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https://git.code.sf.net/p/quake/quakeforge
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Add a function to get the barycentric coords of a point.
It "works" for lines, triangles and tetrahedrons. For lines and triangles, it gives the barycentric coordinates of the perpendicular projection of the point onto to features. Only tetrahedrons are guaranteed to reproduce the original point.
This commit is contained in:
Bill Currie
parent
fe55bb678e
commit
0cd6d93030
4 changed files with 174 additions and 2 deletions
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@ -213,6 +213,9 @@ R_CullSphere (const vec3_t origin, const float radius)
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return false;
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}
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void BarycentricCoords (const vec_t **points, int num_points, const vec3_t p,
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vec_t *lambda);
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//@}
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#endif // __mathlib_h
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@ -1151,3 +1151,52 @@ Mat4Decompose (const mat4_t mat, quat_t rot, vec3_t shear, vec3_t scale,
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Mat4toMat3 (mat, m3);
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return Mat3Decompose (m3, rot, shear, scale);
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}
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void
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BarycentricCoords (const vec_t **points, int num_points, const vec3_t p,
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vec_t *lambda)
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{
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vec3_t a, b, c, x, ab, bc, ca, n;
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vec_t div;
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if (num_points > 4)
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Sys_Error ("Don't know how to compute the barycentric coordinates "
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"for %d points", num_points);
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switch (num_points) {
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case 1:
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lambda[0] = 1;
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return;
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case 2:
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VectorSubtract (p, points[0], x);
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VectorSubtract (points[1], points[0], a);
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lambda[1] = DotProduct (x, a) / DotProduct (a, a);
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lambda[0] = 1 - lambda[1];
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return;
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case 3:
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VectorSubtract (p, points[0], x);
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VectorSubtract (points[1], points[0], a);
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VectorSubtract (points[2], points[0], b);
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CrossProduct (a, b, ab);
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div = DotProduct (ab, ab);
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CrossProduct (x, b, n);
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lambda[1] = DotProduct (n, ab) / div;
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CrossProduct (a, x, n);
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lambda[2] = DotProduct (n, ab) / div;
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lambda[0] = 1 - lambda[1] - lambda[2];
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return;
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case 4:
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VectorSubtract (p, points[0], x);
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VectorSubtract (points[1], points[0], a);
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VectorSubtract (points[2], points[0], b);
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VectorSubtract (points[3], points[0], c);
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CrossProduct (a, b, ab);
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CrossProduct (b, c, bc);
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CrossProduct (c, a, ca);
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div = DotProduct (a, bc);
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lambda[1] = DotProduct (x, bc) / div;
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lambda[2] = DotProduct (x, ca) / div;
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lambda[3] = DotProduct (x, ab) / div;
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lambda[0] = 1 - lambda[1] - lambda[2] - lambda[3];
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return;
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}
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Sys_Error ("Not enough points to project or enclose the point");
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}
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@ -3,8 +3,12 @@ AUTOMAKE_OPTIONS= foreign
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INCLUDES= -I$(top_srcdir)/include
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check_PROGRAMS= \
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test-dq test-half test-mat3 test-mat4 test-plist test-qfs test-quat \
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test-set test-vrect
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test-bary test-dq test-half test-mat3 test-mat4 test-plist test-qfs \
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test-quat test-set test-vrect
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test_bary_SOURCES=test-bary.c
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test_bary_LDADD=$(top_builddir)/libs/util/libQFutil.la
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test_bary_DEPENDENCIES=$(top_builddir)/libs/util/libQFutil.la
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test_dq_SOURCES=test-dq.c
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test_dq_LDADD=$(top_builddir)/libs/util/libQFutil.la
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116
libs/util/test/test-bary.c
Normal file
116
libs/util/test/test-bary.c
Normal file
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@ -0,0 +1,116 @@
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#ifdef HAVE_CONFIG_H
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# include "config.h"
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#endif
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#include "QF/mathlib.h"
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#include "QF/mersenne.h"
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#include "QF/sys.h"
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vec3_t points[] = {
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{-1, -1, 1},
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{ 1, 1, 1},
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{-1, 1, -1},
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{ 1, -1, -1},
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{-1, -1, -1},
