//http://cse.csusb.edu/tong/courses/cs621/notes/ray.php
Vector3 SimpleMaterial::getReflectionDirection(const ONB& normal, const Vector3& in_dir) {
Vector3 reflection = normal.w();
reflection *= -2.0 * dot(in_dir, normal.w());
reflection += in_dir;
reflection.normalize();
return reflection;
}
bool PhongMetalMaterial::specularDirection(const ONB& uvw, const Vector3D& v_in, const Vector3D& p, const Vector2D& uv,
Vector2D& seed, ColorRGB& color, Vector3D& v_out)
{
float phi = 2* PI* seed.getX();
//the phong exponent is stored in the red value for the texture at that point
float exponent = phong_exp->value(uv, p).getRed();
float cosTheta = pow(1-seed.getY(), 1.0/(exponent+1));
float sinTheta = sqrt(1-cosTheta*cosTheta);
float x = cos(phi) * sinTheta;
float y = sin(phi) * sinTheta;
float z = cosTheta;
ONB basis;
Vector3D w = v_in - 2*dotProduct(v_in, uvw.w())*uvw.w();
basis.initFromW(w);
//color = R->value(uv, p);
ColorRGB r = R->value(uv, p);
float c = 1 - (dotProduct(v_in, uvw.w()));
color = r + (ColorRGB(1, 1, 1) + (-r))*(c*c*c*c*c);
v_out = x*basis.u() + y*basis.v() + z*basis.w();
if(exponent <10000) seed.scramble();
return (dotProduct(v_out, uvw.w()) >0 );
}
bool SimpleMaterial::getTransmissionDirection(const ONB &uvw, const Vector3 &in_dir, Color& _extinction, float &fresnel_scale, Vector3& transmission) {
Vector3 normal = uvw.w();
//printf("COS = %f \n", dot(in_dir, normal));
float cosine = dot(in_dir, normal);
if (cosine < 0.0f) {//incoming ray
float temp1 = 1.0f / n;
cosine = -cosine;
float root = 1.0f - (temp1 * temp1) * (1.0f - cosine * cosine);
//assume dielectrics embedded in air dont check for total internal refelction, yay physics
transmission = in_dir * temp1 + normal * (temp1 * cosine - sqrt(root));
_extinction = Color(1.0f, 1.0f, 1.0f);
}
else { //(cosine > 0.0f) ray outgoing
float temp2 = (dot(in_dir, normal));
float root = 1.0f - (n*n) * (1.0f - temp2 * temp2);
if (root < 0.0f) {return false;} //total internal reflection
else {transmission = in_dir * n + -normal * (n * temp2 - sqrt(root));}
_extinction = transmissive;
}
//printf("COS = %f", cosine);
//printf("R = %f", R0);
//printf("%f", 1.0f - (R0 + (1.0f - R0) * pow(1.0f - cosine, 5)));
fresnel_scale = 1.0f - (R0 + (1.0f - R0) * pow(1.0f - cosine, 5));
return true;
}
bool DSphere::randomPoint(const Vector3 &viewpoint, const Vector2 &seed, float time, Vector3 &light_point, Vector3 &N, float &pdf, Color &radiance) const {
float d = (viewpoint - getCenter(0)).magnitude();
if (d < radius) {return false;}
float r = radius;
//internal angle of cone surrounding light seen from viewpoint
float sin_alpha_max = r / d;
float cos_alpha_max = sqrt(1 - sin_alpha_max * sin_alpha_max);
float q = 1.0 / (2*M_PI*(1 - cos_alpha_max));
float cos_alpha = 1 + seed.x() * (cos_alpha_max - 1);
float sin_alpha = sqrt(1 - cos_alpha * cos_alpha);
float phi = 2*M_PI*seed.y();
float cos_phi = cos(phi);
float sin_phi = sin(phi);
Vector3 k_i(cos_phi * sin_alpha, sin_phi * sin_alpha, cos_alpha);
//construct local coordinate system UVW where viewpoint at origin and sphere at (0,0,d) in UVW
ONB UVW;
UVW.initFromW(getCenter(0) - viewpoint);
Ray to_light(viewpoint, k_i.x() * UVW.u() + k_i.y() * UVW.v() + k_i.z() * UVW.w());
IntersectRecord rec;
if (this -> intersect(to_light, 0.00001, FLT_MAX, time, rec)) {
light_point = rec.intersection;
float cos_theta_prime = -dot(rec.uvw.w(), to_light.direction());
pdf = q * cos_theta_prime / (light_point - viewpoint).squaredMagnitude();
N = rec.uvw.w();
radiance = mptr -> emittedRadiance(rec.uvw, -to_light.direction(), light_point, rec.uv);
return true;
}
return false;
}
Color SimpleMaterial::specularResponse(const ONB& normal, const Vector3& light_vector, const Vector3& eye_vector) {
Vector3 bisector = normalize(light_vector + eye_vector);
float specular_term = dot(normal.w(), bisector);
if (specular_term < 0.0) specular_term = 0.0;
if (specular_term > 1.0) specular_term = 1.0;
float phong_constant = pow(specular_term, phong_exp);
return specular * phong_constant;
}
bool PhongMetalMaterial::specularDirection(const ONB& uvw, const Vector3& v_in, const Vector3& p, const Vector2& uv, Vector2& seed, Color& color, Vector3& v_out) {
float phi = 2 * M_PI * seed.x();
float exponent = phong_exp -> value(uv, p).getRed();
float cosTheta = pow(1 - seed.y(), 1.0 / (exponent + 1));
float sinTheta = sqrt(1 - cosTheta*cosTheta);
float x = cos(phi) * sinTheta;
float y = sin(phi) * sinTheta;
float z = cosTheta;
ONB basis;
Vector3 w = v_in - 2*dot(v_in, uvw.w()) * uvw.w();
basis.initFromW(w);
color = tex -> value(uv, p);
v_out = x*basis.u() + y*basis.v() + z*basis.w();
if (exponent < 10000) {/*seed.scramble();*/}
return dot(v_out, uvw.w()) > 0;
}
ColorRGB DiffSpecMaterial::ambientResponse(const ONB& uvw, const Vector3D& v_in, const Vector3D& p, const Vector2D& uv)
{
float cosine = dotProduct(v_in, uvw.w());
if (cosine < 0.0f) cosine = -cosine;
float temp1 = 1.0f - cosine;
float R = R0 + (1.0f - R0) *temp1*temp1*temp1*temp1*temp1;
float P = (R + 0.5f) / 2.0f;
if(rng() <= P)
return spec_mat->ambientResponse(uvw, v_in, p, uv);
else
return diff_mat->ambientResponse(uvw, v_in, p, uv);
}
Color SimpleMaterial::diffuseResponse(const ONB& normal, const Vector3& light_vector) {
float diffuse_term = dot(normal.w(), normalize(light_vector));
if (diffuse_term < 0.0) diffuse_term = 0.0;
if (diffuse_term > 1.0) diffuse_term = 1.0;
return diffuse * diffuse_term;
}