// For Shading Purposes
void RT_shade(Ray* ray, int depth) {
if (depth <= MAX_DEPTH){
// Color Coefficients
Vector4* diffuseCoeff = new Vector4();
Vector4* specularCoeff = new Vector4();
double shininess;
// Diffuse and Specular Terms
double diffuseTerm[3] = {0.0, 0.0, 0.0};
double specularTerm[3] = {0.0, 0.0, 0.0};
if (ray->intersectedObject == SPHERE) {
diffuseCoeff->ReInitialize(spheres[ray->intersectID].color_diffuse);
specularCoeff->ReInitialize(spheres[ray->intersectID].color_specular);
shininess = spheres[ray->intersectID].shininess;
}
else if (ray->intersectedObject == TRIANGLE) {
// Interpolate diffuse and specular coefficients
double alpha, beta;
ObtainIntermediateTriangleIntersection(ray->intersectID, ray->intersectPoint, &alpha, &beta);
diffuseCoeff->ReInitialize();
InterpolateTriangleProperty(triangles[ray->intersectID].v[0].color_diffuse,
triangles[ray->intersectID].v[1].color_diffuse,
triangles[ray->intersectID].v[2].color_diffuse,
alpha, beta, diffuseCoeff, false);
specularCoeff->ReInitialize();
InterpolateTriangleProperty(triangles[ray->intersectID].v[0].color_specular,
triangles[ray->intersectID].v[1].color_specular,
triangles[ray->intersectID].v[2].color_specular,
alpha, beta, specularCoeff, false);
// Interpolate shininess
if (alpha > 0) {
double intermediateShininess = beta * triangles[ray->intersectID].v[2].shininess
+ (1 - beta) * triangles[ray->intersectID].v[1].shininess;
shininess = ((alpha - 1) * triangles[ray->intersectID].v[0].shininess
+ intermediateShininess) / alpha;
}
else {
shininess = triangles[ray->intersectID].v[0].shininess;
}
}
// Boundary Checking
assert(diffuseCoeff->HasNonNegativeEntries());
assert(!diffuseCoeff->HasGreaterThanOneEntries());
assert(specularCoeff->HasNonNegativeEntries());
assert(!specularCoeff->HasGreaterThanOneEntries());
assert(shininess >= 0);
// Normal Vector: N
Vector4* N = new Vector4(ray->normal);
N->ConvertToUnitVector();
// Viewer Direction: V = ray->intersectedPoint - ray->source = -ray->dir
Vector4* V = new Vector4(ray->dir);
V->Scale(-1);
V->ConvertToUnitVector();
int dontCheckObject = NONE;
int dontCheckObjectID = NONE;
if (ray->intersectedObject == TRIANGLE) {
dontCheckObject = ray->intersectedObject;
dontCheckObjectID = ray->intersectID;
}
unsigned int i;
for (i = 0; i < num_lights; i++) {
// Shoot a ray in the direction of the light
Vector4* lightPos = new Vector4(lights[i].position);
Ray* checkShadow = new Ray(ray->intersectPoint, lightPos);
bool shadow = false;
double nearestTIntersect = FindNearestTIntersection(checkShadow,dontCheckObject,dontCheckObjectID);
double point2LightDistance = FindDistanceOfIntersectedPointWithLight(ray,i);
if (nearestTIntersect != INFINITY
&& nearestTIntersect< point2LightDistance)
{
shadow = true;
}
// Point to Light Vector: L = light_pos - intersectedPoint
Vector4* L = new Vector4(lights[i].position);
L->Subtraction(ray->intersectPoint);
L->ConvertToUnitVector();
// Reflected Ray: R = 2(N.L)N - L
Vector4* R = new Vector4(ray->normal);
R->Scale(2 * N->DotProduct(L));
R->Subtraction(L);
R->ConvertToUnitVector();
// Dot Product of N and L: NL
double NL = N->DotProduct(L);
if (NL < 0) {
NL = 0;
}
// Dot Product of R and V: RV
double RV = R->DotProduct(V);
if (RV < 0) {
RV = 0;
}
assert(NL <= 1 && RV <= 1);
double attenuationTerm = depth==1?1:1;
if (!shadow) {
unsigned int j;
for (j = 0; j < 3; j++) {
diffuseTerm[j] += attenuationTerm * lights[i].color[j] * diffuseCoeff->vector[j] * NL;
specularTerm[j] += attenuationTerm * lights[i].color[j] * specularCoeff->vector[j] * pow(RV, shininess);
}
}
delete(L);
delete(R);
delete(lightPos);
delete(checkShadow);
}
// Adding diffused light
Vector4* diffusedColor = new Vector4(diffuseTerm);
// //For Debugging Purposes
// if(ray->intersectedObject == SPHERE){
// ray->color->Display();
// diffusedColor->Display();
