//intersect sphere with a ray
bool Sphere::intersect(const Ray &ray, IntersectionData* iData) {
//=== EXERCISE 1.3.2 ===
//Resolving the problem algebraicaly, we get the following coefficients of a quadratic equation in t:
double a=ray.direction.dot(ray.direction);
double b=2*(ray.point.dot(ray.direction) - m_center.dot(ray.direction));
double c=m_center.dot(m_center)+ray.point.dot(ray.point) - 2.0*m_center.dot(ray.point) - m_radius*m_radius;
double discriminant = b*b - 4.0*a*c;
if (discriminant<0)
{
return false;
}else{
double t1=(-b+sqrt(discriminant))/(2.0*a);
double t2=(-b-sqrt(discriminant))/(2.0*a);
bool b1= (t1>=ray.min_t && t1<=ray.max_t) && t1<iData->t ;
bool b2= (t2>=ray.min_t && t2<=ray.max_t) && t2<iData->t ;
if (b1||b2)
{
if(b1)
iData->t=t1;
if(b2)
iData->t=t2;
if (b1 && b2)
{
iData->t=(t2<t1?t2:t1);
}
iData->position=ray.getPointOnRay(iData->t);
iData->color=getColor();
iData->material=getMaterial();
iData->sourcePosition=ray.point;
iData->normal=(ray.getPointOnRay(iData->t) - m_center).normalize();
iData->reflectionPercentage=getReflectionPercentage();
iData->refractionIndex=getRefractionIndex();
iData->refractionPercentage=getRefractionPercentage();
iData->rayEntersObject= (ray.direction.dot(iData->normal)<0.0);
iData->reflectionPercentage = getReflectionPercentage();
return true;
}
}
return false;
}
//intersect triangle with a ray
bool Triangle::intersect(const Ray &ray, IntersectionData* iData) {
//=== EXERCISE 1.4.2 ===
Vector3 n = (m_p3 - m_p1).cross(m_p2 - m_p1);
if (ray.direction.dot(n) == 0)
{
// no solution
return false;
}else{
// compute the solution
double t = - ((ray.point - m_p1).dot(n))/(ray.direction.dot(n));
// check if solution is valid for our problem
bool b = (t>=ray.min_t && t<=ray.max_t) && t<iData->t;
if(b){
// normal vector of small triangles
Vector3 x = ray.getPointOnRay(t);
Vector3 n_s1 = (m_p2 - m_p3).cross(x - m_p3);
Vector3 n_s2 = (m_p1 - m_p2).cross(x - m_p2);
Vector3 n_s3 = (m_p3 - m_p1).cross(x - m_p1);
// compute s1 s2 s3 (normalise)
double s1 = (n.dot(n_s1))/(n.x*n.x + n.y*n.y + n.z*n.z);
double s2 = (n.dot(n_s2))/(n.x*n.x + n.y*n.y + n.z*n.z);
double s3 = (n.dot(n_s3))/(n.x*n.x + n.y*n.y + n.z*n.z);
// test if p is in triangle
if(1-ray.epsilon_t < s1+s2+s3 && s1+s2+s3 < 1+ray.epsilon_t && 0 < s1 && s1<1 && 0<s2 && s2<1 && 0<s3 && s3<1){
iData->t=t;
//Intersection information
iData->position=ray.getPointOnRay(iData->t);
iData->color=getColor();
iData->sourcePosition=ray.point;
return true;
}else{
return false;
}
}else{
return false;
}
}
return false;
}
//intersect triangle with a ray
bool Triangle::intersect(const Ray &ray, IntersectionData* iData) {
//=== EXERCISE 1.4.2 ===
Vector3 n = (m_p3 - m_p1).cross(m_p2 - m_p1);
if (ray.direction.dot(n) == 0)
{
// no solution
return false;
}else{
// compute the solution
double t = - ((ray.point - m_p1).dot(n))/(ray.direction.dot(n));
// check if solution is valid for our problem
bool b = (t>=ray.min_t && t<=ray.max_t) && t<iData->t;
if(b){
// normal vector of small triangles
Vector3 x = ray.getPointOnRay(t);
Vector3 n_s1 = (m_p2 - m_p3).cross(x - m_p3);
Vector3 n_s2 = (m_p1 - m_p2).cross(x - m_p2);
Vector3 n_s3 = (m_p3 - m_p1).cross(x - m_p1);
// compute s1 s2 s3 (normalise)
double s1 = (n.dot(n_s1))/(n.x*n.x + n.y*n.y + n.z*n.z);
double s2 = (n.dot(n_s2))/(n.x*n.x + n.y*n.y + n.z*n.z);
double s3 = (n.dot(n_s3))/(n.x*n.x + n.y*n.y + n.z*n.z);
// test if p is in triangle
if(1-ray.epsilon_t < s1+s2+s3 && s1+s2+s3 < 1+ray.epsilon_t && 0 < s1 && s1<1 && 0<s2 && s2<1 && 0<s3 && s3<1){
iData->t=t;
//Intersection information
iData->position=ray.getPointOnRay(iData->t);
iData->color=getColor();
iData->sourcePosition=ray.point;
iData->reflectionPercentage = getReflectionPercentage();
// Exercice 2.1.1
iData->material = getMaterial();
//Normal interpolation
Vector3 normal1 = m_n1.operator*(s1);
Vector3 normal2 = m_n2.operator*(s3);
Vector3 normal3 = m_n3.operator*(s2); // s2 and s3 are inverted du to the typing error on the triangle in slide
Vector3 normal = (normal1+normal2+normal3).normalize(); // get the interpolated normal in x
iData->normal = normal;
return true;
}else{
return false;
}
}else{
return false;
}
}
return false;
}