bool Torus::shadowHit(const Ray& ray, float& tmin) const
{
if(!castsShadows)
return false;
if(!bbox.hit(ray))
return false;
glm::vec3 origin = ray.getOrigin();
glm::vec3 dir = ray.getDirection();
float coefs[5];
float roots[4];
//define coefficients
float sumDSquared = glm::dot(dir,dir);
float e = glm::dot(origin,origin) - sweptRadiusSQ - tubeRadiusSQ;
float f = glm::dot(origin,dir);
float fourASquared = 4.0f * sweptRadiusSQ;
coefs[0] = e * e - fourASquared * (tubeRadiusSQ - origin.y * origin.y);
coefs[1] = 4.0f * f * e + 2.0f * fourASquared * origin.y * dir.y;
coefs[2] = 2.0f * sumDSquared * e + 4.0f * f * f + fourASquared * dir.y * dir.y;
coefs[3] = 4.0f * sumDSquared * f;
coefs[4] = sumDSquared * sumDSquared;
int numRealRoots = solveQuartic(coefs,roots);
bool intersected = false;
float t = kHugeValue;
if(numRealRoots == 0)
return false;
for(int i=0;i<numRealRoots;i++)
if(roots[i] > KEpsilon)
{
intersected = true;
if(roots[i] < t)
t = roots[i];
}
if(!intersected)
return false;
tmin = t;
return true;
}
float TorusObject::hit_test(const Ray &ray, Vector &normal, const Point *max_pos, bool *inside)
{
Ray inv_ray;
inv_ray.origin = mul_point(inv_trans, ray.origin);
inv_ray.direction = mul_vec(inv_trans, ray.direction);
inv_ray.direction.normalize();
double x1 = inv_ray.origin.x; double y1 = inv_ray.origin.y; double z1 = inv_ray.origin.z;
double d1 = inv_ray.direction.x; double d2 = inv_ray.direction.y; double d3 = inv_ray.direction.z;
double coeffs[5]; // coefficient array
double roots[4]; // solution array
//define the coefficients
double sum_d_sqrd = d1*d1 + d2*d2 + d3*d3;
double e = x1*x1 + y1*y1 + z1*z1 - radius*radius - thickness*thickness;
double f = x1*d1 + y1*d2 + z1*d3;
double four_a_sqrd = 4.0 * radius*radius;
coeffs[0] = e*e - four_a_sqrd * (thickness*thickness-y1*y1); // constante term
coeffs[1] = 4.0 * f * e + 2.0 * four_a_sqrd * y1 *d2;
coeffs[2] = 2.0 * sum_d_sqrd * e + 4.0 * f * f + four_a_sqrd * d2 * d2;
coeffs[3] = 4.0 * sum_d_sqrd * f;
coeffs[4] = sum_d_sqrd * sum_d_sqrd; // coefficient of t^4
//fin the roots
int num_real_roots = solveQuartic(coeffs, roots);
bool intersected = false;
double t = FLT_MAX;
if ( num_real_roots == 0) // ray misses the torus
return -1.0;
//find the smallest root greater than FLT_EPSILON, if any
for( int j = 0; j < num_real_roots; j++)
{
if(roots[j] > FLT_EPSILON)
{
intersected = true;
if(roots[j] < t)
t = roots[j];
}
}
double max_t;
if(max_pos)
max_t = (max_pos->x - ray.origin.x) / ray.direction.x;
else
max_t = FLT_MAX;
if( t > max_t || !intersected)
return -1.0;
Point hit = inv_ray.origin + t*inv_ray.direction;
normal = compute_normal(hit);
normal = mul_vec(inv_trans, normal);
normal.normalize();
return t;
}
