/* calculate sphere that goes through 4 points */
struct sphere* sphere_circum(struct sphere* rs, const struct vec4f* v0,
const struct vec4f* v1, const struct vec4f* v2, const struct vec4f* v3)
{
struct vec4f a;
vec3_sub(&a, v1, v0);
struct vec4f b;
vec3_sub(&b, v2, v0);
struct vec4f c;
vec3_sub(&c, v3, v0);
struct vec4f o;
struct vec4f tmp;
struct mat3f m;
mat3_setf(&m,
a.x, a.y, a.z,
b.x, b.y, b.z,
c.x, c.y, c.z,
0.0f, 0.0f, 0.0f);
float denom = 2.0f * mat3_det(&m);
vec3_muls(&o, vec3_cross(&tmp, &a, &b), vec3_dot(&c, &c));
vec3_add(&o, &o, vec3_muls(&tmp, vec3_cross(&tmp, &c, &a), vec3_dot(&b, &b)));
vec3_add(&o, &o, vec3_muls(&tmp, vec3_cross(&tmp, &b, &c), vec3_dot(&a, &a)));
vec3_muls(&o, &o, 1.0f/denom);
return sphere_setf(rs, v0->x + o.x, v0->y + o.y, v0->z + o.z, vec3_len(&o) + EPSILON);
}
float mat4_det(mat4 m)
{
mat3 n;
int j;
float t = 0.0;
//m[3][0]
for(j=0;j<3;j++)
{
n[j][0] = m[j][1];
n[j][1] = m[j][2];
n[j][2] = m[j][3];
}
t -= m[3][0]*mat3_det(n);
//m[3][1]
for(j=0;j<3;j++)
{
n[j][0] = m[j][0];
n[j][1] = m[j][2];
n[j][2] = m[j][3];
}
t += m[3][1]*mat3_det(n);
//m[3][2]
for(j=0;j<3;j++)
{
n[j][0] = m[j][0];
n[j][1] = m[j][1];
n[j][2] = m[j][3];
}
t -= m[3][2]*mat3_det(n);
//m[3][3]
for(j=0;j<3;j++)
{
n[j][0] = m[j][0];
n[j][1] = m[j][1];
n[j][2] = m[j][2];
}
t += m[3][3]*mat3_det(n);
return t;
}
