IntersectionInfo Sphere::rayIntersect(Ray _ray) {
Point3f e = _ray.e();
Point3f c = center_;
Vector3f d = _ray.d();
float discriminant = dot(d,(e-c))*dot(d,(e-c))-
dot(d,d)*(dot((e-c),(e-c))-radius_*radius_);
if (discriminant < 0.0) {
return IntersectionInfo(0.0,
Point3f(),
Vector3f(),
IntersectionInfo::miss());
} else {
float t1 = (dot(d*-1.0,(e-c))+sqrt(discriminant))/dot(d,d);
float t2 = (dot(d*-1.0,(e-c))-sqrt(discriminant))/dot(d,d);
float t;
if (t1 < t2) {
t = t1;
} else {
t = t2;
}
if (t < _ray.tMin() || t > _ray.tMax()) {
return IntersectionInfo(0.0,
Point3f(),
Vector3f(),
IntersectionInfo::miss());
}
Point3f p = e + d*t;
Vector3f n = 2.0*(p-c);
n.normalize();
return IntersectionInfo(t, p, n, IntersectionInfo::hit());
}
}
bool MeshShape::intersectTri(const Ray &r, float &t, Vector &p, Vector &n, float &u, float &v)
{
// Transform the ray for the local transformation matrix
Ray rt = _transform.inverse() * Ray(r);
Vector A, B, C;
float nearest_t = -1.0f, temp_t;
int face_index = -1; // Index of intersected face
for(unsigned int faceI=0; faceI<mesh->faces.size(); faceI+=3)
{
A = mesh->vertices[mesh->faces[faceI]];
B = mesh->vertices[mesh->faces[faceI+1]];
C = mesh->vertices[mesh->faces[faceI+2]];
// Skip face if triangle plane and ray are parallel
float temp = ((B-A).cross(C-A)).dot(rt.d());
if(temp < eps && temp > -eps)
continue;
else
{
double a = A.x() - B.x();
double b = A.y() - B.y();
double c = A.z() - B.z();
double d = A.x() - C.x();
double e = A.y() - C.y();
double f = A.z() - C.z();
double g = rt.d().x();
double h = rt.d().y();
double i = rt.d().z();
double j = A.x() - rt.e().x();
double k = A.y() - rt.e().y();
double l = A.z() - rt.e().z();
double eiSubhf = e*i - h*f;
double gfSubdi = g*f - d*i;
double dhSubeg = d*h - e*g;
double M = a*eiSubhf + b*gfSubdi + c*dhSubeg;
double akSubjb = a*k - j*b;
double jcSubal = j*c - a*l;
double blSubkc = b*l - k*c;
// Gamma and Beta represent distance along vectors (c-a) and (b-a) respectively,
// if Gamma or Beta are beyond their respective vectors, then intersection is not within the surface of the triangle
double Gamma = (i*akSubjb + h*jcSubal + g*blSubkc)/M;
if(Gamma < 0 || Gamma > 1)
continue;
double Beta = (j*eiSubhf + k*gfSubdi + l*dhSubeg)/M;
if(Beta < 0 || Beta > (1-Gamma))
continue;
temp_t = -((f*akSubjb + e*jcSubal + d*blSubkc)/M);
if(temp_t > eps && (nearest_t <= eps || temp_t < nearest_t))
{
nearest_t = temp_t;
// Retain intersected face index (remember face is specified by i*3,i*3+1,i*3+2)
face_index = faceI;
}
}
}
// Return intersection details
if(nearest_t > eps)
{
t = nearest_t;
p = r.e() + r.d()*t;
// Get the intersected triangle vertices
A = mesh->vertices[mesh->faces[face_index]];
B = mesh->vertices[mesh->faces[face_index+1]];
C = mesh->vertices[mesh->faces[face_index+2]];
// Compute flat face normal
n = _transform.inverse().transpose().mult((B-A).cross(C-A).normalized()).normalized();
Vector pLocal = rt.e() + rt.d()*t;
Vector v0 = C - A;
Vector v1 = B - A;
Vector v2 = pLocal - A;
float dot00 = v0.dot(v0);
float dot01 = v0.dot(v1);
float dot02 = v0.dot(v2);
float dot11 = v1.dot(v1);
float dot12 = v1.dot(v2);
float invDenom = 1.0f / (dot00*dot11 - dot01*dot01);
float local_u = (dot11*dot02 - dot01*dot12) * invDenom;
float local_v = (dot00*dot12 - dot01*dot02) * invDenom;
// Recall faces[face_index] is the index for the vertex, faces[face_index]*2 then maps to the correct u,v position in the uvList since uvList=(u0,v0,u1,v1,...)
int uv_index = mesh->faces[face_index]*2;
float u_0 = mesh->uvList[uv_index];
float v_0 = mesh->uvList[uv_index+1];
uv_index = mesh->faces[face_index+1]*2;
float u_1 = mesh->uvList[uv_index];
float v_1 = mesh->uvList[uv_index+1];
uv_index = mesh->faces[face_index+2]*2;
float u_2 = mesh->uvList[uv_index];
float v_2 = mesh->uvList[uv_index+1];
float tu1 = u_1 - u_0;
float tv1 = v_1 - v_0;
float tu0 = u_2 - u_0;
float tv0 = v_2 - v_0;
u = u_0 + tu0*local_u + tu1*local_v;
v = v_0 + tv0*local_u + tv1*local_v;
return true;
}
else
return false;
}