bool
Torus::hit(const Ray& ray, double& tmin, ShadeRec& sr) const {
if (!bbox.hit(ray))
return (false);
double x1 = ray.o.x; double y1 = ray.o.y; double z1 = ray.o.z;
double d1 = ray.d.x; double d2 = ray.d.y; double d3 = ray.d.z;
double coeffs[5]; // coefficient array for the quartic equation
double roots[4]; // solution array for the quartic equation
// define the coefficients of the quartic equation
double sum_d_sqrd = d1 * d1 + d2 * d2 + d3 * d3;
double e = x1 * x1 + y1 * y1 + z1 * z1 - a * a - b * b;
double f = x1 * d1 + y1 * d2 + z1 * d3;
double four_a_sqrd = 4.0 * a * a;
coeffs[0] = e * e - four_a_sqrd * (b * b - y1 * y1); // constant 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
// find roots of the quartic equation
int num_real_roots = SolveQuartic(coeffs, roots);
bool intersected = false;
double t = kHugeValue;
if (num_real_roots == 0) // ray misses the torus
return(false);
// find the smallest root greater than kEpsilon, if any
// the roots array is not sorted
for (int j = 0; j < num_real_roots; j++)
if (roots[j] > kEpsilon) {
intersected = true;
if (roots[j] < t)
t = roots[j];
}
if(!intersected)
return (false);
tmin = t;
sr.local_hit_point = ray.o + t * ray.d;
sr.normal = compute_normal(sr.local_hit_point);
return (true);
}
bool ConcavePartTorus::shadow_hit(const Ray& ray, float& tmin) const {
if (!shadows)
return false;
if (!bbox.hit(ray))
return false;
double x1 = ray.o.x; double y1 = ray.o.y; double z1 = ray.o.z;
double d1 = ray.d.x; double d2 = ray.d.y; double d3 = ray.d.z;
double coeffs[5]; // coefficient array for the quartic equation
double roots[4]; // solution array for the quartic equation
// define the coefficients of the quartic equation
double sum_d_sqrd = d1 * d1 + d2 * d2 + d3 * d3;
double e = x1 * x1 + y1 * y1 + z1 * z1 - a * a - b * b;
double f = x1 * d1 + y1 * d2 + z1 * d3;
double four_a_sqrd = 4.0 * a * a;
coeffs[0] = e * e - four_a_sqrd * (b * b - y1 * y1); // constant 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
// find roots of the quartic equation
int num_real_roots = SolveQuartic(coeffs, roots);
bool intersected = false;
double t = kHugeValue;
if (num_real_roots == 0) // ray misses the torus
return false;
// find the smallest root greater than kEpsilon, if any
// the roots array is not sorted
for (int j = 0; j < num_real_roots; j++) {
if (roots[j] > kEpsilon) {
if (roots[j] < t) {
Vector3D hit = ray.o + roots[j] * ray.d;
double phi = atan2(hit.x, hit.z);
if (phi < 0.0)
phi += TWO_PI;
double theta = atan2(hit.y, sqrt(hit.x * hit.x + hit.z * hit.z) - a);
if (theta < 0.0)
theta += TWO_PI;
bool good_theta;
if (theta_max < theta_min) {
good_theta = ((theta_min <= theta && theta <= 360)
|| (0 <= theta && theta <= theta_max));
} else {
good_theta = (theta_min <= theta && theta <= theta_max);
}
if (phi_min <= phi && phi <= phi_max && good_theta) {
intersected = true;
t = roots[j];
}
}
}
}
if(!intersected)
return false;
tmin = t;
return true;
}
