Real
raySphereIntersectionTime(Ray3 const & ray, Vector3 const & center, Real radius)
{
Vector3 pmc = ray.getOrigin() - center;
double s[3];
s[2] = ray.getDirection().squaredLength();
s[1] = 2 * pmc.dot(ray.getDirection());
s[0] = pmc.squaredLength() - radius * radius;
double roots[2];
int num_roots = Math::solveQuadratic(s[0], s[1], s[2], roots);
double min_root = -1;
for (int i = 0; i < num_roots; ++i)
if (roots[i] >= 0 && (min_root < 0 || roots[i] < min_root))
min_root = roots[i];
#if 0
if (min_root >= 0)
qDebug() << "min_root =" << min_root;
#endif
return (Real)min_root;
}
Real
closestPtRayTriangle(Ray3 const & ray, Vector3 const & v0, Vector3 const & edge01, Vector3 const & edge02, Real & s,
Vector3 & c1, Vector3 & c2)
{
Real sqdist = closestPtLineTriangle(Line3::fromPointAndDirection(ray.getOrigin(), ray.getDirection()), v0, edge01, edge02,
s, c1, c2);
if (s >= 0)
return sqdist;
// Not the most efficient way but the most convenient
LocalTriangle3 tri(v0, v0 + edge01, v0 + edge02);
s = 0;
c1 = ray.getOrigin();
c2 = tri.closestPoint(c1);
return (c1 - c2).squaredLength();
}
Real
rayTorusIntersectionTime(Ray3 const & ray, Real torus_radius, Real torus_width)
{
double r2pw2 = torus_radius * torus_radius + torus_width * torus_width;
double r2mw2 = r2pw2 - 2 * torus_width * torus_width;
Vector3 p2 = ray.getOrigin() * ray.getOrigin();
Vector3 pu = ray.getOrigin() * ray.getDirection();
Vector3 u2 = ray.getDirection() * ray.getDirection();
double s[5];
s[4] = u2[0] * (u2[0] + 2 * u2[1]) + u2[1] * (u2[1] + 2 * u2[2]) + u2[2] * (u2[2] + 2 * u2[0]);
s[3] = 4 * (pu[0] + pu[1] + pu[2]) * (u2[0] + u2[1] + u2[2]);
s[2] = 2 * (r2mw2 * u2[2] - r2pw2 * (u2[0] + u2[1]))
+ 8 * (pu[0] * pu[1] + pu[1] * pu[2] + pu[2] * pu[0])
+ 6 * (pu[0] * pu[0] + pu[1] * pu[1] + pu[2] * pu[2])
+ 2 * (p2[0] * (u2[1] + u2[2]) + p2[1] * (u2[2] + u2[0]) + p2[2] * (u2[0] + u2[1]));
s[1] = 4 * (r2mw2 * pu[2] - r2pw2 * (pu[0] + pu[1]) + (p2[0] + p2[1] + p2[2]) * (pu[0] + pu[1] + pu[2]));
s[0] = 2 * (r2mw2 * p2[2] - r2pw2 * (p2[0] + p2[1]) + p2[0] * p2[1] + p2[1] * p2[2] + p2[2] * p2[0])
+ p2[0] * p2[0] + p2[1] * p2[1] + p2[2] * p2[2] + r2mw2 * r2mw2;
double roots[4];
int num_roots = Math::solveQuartic(s[0], s[1], s[2], s[3], s[4], roots);
double min_root = -1;
for (int i = 0; i < num_roots; ++i)
if (roots[i] >= 0 && (min_root < 0 || roots[i] < min_root))
min_root = roots[i];
#if 0
if (min_root >= 0)
qDebug() << "min_root =" << min_root;
#endif
return (Real)min_root;
}