// cout<<"................................................."<<endl;
// }
ray->color->Addition(diffusedColor);
delete(diffusedColor);
// Adding specular light
Vector4* specularColor = new Vector4(specularTerm);
ray->color->Addition(specularColor);
delete(specularColor);
//R = 2*(NI)N - I ; N = N; I = V = ray->source - ray->IntersectPoint
Vector4* R_ = new Vector4(ray->normal);
Vector4* I = new Vector4(ray->dir);
I->Scale(-1);
R_->Scale(2*N->DotProduct(I));
R_->Subtraction(I);
Vector4* end = new Vector4(ray->intersectPoint);
end->Addition(R_);
Ray* reflectedRay = new Ray(ray->intersectPoint, end);
delete(R_);
delete(I);
delete(end);
assert(dontCheckObject!=SPHERE);
RT_trace(reflectedRay, depth+1, dontCheckObject, dontCheckObjectID);
//For Debugging
// if(ray->intersectedObject==TRIANGLE/* && ray->intersectPoint->vector[1]<-2*screenX/4
// && ray->intersectPoint->vector[1]>-3*screenX/4*/){
// cout<<ray->intersectID;
// cout<<"---->";
// ray->normal->Display();
// cout<<"------>";
// I->Display();
// cout<<I->DotProduct(ray->normal)<<"\t";
// cout<<reflectedRay->dir->DotProduct(ray->normal);
// reflectedRay->dir->Display();
// cout<<": "<<reflectedRay->tIntersect<<"\t";
// reflectedRay->color->Display();
// cout<<endl;
// }
if(reflectedRay->tIntersect!=INFINITY){
reflectedRay->color->Scale(specularCoeff->vector[0], specularCoeff->vector[1], specularCoeff->vector[2]);
ray->color->Addition(reflectedRay->color);
}
delete(reflectedRay);
delete(N);
delete(V);
delete(specularCoeff);
delete(diffuseCoeff);
}
}
double FindNearestTIntersectionWithTriangle(Ray* ray, int* index, int noCheckID = NONE){
assert(noCheckID==NONE || (noCheckID>=0 && noCheckID<num_triangles));
double nearestTIntersect = INFINITY;
*index = NONE;
unsigned int i;
for (i = 0; i < num_triangles; i++) {
if (i==noCheckID){
continue;
}
// Vertices V0, V1 and V2
Vector4* V0 = new Vector4(triangles[i].v[0].position);
Vector4* V1 = new Vector4(triangles[i].v[1].position);
Vector4* V2 = new Vector4(triangles[i].v[2].position);
// Edges: VOV1, V0V2
Vector4* V0V1 = new Vector4(V1);
V0V1->Subtraction(V0);
Vector4* V0V2 = new Vector4(V2);
V0V2->Subtraction(V0);
// Normal: N = V0V1 X V0V2
Vector4* N = new Vector4(V0V1);
N->CrossProductPost(V0V2);
N->ConvertToUnitVector();
// ray and normal should be opposite
if (N->DotProduct(ray->dir)>0){
N->Scale(-1);
}
// N = [A B C]
// AX0 + BY0 + CZ0 + D = 0
double D = -1*N->DotProduct(V0);
if (N->DotProduct(ray->dir) != (double) 0) {
// t = -(N.Ro + D)/ (N.Rd)
double candidateT = -1 * (N->DotProduct(ray->source) + D) / N->DotProduct(ray->dir);
if (candidateT > 0){
// P = Ro + tRd
Vector4* point = new Vector4(ray->dir);
point->Scale(candidateT);
point->Addition(ray->source);
// alpha*V0V1 + beta*V0V2 = V0P
Vector4* V0P = new Vector4(point);
V0P->Subtraction(V0);
double alpha = 0.0;
double beta = 0.0;
//(x01)alpha + (x02)beta = x0p;
//(y01)alpha + (y02)beta = y0p;
//(z01)alpha + (z02)beta = z0p;
double A1 = V0V1->vector[0];
double B1 = V0V2->vector[0];
double C1 = V0P->vector[0];
double A2 = V0V1->vector[1];
double B2 = V0V2->vector[1];
double C2 = V0P->vector[1];
double A3 = V0V1->vector[2];
double B3 = V0V2->vector[2];
double C3 = V0P->vector[2];
SolveLinearEquation(A1, B1, C1, A2, B2, C2, &alpha, &beta);
if (alpha == NONE) {
SolveLinearEquation(A2, B2, C2, A3, B3, C3, &alpha, &beta);
}
if (alpha == NONE) {
SolveLinearEquation(A1, B1, C1, A3, B3, C3, &alpha, &beta);
}
// // For Debugging Purposes
// printf("\nTriangle: %d ==> CandidateT: %f ==> (%f,%f)",i,candidateT,alpha,beta);
if (alpha > 0 && beta > 0 && (alpha + beta) < 1) {
if (nearestTIntersect > candidateT) {
nearestTIntersect = candidateT;
*index = i;
}
}
delete(V0P);
delete(point);
}
}
delete(N);
delete(V0V2);
delete(V0V1);
delete(V2);
delete(V1);
delete(V0);
}
return nearestTIntersect;
}