bool Shape::intersectSphere(Ray& ray, float* thit, LocalGeo* local){
// (P-C).(P-C) = r^2
// (P0 + tD - C).(P0 + tD - C) = r^2
// (d.d)t^2 + 2(P0-C).dt + (P0-C).(P0-C)-r^2 = 0
// At^2 + Bt + C = 0
Vector temp1;
temp1.createFromPoints(center, ray.pos);
// set up equation
float A = ray.dir.dotProduct(ray.dir); // dot product for vector needed
float B = 2.0 * (temp1.dotProduct(ray.dir));
float C = temp1.dotProduct(temp1) - (radius * radius);
// solve quadratic equation
float D = B * B - 4 * A * C;
if (D < 0.0) {
return false;
} else {
*thit = (-sqrt(D) - B) / (A * 2.0);
if (*thit < ray.t_min || *thit == ray.t_min || *thit > ray.t_max) {
return false;
} else {
}
}
// get point and normal for local geo
Point point;
point.setValue(ray.pos.x + ray.dir.x * *thit, ray.pos.y + ray.dir.y * *thit, ray.pos.z + ray.dir.z * *thit);
Normal normal;
normal.setValue(point.x - center.x, point.y - center.y, point.z - center.z);
local->setValue(point, normal);
return true;
}
bool Shape::intersectTriangle(Ray& ray, float* thit, LocalGeo* local){
Vector edge21;
Vector edge32;
Vector edge13;
Vector edge31;
Vector edge12;
Vector edge23;
edge21.setValue(v2.x-v1.x, v2.y-v1.y, v2.z-v1.z); // one edge of the triangle
edge32.setValue(v3.x-v2.x, v3.y-v2.y, v3.z-v2.z); // another edge of the triangle (counterclockwise fashion)
edge13.setValue(v1.x-v3.x, v1.y-v3.y, v1.z-v3.z); // third edge of the triangle
edge31.setValue(-edge13.x, -edge13.y, -edge13.z);
edge12.setValue(-edge21.x, -edge21.y, -edge21.z);
edge23.setValue(-edge32.x, -edge32.y, -edge32.z);
Vector normal = edge23.crossProduct(edge31); // normal of the triangle's plane
float A = normal.x; // equation of the plane = Ax + By + Cz + D = 0
float B = normal.y;
float C = normal.z;
Vector tempV;
tempV.setValue(v1.x, v1.y, v1.z);
Vector rayOrigin;
rayOrigin.setValue(ray.pos.x, ray.pos.y, ray.pos.z);
rayOrigin.subtract(tempV);
float num = normal.dotProduct(rayOrigin);
float denom = normal.dotProduct(ray.dir);
if (abs(denom) < 0.00000001){ // the direction of the ray and the normal of the plane is perpendicular
//cout << "perpendicular \n";
return false;
}
*thit = - (num / denom);
if (abs(*thit) < 0.0000001) {
*thit = 0;
}
if (*thit < ray.t_min || *thit > ray.t_max){ // hit time outside of boundary
//cout << "outside boundary \n";
return false;
}
Point hitPoint;
hitPoint.setValue(ray.pos.x + ray.dir.x * *thit, ray.pos.y + ray.dir.y * *thit, ray.pos.z + ray.dir.z * *thit);
Vector vertexToPoint;
vertexToPoint.createFromPoints(v1, hitPoint);
float leftOfEdge1 = (edge21.crossProduct(edge31)).dotProduct(edge21.crossProduct(vertexToPoint));
vertexToPoint.createFromPoints(v2, hitPoint);
float leftOfEdge2 = (edge32.crossProduct(edge12)).dotProduct(edge32.crossProduct(vertexToPoint));
vertexToPoint.createFromPoints(v3, hitPoint);
float leftOfEdge3 = (edge13.crossProduct(edge23)).dotProduct(edge13.crossProduct(vertexToPoint));
//cout << leftOfEdge1 << "and" << leftOfEdge2 << "and" << leftOfEdge3;
if (leftOfEdge1 < 0.0 || leftOfEdge2 < 0.0 || leftOfEdge3 < 0.0){ // hit point not inside the triangle
//cout << "not inside the trianlge \n";
return false;
}
Normal normalizedNormal;
normalizedNormal.setValue(normal.x, normal.y, normal.z);
local->setValue(hitPoint, normalizedNormal);
return true;
}