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{ 1, 1, -1},
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{-1, 1, 1},
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{ 1, -1, 1},
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{ 0, 0, 0},
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};
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const vec_t *line[] = {points[0], points[1]};
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const vec_t *tri[] = {points[0], points[1], points[2]};
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const vec_t *tetra[] = {points[0], points[1], points[2], points[3]};
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struct {
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const vec_t **points;
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int num_points;
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vec_t *x;
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vec_t expect[4];
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} tests[] = {
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{line, 2, points[0], {1, 0}},
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{line, 2, points[1], {0, 1}},
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{line, 2, points[2], {0.5, 0.5}},
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{line, 2, points[3], {0.5, 0.5}},
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{line, 2, points[8], {0.5, 0.5}},
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{tri, 3, points[0], {1, 0, 0}},
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{tri, 3, points[1], {0, 1, 0}},
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{tri, 3, points[2], {0, 0, 1}},
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{tri, 3, points[3], {0.333333284, 0.333333333, 0.333333333}},//rounding :P
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{tri, 3, points[8], {0.333333284, 0.333333333, 0.333333333}},//rounding :P
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{tetra, 4, points[0], {1, 0, 0, 0}},
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{tetra, 4, points[1], {0, 1, 0, 0}},
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{tetra, 4, points[2], {0, 0, 1, 0}},
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{tetra, 4, points[3], {0, 0, 0, 1}},
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{tetra, 4, points[4], { 0.5, -0.5, 0.5, 0.5}},
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{tetra, 4, points[5], {-0.5, 0.5, 0.5, 0.5}},
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{tetra, 4, points[6], { 0.5, 0.5, 0.5, -0.5}},
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{tetra, 4, points[7], { 0.5, 0.5, -0.5, 0.5}},
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{tetra, 4, points[8], {0.25, 0.25, 0.25, 0.25}},
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};
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#define num_tests (sizeof (tests) / sizeof (tests[0]))
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static inline float
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rnd (mtstate_t *mt)
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{
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union {
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uint32_t u;
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float f;
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} uf;
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do {
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uf.u = mtwist_rand (mt) & 0x3fffffff;
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} while (!uf.u);
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return uf.f - 1.0;
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}
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int
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main (int argc, const char **argv)
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{
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int res = 0;
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size_t i;
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int j;
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vec_t lambda[4];
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mtstate_t mt;
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double start, end;
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for (i = 0; i < num_tests; i ++) {
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BarycentricCoords (tests[i].points, tests[i].num_points, tests[i].x,
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lambda);
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for (j = 0; j < tests[i].num_points; j++) {
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if (tests[i].expect[j] != lambda[j])
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break;
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}
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if (j != tests[i].num_points) {
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res = 1;
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printf ("test %d failed\n", (int) i);
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printf ("expect:");
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for (j = 0; j < tests[i].num_points; j++)
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printf (" %.9g", tests[i].expect[j]);
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printf ("\ngot :");
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for (j = 0; j < tests[i].num_points; j++)
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printf (" %.9g", lambda[j]);
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printf ("\n");
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}
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}
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mtwist_seed (&mt, 0);
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start = Sys_DoubleTime ();
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for (i = 0; i < 1000000; i++) {
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vec3_t p, x;
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VectorSet (rnd (&mt), rnd (&mt), rnd (&mt), p);
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BarycentricCoords (tetra, 4, p, lambda);
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VectorZero (x);
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for (j = 0; j < 4; j++)
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VectorMultAdd (x, lambda[j], tetra[j], x);
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if (VectorDistance_fast (x, p) > 1e-4) {
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res = 1;
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printf ("[%.9g %.9g %.9g] != [%.9g %.9g %.9g]: [%g %g %g %g]\n",
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VectorExpand (x), VectorExpand (p), QuatExpand (lambda));
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break;
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}
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}
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end = Sys_DoubleTime ();
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printf ("%d itterations in %gs: %g itters/second\n", (int) i, end - start,
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i / (end - start));
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return res;
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}
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