/*! \brief intersect a ray with a sphere, only returns the first intersection point
*/
Intersection_t *Intersect_Sphere(Rayf_t *ray, Geo_Sphere_t *sphere) {
/* values for the quadric equation */
float a = LengthSqV3f(ray->dir);
float b = 2 * DotV3f(ray->dir, ray->orig);
float c = LengthSqV3f(ray->orig) - Sqrf(sphere->radius);
float D = Sqrf(b) - (4 * a * c);
if (D >= 0) {
float t1 = (-b - sqrtf(D)) / (2 * a), t2 = (-b + sqrtf(D)) / (2 * a); /* two candidate intersection parameters */
float t; /* the smallest positive candidate intersection parameter */
/* if only 1 is negative the ray starts inside the sphere
* if both are negative the sphere is behind the ray
* either way there's no intersection
*/
if (t1 <= EPSILON || t2 <= EPSILON)
return NULL;
else if (t1 <= EPSILON)
t = t2;
else if (t2 <= EPSILON)
t = t1;
else
t = Minf(t1, t2);
Intersection_t *intersection = NEW(Intersection_t);
intersection->t = t;
RayToPointf(ray, t, intersection->point);
/* for a sphere centered at the origin the normal of a point is the vector from the point to the origin */
CopyV3f(intersection->point, intersection->norm);
NormalizeV3f(intersection->norm);
/* compute texture coordinates */
intersection->u = ((atan2(intersection->norm[1], intersection->norm[0]) / 3.142) + 1) / 2;
intersection->v = (intersection->norm[2] + 1) / 2;
return intersection;
}
return NULL;
}
float Vector4::Min()const{
return Minf(Minf(w,x),Minf(y,z));
}
float Vector3::Min()const{
return Minf(x,y);
}