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Add function to find closest point in triangle to another point

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New function is closest_to_tri_v3() in BLI_math_geom.
This commit is contained in:
Nicholas Bishop
2012-12-30 18:23:03 +00:00
parent 2d39e46414
commit 66e70e6caa
2 changed files with 85 additions and 0 deletions
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3
source/blender/blenlib/BLI_math_geom.h
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@@ -72,6 +72,9 @@ float closest_to_line_v2(float r[2], const float p[2], const float l1[2], const
void closest_to_line_segment_v3(float r[3], const float p[3], const float l1[3], const float l2[3]);
void closest_to_plane_v3(float r[3], const float plane_co[3], const float plane_no_unit[3], const float pt[3]);
/* Set 'r' to the point in triangle (t1, t2, t3) closest to point 'p' */
void closest_on_tri_to_point_v3(float r[3], const float p[3], const float t1[3], const float t2[3], const float t3[3]);
float line_point_factor_v3(const float p[3], const float l1[3], const float l2[3]);
float line_point_factor_v2(const float p[2], const float l1[2], const float l2[2]);

82
source/blender/blenlib/intern/math_geom.c
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@@ -296,6 +296,88 @@ float dist_to_line_segment_v3(const float v1[3], const float v2[3], const float
return len_v3v3(closest, v1);
}
/* Adapted from "Real-Time Collision Detection" by Christer Ericson,
* published by Morgan Kaufmann Publishers, copyright 2005 Elsevier Inc.
*
* Set 'r' to the point in triangle (a, b, c) closest to point 'p' */
void closest_on_tri_to_point_v3(float r[3], const float p[3],
const float a[3], const float b[3], const float c[3])
{
float ab[3], ac[3], ap[3], d1, d2;
float bp[3], d3, d4, vc, cp[3], d5, d6, vb, va;
float denom, v, w;
/* Check if P in vertex region outside A */
sub_v3_v3v3(ab, b, a);
sub_v3_v3v3(ac, c, a);
sub_v3_v3v3(ap, p, a);
d1 = dot_v3v3(ab, ap);
d2 = dot_v3v3(ac, ap);
if (d1 <= 0.0f && d2 <= 0.0f) {
/* barycentric coordinates (1,0,0) */
copy_v3_v3(r, a);
return;
}
/* Check if P in vertex region outside B */
sub_v3_v3v3(bp, p, b);
d3 = dot_v3v3(ab, bp);
d4 = dot_v3v3(ac, bp);
if (d3 >= 0.0f && d4 <= d3) {
/* barycentric coordinates (0,1,0) */
copy_v3_v3(r, b);
return;
}
/* Check if P in edge region of AB, if so return projection of P onto AB */
vc = d1*d4 - d3*d2;
if (vc <= 0.0f && d1 >= 0.0f && d3 <= 0.0f) {
float v = d1 / (d1 - d3);
/* barycentric coordinates (1-v,v,0) */
madd_v3_v3v3fl(r, a, ab, v);
return;
}
/* Check if P in vertex region outside C */
sub_v3_v3v3(cp, p, c);
d5 = dot_v3v3(ab, cp);
d6 = dot_v3v3(ac, cp);
if (d6 >= 0.0f && d5 <= d6) {
/* barycentric coordinates (0,0,1) */
copy_v3_v3(r, c);
return;
}
/* Check if P in edge region of AC, if so return projection of P onto AC */
vb = d5*d2 - d1*d6;
if (vb <= 0.0f && d2 >= 0.0f && d6 <= 0.0f) {
float w = d2 / (d2 - d6);
/* barycentric coordinates (1-w,0,w) */
madd_v3_v3v3fl(r, a, ac, w);
return;
}
/* Check if P in edge region of BC, if so return projection of P onto BC */
va = d3*d6 - d5*d4;
if (va <= 0.0f && (d4 - d3) >= 0.0f && (d5 - d6) >= 0.0f) {
float w = (d4 - d3) / ((d4 - d3) + (d5 - d6));
/* barycentric coordinates (0,1-w,w) */
sub_v3_v3v3(r, c, b);
mul_v3_fl(r, w);
add_v3_v3(r, b);
return;
}
/* P inside face region. Compute Q through its barycentric coordinates (u,v,w) */
denom = 1.0f / (va + vb + vc);
v = vb * denom;
w = vc * denom;
/* = u*a + v*b + w*c, u = va * denom = 1.0f - v - w */
/* ac * w */
mul_v3_fl(ac, w);
/* a + ab * v */
madd_v3_v3v3fl(r, a, ab, v);
/* a + ab * v + ac * w */
add_v3_v3(r, ac);
}
/******************************* Intersection ********************************/
/* intersect Line-Line, shorts */