//! Intersect ray and sphere, returning true if there is an intersection.
bool intersect(const ray<Type>& r, Type& tmin, Type& tmax) const
{
const vec3<Type> r_to_s = r.getOrigin() - m_center;
//Compute A, B and C coefficients
const Type A = r.getDirection().sqrLength();
const Type B = 2.0f * r_to_s.dot(r.getDirection());
const Type C = r_to_s.sqrLength() - m_radius * m_radius;
//Find discriminant
Type disc = B * B - 4.0 * A * C;
// if discriminant is negative there are no real roots
if (disc < 0.0)
return false;
disc = (Type)std::sqrt((double)disc);
tmin = (-B + disc) / (2.0 * A);
tmax = (-B - disc) / (2.0 * A);
// check if we're inside it
if ((tmin < 0.0 && tmax > 0) || (tmin > 0 && tmax < 0))
return false;
if (tmin > tmax)
std::swap(tmin, tmax);
return (tmin > 0);
}
Segments CSGNode::intersectLocal(const ray& r) const{
Segments ret;
if (isLeaf){
SegmentPoint pNear, pFar;
isect i;
ray backR(r.at(-10000), r.getDirection());
if(!item->intersect(backR, i))return ret;
pNear.t = i.t - 10000;
pNear.normal = i.N;
pNear.isRight = false;
ray contiR(r.at(pNear.t+RAY_EPSILON*10),r.getDirection());
if (!item->intersect(contiR, i))pFar = pNear;
else {
pFar.t = i.t + pNear.t;
pFar.normal = i.N;
}
pFar.isRight = true;
ret.addPoint(pNear);
ret.addPoint(pFar);
return ret;
}
else {
if (!lchild || !rchild)return ret;
Segments leftSeg, rightSeg;
leftSeg = lchild->intersectLocal(r);
rightSeg = rchild->intersectLocal(r);
leftSeg.Merge(rightSeg,relation);
return leftSeg;
}
}
bool Cone::intersectBody( const ray& r, isect& i ) const
{
vec3f d = r.getDirection();
vec3f p = r.getPosition();
double a = (d[0]*d[0]) + (d[1]*d[1]) - (C*d[2]*d[2]);
double b = 2.0 * (d[0]*p[0] + d[1]*p[1] - C*d[2]*p[2]) - B*d[2];
double c = (p[0]*p[0]) + (p[1]*p[1]) - A - (B*p[2]) - (C*p[2]*p[2]);
double disc = b*b - 4.0*a*c;
if( disc <= 0.0 ) {
return false;
}
disc = sqrt( disc );
double t1 = (-b - disc) / (2.0 * a);
double t2 = (-b + disc) / (2.0 * a);
if( t2 < RAY_EPSILON ) {
return false;
}
if( t1 > RAY_EPSILON ) {
// Two intersections.
vec3f P = r.at( t1 );
double z = P[2];
if( z >= 0.0 && z <= height ) {
// It's okay.
i.t = t1;
double p3 = -C*P[2] + (b_radius - t_radius)*b_radius / height;
i.N = vec3f(P[0], P[1], p3).normalize();
#ifdef _DEBUG
printf("two intersections!\n");
#endif
return true;
}
}
vec3f P = r.at( t2 );
double z = P[2];
if( z >= 0.0 && z <= height ) {
i.t = t2;
double p3 = -C*P[2] + (b_radius - t_radius)*b_radius / height;
i.N = vec3f(P[0], P[1], p3).normalize();
// In case we are _inside_ the _uncapped_ cone, we need to flip the normal.
