarray[loopstart[0].v].co,
mvarray[loopstart[1].v].co,
mvarray[loopstart[2].v].co,
mvarray[loopstart[3].v].co
);
}
else {
int i;
MLoop *l_iter = loopstart;

7
source/blender/blenlib/BLI_math_geom.h
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@ -52,16 +52,23 @@ float normal_quad_v3(float r[3], const float a[3], const float b[3], const float
float normal_poly_v3(float r[3], const float verts[][3], unsigned int nr);
MINLINE float area_tri_v2(const float a[2], const float b[2], const float c[2]);
MINLINE float area_squared_tri_v2(const float a[2], const float b[2], const float c[2]);
MINLINE float area_tri_signed_v2(const float v1[2], const float v2[2], const float v3[2]);
float area_tri_v3(const float a[3], const float b[3], const float c[3]);
float area_squared_tri_v3(const float a[3], const float b[3], const float c[3]);
float area_tri_signed_v3(const float v1[3], const float v2[3], const float v3[3], const float normal[3]);
float area_quad_v3(const float a[3], const float b[3], const float c[3], const float d[3]);
float area_squared_quad_v3(const float a[3], const float b[3], const float c[3], const float d[3]);
float area_poly_v3(const float verts[][3], unsigned int nr);
float area_poly_v2(const float verts[][2], unsigned int nr);
float area_squared_poly_v3(const float verts[][3], unsigned int nr);
float area_squared_poly_v2(const float verts[][2], unsigned int nr);
float area_poly_signed_v2(const float verts[][2], unsigned int nr);
float cotangent_tri_weight_v3(const float v1[3], const float v2[3], const float v3[3]);
void cross_tri_v3(float n[3], const float v1[3], const float v2[3], const float v3[3]);
MINLINE float cross_tri_v2(const float v1[2], const float v2[2], const float v3[2]);
void cross_poly_v3(float n[3], const float verts[][3], unsigned int nr);
float cross_poly_v2(const float verts[][2], unsigned int nr);
/********************************* Planes **********************************/

