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https://git.code.sf.net/p/quake/quakeforge
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Add a function to find the circumsphere of up to 4 points.
It seems to be a little sloppy (an error of a bit less than 1e-4). This might be why I'm having trouble with my SEB code.
This commit is contained in:
Bill Currie
parent
0cd6d93030
commit
b6d4766201
5 changed files with 195 additions and 2 deletions
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@ -213,6 +213,7 @@ R_CullSphere (const vec3_t origin, const float radius)
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return false;
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}
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int CircumSphere (const vec3_t points[], int num_points, sphere_t *sphere);
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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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@ -110,4 +110,9 @@ typedef struct plane_s {
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byte pad[2];
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} plane_t;
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typedef struct sphere_s {
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vec3_t center;
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vec_t radius;
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} sphere_t;
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#endif // __qtypes_h
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@ -1200,3 +1200,84 @@ BarycentricCoords (const vec_t **points, int num_points, const vec3_t p,
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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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static int
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circum_circle (const vec_t **points, int num_points, sphere_t *sphere)
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{
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vec3_t a, c, b;
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vec3_t bc, ca, ab;
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vec_t aa, bb, cc;
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vec_t div;
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vec_t alpha, beta, gamma;
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switch (num_points) {
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case 1:
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VectorCopy (points[0], sphere->center);
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return 1;
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case 2:
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VectorBlend (points[0], points[1], 0.5, sphere->center);
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return 1;
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case 3:
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VectorSubtract (points[0], points[1], a);
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VectorSubtract (points[0], points[2], b);
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VectorSubtract (points[1], points[2], c);
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aa = DotProduct (a, a);
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bb = DotProduct (b, b);
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cc = DotProduct (c, c);
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div = DotProduct (a, c);
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div = 2 * (aa * cc - div * div);
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if (fabs (div) < EQUAL_EPSILON) {
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// degenerate
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return 0;
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}
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alpha = cc * DotProduct (a, b) / div;
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beta = -bb * DotProduct (a, c) / div;
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gamma = aa * DotProduct (b, c) / div;
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VectorScale (points[0], alpha, sphere->center);
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VectorMultAdd (sphere->center, beta, points[1], sphere->center);
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VectorMultAdd (sphere->center, gamma, points[2], sphere->center);
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return 1;
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case 4:
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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 (b, c, bc);
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CrossProduct (c, a, ca);
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CrossProduct (a, b, ab);
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div = 2 * DotProduct (a, bc);
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if (fabs (div) < EQUAL_EPSILON) {
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// degenerate
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return 0;
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}
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aa = DotProduct (a, a) / div;
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bb = DotProduct (b, b) / div;
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cc = DotProduct (c, c) / div;
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VectorScale (bc, aa, sphere->center);
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VectorMultAdd (sphere->center, bb, ca, sphere->center);
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VectorMultAdd (sphere->center, cc, ab, sphere->center);
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VectorAdd (sphere->center, points[0], sphere->center);
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sphere->radius = VectorDistance (sphere->center, points[0]);
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return 1;
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}
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return 0;
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}
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int
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CircumSphere (const vec3_t points[], int num_points, sphere_t *sphere)
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{
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const vec_t *p[] = {points[0], points[1], points[2], points[3]};
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if (num_points > 4)
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return 0;
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sphere->radius = 0;
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if (num_points) {
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if (circum_circle (p, num_points, sphere)) {
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if (num_points > 1)
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sphere->radius = VectorDistance (sphere->center, points[0]);
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return 1;
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}
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return 0;
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}
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VectorZero (sphere->center);
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return 1;
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}
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@ -3,13 +3,17 @@ AUTOMAKE_OPTIONS= foreign
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INCLUDES= -I$(top_srcdir)/include
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check_PROGRAMS= \
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test-bary test-dq test-half test-mat3 test-mat4 test-plist test-qfs \
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test-quat test-set test-vrect
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test-bary test-cs test-dq test-half test-mat3 test-mat4 \
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test-plist test-qfs test-quat test-set test-vrect
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test_bary_SOURCES=test-bary.c
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test_bary_LDADD=$(top_builddir)/libs/util/libQFutil.la
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test_bary_DEPENDENCIES=$(top_builddir)/libs/util/libQFutil.la
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test_cs_SOURCES=test-cs.c
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test_cs_LDADD=$(top_builddir)/libs/util/libQFutil.la
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test_cs_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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test_dq_DEPENDENCIES=$(top_builddir)/libs/util/libQFutil.la
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102
libs/util/test/test-cs.c
Normal file
102
libs/util/test/test-cs.c
Normal file
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@ -0,0 +1,102 @@
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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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const 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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struct {
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const vec3_t *points;
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int num_points;
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sphere_t expect;
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} tests[] = {
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{0, 0, {{ 0, 0, 0}, 0}},
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{points, 1, {{-1, -1, 1}, 0}},
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{points, 2, {{ 0, 0, 1}, 1.41421356}},
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{points, 3, {{-0.333333343, 0.333333343, 0.333333343}, 1.63299322}},
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{points, 4, {{0, 0, 0}, 1.73205081}},
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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) & 0x007fffff;
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} while (!uf.u);
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uf.u |= 0x40000000;
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return uf.f - 3.0;
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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, j;
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sphere_t sphere;
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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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sphere = BoundingSphere (tests[i].points, tests[i].num_points);
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if (VectorDistance_fast (sphere.center, tests[i].expect.center) > 1e-4
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|| fabs (sphere.radius - tests[i].expect.radius) > 1e-4) {
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res = 1;
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printf ("test %d failed\n", (int) i);
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printf ("expect: [%.9g %.9g %.9g],%.9g\n",
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VectorExpand (tests[i].expect.center),
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tests[i].expect.radius);
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printf ("got : [%.9g %.9g %.9g],%.9g\n",
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VectorExpand (sphere.center),
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sphere.radius);
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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; !res && i < 100000; i++) {
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vec3_t cloud[4];
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sphere_t cc;
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vec_t r2;
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for (j = 0; j < 4; j++) {
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VectorSet (rnd (&mt), rnd (&mt), rnd (&mt), cloud[j]);
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}
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if (!CircumSphere ((const vec_t (*)[3]) cloud, 4, &cc))
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continue;
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r2 = cc.radius * cc.radius;
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for (j = 0; j < 4; j++) {
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if (fabs (VectorDistance_fast (cloud[j], cc.center) - r2)
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< 1e-4 * r2)
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continue;
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printf ("%d %.9g - %.9g = %.9g\n", (int)j,
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VectorDistance_fast (cloud[j], cc.center), r2,
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VectorDistance_fast (cloud[j], cc.center) - r2);
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printf ("[%.9g %.9g %.9g] - [%.9g %.9g %.9g] = %.9g > %.9g\n",
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VectorExpand (cloud[j]), VectorExpand (cc.center),
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VectorDistance_fast (cloud[j], cc.center), r2);
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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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