// Essentially, the cone in this case is a double-sided surface
// and has _2_ normals
if( !capped && (i.N).dot( r.getDirection() ) > 0 )
i.N = -i.N;
#ifdef _DEBUG
printf("one intersection!\n");
#endif
return true;
}
return false;
}
// Intersect ray r with the triangle abc. If it hits returns true,
// and puts the t parameter, barycentric coordinates, normal, object id,
// and object material in the isect object
bool TrimeshFace::intersectLocal( const ray& r, isect& i ) const
{
const Vec3d& a = parent->vertices[ids[0]];
const Vec3d& b = parent->vertices[ids[1]];
const Vec3d& c = parent->vertices[ids[2]];
// tangent vectors
Vec3d t1 = b - a;
Vec3d t2 = c - a;
Vec3d n = crossProd(t1,t2);
double D = -n*a;
// if the surface is parallel to the ray there is no intersection
if(r.getDirection()*n == 0)
{
return false;
}
double t = -(n*r.getPosition() + D)/(n*r.getDirection() );
if (t <= RAY_EPSILON)
return false;
// point of intersection with the same plane (doesn't mean intersection with triangle) p(t)=p+t*d
Vec3d p = r.at(t);
// triangle area
double A = n.length()/2.0;
// barycentric coords
double wa = crossProd(c-b, p-b).length() / (2.0*A);
double wb = crossProd(a-c, p-c).length() / (2.0*A);
double wc = crossProd(b-a, p-a).length() / (2.0*A);
if((wa >= 0.0) && (wb >= 0.0) && (wc >= 0.0) && (wa+wb+wc-1.0 <= 0.00001)) {
i.setT(t);
i.setBary(wa, wb, wc);
if (parent->normals.size() == 0) {
i.setN(n);
} else {
Vec3d inter_n = wa*parent->normals[ids[0]] + wb*parent->normals[ids[1]]
+ wc*parent->normals[ids[2]];
inter_n.normalize();
i.setN(inter_n);
}
i.setObject(this);
if (parent->materials.size() == 0) {
i.setMaterial(this->getMaterial() );
} else {
Material inter_m = wa*(*parent->materials[ids[0]]);
inter_m += wb*(*parent->materials[ids[1]]);
inter_m += wc*(*parent->materials[ids[2]]);
i.setMaterial(inter_m);
}
return true;
}
return false;
}
// Apply the Blinn-Phong model to this point on the surface of the object,
// returning the color of that point.
Vec3d Material::shade( Scene *scene, const ray& r, const isect& i ) const
{
// YOUR CODE HERE
// For now, this method just returns the diffuse color of the object.
// This gives a single matte color for every distinct surface in the
// scene, and that's it. Simple, but enough to get you started.
// (It's also inconsistent with the Phong model...)
// Your mission is to fill in this method with the rest of the phong
// shading model, including the contributions of all the light sources.
// You will need to call both distanceAttenuation() and shadowAttenuation()
// somewhere in your code in order to compute shadows and light falloff.
if (debugMode)
std::cout << "Debugging the Phong code (or lack thereof...)" << std::endl;
// When you're iterating through the lights,
// you'll want to use code that looks something
// like this:
Vec3d light = ke(i);
Vec3d normal = i.N;
Vec3d iDot = r.at(i.t);
if (r.getDirection() * normal > 0) {
normal = -normal;
light += prod(prod(scene->ambient(), ka(i)), kt(i));
}
else {
light += prod(scene->ambient(), ka(i));
}
for (vector<Light*>::const_iterator litr = scene->beginLights();
litr != scene->endLights();
++litr)
{
Light* pLight = *litr;
double distAttenuation = pLight->distanceAttenuation(iDot);
Vec3d shadowAttenuation = pLight->shadowAttenuation(iDot);
Vec3d atten = distAttenuation * shadowAttenuation;
Vec3d L = pLight->getDirection(iDot);
if (L * normal > 0) {
Vec3d H = (L + -1 * r.getDirection());
if (H.length() != 0)
H.normalize();
double sDot = max(0.0, normal * H);
Vec3d dTerm = kd(i) * (normal * L);
Vec3d sTerm = ks(i) * (pow(sDot, shininess(i)));
Vec3d newLight = dTerm + sTerm;
newLight = prod(newLight, pLight->getColor());
light += prod(atten, newLight);
}
}
return light;
}
bool Cone::intersectBody( const ray& r, isect& i ) const
{
vec3f d = r.getDirection();
vec3f p = r.getPosition();
double a = (d[0]*d[0]) + (d[1]*d[1]) - (C*d[2]*d[2]);
double b = 2.0 * (d[0]*p[0] + d[1]*p[1] - C*d[2]*p[2]) - B*d[2];
double c = (p[0]*p[0]) + (p[1]*p[1]) - A - (B*p[2]) - (C*p[2]*p[2]);
double disc = b*b - 4.0*a*c;
if( disc <= 0.0 ) {
return false;
}
disc = sqrt( disc );
double t1 = (-b - disc) / (2.0 * a);
double t2 = (-b + disc) / (2.0 * a);
if( t2 < RAY_EPSILON ) {
return false;
}
if( t1 > RAY_EPSILON ) {
// Two intersections.