93
source/blender/blenlib/intern/math_geom.c
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@ -109,58 +109,44 @@ float normal_quad_v3(float n[3], const float v1[3], const float v2[3], const flo
*/
float normal_poly_v3(float n[3], const float verts[][3], unsigned int nr)
{
const float *v_prev = verts[nr - 1];
const float *v_curr = verts[0];
unsigned int i;
zero_v3(n);
/* Newell's Method */
for (i = 0; i < nr; v_prev = v_curr, v_curr = verts[++i]) {
add_newell_cross_v3_v3v3(n, v_prev, v_curr);
}
cross_poly_v3(n, verts, nr);
return normalize_v3(n);
}
/* only convex Quadrilaterals */
float area_quad_v3(const float v1[3], const float v2[3], const float v3[3], const float v4[3])
{
float len, vec1[3], vec2[3], n[3];
const float verts[4][3] = {{UNPACK3(v1)}, {UNPACK3(v2)}, {UNPACK3(v3)}, {UNPACK3(v4)}};
return area_poly_v3(verts, 4);
}
sub_v3_v3v3(vec1, v2, v1);
sub_v3_v3v3(vec2, v4, v1);
cross_v3_v3v3(n, vec1, vec2);
len = len_v3(n);
sub_v3_v3v3(vec1, v4, v3);
sub_v3_v3v3(vec2, v2, v3);
cross_v3_v3v3(n, vec1, vec2);
len += len_v3(n);
return (len / 2.0f);
float area_squared_quad_v3(const float v1[3], const float v2[3], const float v3[3], const float v4[3])
{
const float verts[4][3] = {{UNPACK3(v1)}, {UNPACK3(v2)}, {UNPACK3(v3)}, {UNPACK3(v4)}};
return area_squared_poly_v3(verts, 4);
}
/* Triangles */
float area_tri_v3(const float v1[3], const float v2[3], const float v3[3])
{
float vec1[3], vec2[3], n[3];
float n[3];
cross_tri_v3(n, v1, v2, v3);
return len_v3(n) * 0.5f;
}
sub_v3_v3v3(vec1, v3, v2);
sub_v3_v3v3(vec2, v1, v2);
cross_v3_v3v3(n, vec1, vec2);
return len_v3(n) / 2.0f;
float area_squared_tri_v3(const float v1[3], const float v2[3], const float v3[3])
{
float n[3];
cross_tri_v3(n, v1, v2, v3);
mul_v3_fl(n, 0.5f);
return len_squared_v3(n);
}
float area_tri_signed_v3(const float v1[3], const float v2[3], const float v3[3], const float normal[3])
{
float area, vec1[3], vec2[3], n[3];
float area, n[3];
sub_v3_v3v3(vec1, v3, v2);
sub_v3_v3v3(vec2, v1, v2);
cross_v3_v3v3(n, vec1, vec2);
area = len_v3(n) / 2.0f;
cross_tri_v3(n, v1, v2, v3);
area = len_v3(n) * 0.5f;
/* negate area for flipped triangles */
if (dot_v3v3(n, normal) < 0.0f)
@ -172,7 +158,17 @@ float area_tri_signed_v3(const float v1[3], const float v2[3], const float v3[3]
float area_poly_v3(const float verts[][3], unsigned int nr)
{
float n[3];
return normal_poly_v3(n, verts, nr) * 0.5f;
cross_poly_v3(n, verts, nr);
return len_v3(n) * 0.5f;
}
float area_squared_poly_v3(const float verts[][3], unsigned int nr)
{
float n[3];
cross_poly_v3(n, verts, nr);
mul_v3_fl(n, 0.5f);
return len_squared_v3(n);
}
/**
@ -200,11 +196,36 @@ float cross_poly_v2(const float verts[][2], unsigned int nr)
return cross;
}
void cross_poly_v3(float n[3], const float verts[][3], unsigned int nr)
{
const float *v_prev = verts[nr - 1];
const float *v_curr = verts[0];
unsigned int i;
zero_v3(n);
/* Newell's Method */
for (i = 0; i < nr; v_prev = v_curr, v_curr = verts[++i]) {
add_newell_cross_v3_v3v3(n, v_prev, v_curr);
}
}
float area_poly_v2(const float verts[][2], unsigned int nr)
{
return fabsf(0.5f * cross_poly_v2(verts, nr));
}
float area_poly_signed_v2(const float verts[][2], unsigned int nr)
{
return (0.5f * cross_poly_v2(verts, nr));
}
float area_squared_poly_v2(const float verts[][2], unsigned int nr)
{
float area = area_poly_signed_v2(verts, nr);
return area * area;
}
float cotangent_tri_weight_v3(const float v1[3], const float v2[3], const float v3[3])
{
float a[3], b[3], c[3], c_len;

6
source/blender/blenlib/intern/math_geom_inline.c
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@ -54,6 +54,12 @@ MINLINE float area_tri_v2(const float v1[2], const float v2[2], const float v3[2
return fabsf(area_tri_signed_v2(v1, v2, v3));
}
MINLINE float area_squared_tri_v2(const float v1[2], const float v2[2], const float v3[2])
{
float area = area_tri_signed_v2(v1, v2, v3);
return area * area;
}
/****************************** Spherical Harmonics **************************/
MINLINE void zero_sh(float r[9])

3
source/blender/bmesh/intern/bmesh_polygon.c
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@ -214,9 +214,6 @@ float BM_face_calc_area(BMFace *f)
if (f->len == 3) {
area = area_tri_v3(verts[0], verts[1], verts[2]);
}
else if (f->len == 4) {
area = area_quad_v3(verts[0], verts[1], verts[2], verts[3]);
}
else {
area = area_poly_v3((const float (*)[3])verts, f->len);
}