Intersection Sphere::intersects(Ray ray) {
Intersection is(ray, this);
// Transforming ray to object space
Vect transformedOrigin = ray.getOrigin() - getOrigin();
//Compute A, B and C coefficients
Vect dest = ray.getDirection();
Vect orig = transformedOrigin;
float a = dest.dotProduct(dest);
float b = 2 * dest.dotProduct(orig);
float c = orig.dotProduct(orig) - (radius * radius);
//Find discriminant
float disc = b * b - 4 * a * c;
// if discriminant is negative there are no real roots, so return
// false as ray misses sphere
if (disc < 0)
return is;
// compute q as described above
float distSqrt = sqrtf(disc);
float q;
if (b < 0)
q = (-b - distSqrt) / 2.0f;
else
q = (-b + distSqrt) / 2.0f;
// compute t0 and t1
float t0 = q / a;
float t1 = c / q;
// make sure t0 is smaller than t1
if (t0 > t1) {
// if t0 is bigger than t1 swap them around
float temp = t0;
t0 = t1;
t1 = temp;
}
// if t1 is less than zero, the object is in the ray's negative direction
// and consequently the ray misses the sphere
if (t1 < 0)
return is;
// if t0 is less than zero, the intersection point is at t1
if (t0 < 0) {
is.setIntersectionPoint(t1);
return is;
}
// else the intersection point is at t0
else {
is.setIntersectionPoint(t0);
return is;
}
}
Vect Triangle::surfaceNormal(Vect dir, Vect pt) {
(void) pt;
Vect v = getB() - getA();
Vect w = getC() - getA();
Vect N = v.crossProduct(w);
N.normalize();
if (N.dotProduct(dir) > 0)
N = N.linearMult(-1);
return N;
}
Intersection Triangle::intersects(Ray ray) {
Intersection is(ray, this);
Vect p = ray.getOrigin();
Vect d = ray.getDirection();
Vect v0 = getA();
Vect v1 = getB();
Vect v2 = getC();
Vect e1, e2, h, s, q;
float a0, f, u, v;
e1 = v1 - v0;
e2 = v2 - v0;
h = d.crossProduct(e2);
a0 = e1.dotProduct(h);
if (a0 > -0.00001 && a0 < 0.00001)
return is;
f = 1 / a0;
s = p - v0;
u = f * (s.dotProduct(h));
if (u < 0.0 || u > 1.0)
return is;
q = s.crossProduct(e1);
v = f * d.dotProduct(q);
if (v < 0.0 || u + v > 1.0)
return is;
// at this stage we can compute t to find out where
// the intersection point is on the line
float t = f * e2.dotProduct(q);
if (t > 0.00001) { // ray intersection
is.setIntersectionPoint(t);
return is;
}
else // this means that there is a line intersection
// but not a ray intersection
return is;
}
