Ray tracing cylinder degenerates when rotated

Question

I am trying to develop a simple ray tracer and got the sphere, plane and cone right but I am facing an issue I can't wrap my head around. I tried several different formulas for the infinite cylinder and all those who are supposed to take rotation into account makes it "degenerate" when using a rotation that's not 0 or 1 and on only one axis... For instance :

0,0,1 works but 0,0,0.5 gives me an ellipsoid sphere and 0,1,1 gives me an hyperboloid...

Here is the the code I am using to intersect the ray with the cylinder.

enum e_bool test_intersect(double t[2], double *current_z)
{
    enum e_bool retvalue;

    retvalue = false;
    if ((t[0] > DOUBLE_ZERO)
    && (t[0] < *(current_z) || double_equal(*(current_z), t[0])))
    {
        *(current_z) = t[0];
        retvalue = true;
    }
    if (!double_equal(t[0], t[1])
    && (t[1] > DOUBLE_ZERO) 
    && (t[1] < *(current_z) || double_equal(*(current_z), t[1])))
    {
        *(current_z) = t[1];
        retvalue = true;
    }
    return (retvalue);
}

enum e_bool intersect_cylinder(t_primitive cp, t_ray r, double *current_z)
{
    t_vec3 eye = vec3_substract(r.origin, cp.position);
    double a = vec3_dot(r.direction, r.direction) - pow(vec3_dot(r.direction, cp.direction), 2);
    double b = 2 * (vec3_dot(r.direction, eye) - vec3_dot(r.direction, cp.direction) * vec3_dot(eye, cp.direction));
    double c = vec3_dot(eye, eye) - pow(vec3_dot(eye, cp.direction), 2) - cp.radius * cp.radius;
    double  t[2];
    double delta;
    delta = sqrt((b * b) - (4.0 * a * c));
    if (delta < 0)
        return (false);
    t[0] = (-b - (delta)) / (2.0 * a);
    t[1] = (-b + (delta)) / (2.0 * a);
    return (test_intersect(t, current_z));
}

Here is the cylinder with a rotation of 1, 0, 0

Here it is with a rotation of 1, 1, 0

What am I missing, the issue is the same with perspective or isometric ray casting, so it has to do with the intersection algorithm, but I can't find what is wrong...

Answer 1

I found the solution to my issue, after reading these pages (gamedev helped me a lot) :

http://mrl.nyu.edu/~dzorin/cg05/lecture12.pdf

http://www.gamedev.net/topic/467789-raycylinder-intersection/

I re-did my intersection equation like so and it's working properly :

enum e_bool intersect_cylinder(t_primitive cp, t_ray r, double *current_z)
{
    t_vec3  pdp = vec3_substract(cp.direction, cp.position);
    t_vec3  eyexpdp = vec3_cross(vec3_substract(r.origin, cp.position), pdp);
    t_vec3  rdxpdp = vec3_cross(r.direction, pdp);
    float   a = vec3_dot(rdxpdp, rdxpdp);
    float   b = 2 * vec3_dot(rdxpdp, eyexpdp);
    float   c = vec3_dot(eyexpdp, eyexpdp) - (cp.radius * cp.radius * vec3_dot(pdp, pdp));
    double  t[2];
    double delta;
    delta = sqrt((b * b) - (4.0 * a * c));
    if (delta < 0)
        return (false);
    t[0] = (-b - (delta)) / (2.0 * a);
    t[1] = (-b + (delta)) / (2.0 * a);
    return (test_intersect(t, current_z));
}

Now my normals are wrong, but that's not that big of an issue to fix.