vec3f P = r.at( t1 );
double z = P[2];
if( z >= 0.0 && z <= height ) {
double n3 = -C*P[2] + (b_radius - t_radius)*b_radius / height;
i.t = t1;
i.N = vec3f( P[0], P[1], n3).normalize();
if (!capped && (i.N).dot(r.getDirection()) > 0)
i.N = -i.N;
return true;
}
}
vec3f P = r.at( t2 );
double z = P[2];
if( z >= 0.0 && z <= height ) {
double n3 = -C*P[2] + (b_radius - t_radius)*b_radius / height;
i.t = t2;
i.N = vec3f( P[0], P[1], n3).normalize();
if( !capped && (i.N).dot( r.getDirection() ) > 0 )
i.N = -i.N;
return true;
}
return false;
}
bool intersectCircle(const ray& r0, double& tnear, double& tfar, const vec3f& center)
{
ray r(r0.getPosition() - center, r0.getDirection());
vec3f v = -r.getPosition();
double b = v.dot(r.getDirection());
double discriminant = b*b - v.dot(v) + 1;
if (discriminant < 0.0) {
return false;
}
discriminant = sqrt(discriminant);
double t2 = b + discriminant;
if (t2 <= RAY_EPSILON) {
return false;
}
double t1 = b - discriminant;
if (t1 > RAY_EPSILON) {
tnear = t1;
tfar = t2;
}
else {
tnear = 0;
tfar = t2;
}
return true;
}
bool Square::intersectLocal( const ray& r, isect& i ) const
{
vec3f p = r.getPosition();
vec3f d = r.getDirection();
if( d[2] == 0.0 ) {
return false;
}
double t = -p[2]/d[2];
if( t <= RAY_EPSILON ) {
return false;
}
vec3f P = r.at( t );
if( P[0] < -0.5 || P[0] > 0.5 ) {
return false;
}
if( P[1] < -0.5 || P[1] > 0.5 ) {
return false;
}
i.obj = this;
i.t = t;
if( d[2] > 0.0 ) {
i.N = vec3f( 0.0, 0.0, -1.0 );
} else {
i.N = vec3f( 0.0, 0.0, 1.0 );
}
return true;
}
// Apply the phong model to this point on the surface of the object, returning
// the color of that point. Uses shaddowAttenuation which sends a shadow ray
// to check if there is an intersection that blocks the light sources.
Vec3d Material::shade( Scene *scene, const ray& r, const isect& i ) const
{
Vec3d retVal = ke(i) + prod(ka(i), scene->ambient());
// Applies calculations for each light source
for (vector<Light*>::const_iterator litr = scene->beginLights();
litr != scene->endLights(); ++litr) {
Vec3d point = r.getPosition() + r.getDirection() * i.t;
Light* pLight = *litr;
Vec3d reflectionAngle = 2 * (i.N * pLight->getDirection(point)) * i.N - pLight->getDirection(point);
Vec3d diffIntensity = kd(i) * (max(0, i.N * pLight->getDirection(point)));
Vec3d viewerAngle = scene->getCamera().getEye() - point;
viewerAngle.normalize();
Vec3d specIntensity = ks(i) * pow(max(0, viewerAngle * reflectionAngle), shininess(i));
Vec3d lcolor = pLight->getColor(point);
Vec3d totalColor = prod(diffIntensity + specIntensity, lcolor);
totalColor = totalColor * pLight->distanceAttenuation(point);
totalColor = prod(totalColor, pLight->shadowAttenuation(point));
retVal = retVal + totalColor;
}
return retVal;
}
bool CSGTree::intersect(const ray& r, isect& i) const{
if (!root)return false;
Segments inters = root->intersectLocal(r);
SegmentPoint sp;
if(!inters.firstPositive(sp))return false;
i.t = sp.t;
if (sp.isRight){//right - out
if (sp.normal*r.getDirection() > RAY_EPSILON)i.N = sp.normal;
else i.N = -sp.normal;
}
else {//left - in
if (sp.normal*r.getDirection() > RAY_EPSILON)i.N = -sp.normal;
else i.N = sp.normal;
}
return true;
}
bool Sphere::intersectLocal( const ray& r, isect& i ) const
{
Vec3d v = -r.getPosition();
double b = v * r.getDirection();
double discriminant = b*b - v*v + 1;
if( discriminant < 0.0 ) {
return false;
}
discriminant = sqrt( discriminant );
double t2 = b + discriminant;
if( t2 <= RAY_EPSILON ) {
return false;
}
i.obj = this;
double t1 = b - discriminant;
if( t1 > RAY_EPSILON ) {
i.t = t1;
i.N = r.at( t1 );
i.N.normalize();
} else {
i.t = t2;
i.N = r.at( t2 );
i.N.normalize();
}
return true;
}
bool Cylinder::intersectCaps( const ray& r, isect& i ) const
{
if( !capped ) {
return false;
}
double pz = r.getPosition()[2];
double dz = r.getDirection()[2];
if( 0.0 == dz ) {
return false;
}
double t1;
double t2;
if( dz > 0.0 ) {
t1 = (-pz)/dz;
t2 = (1.0-pz)/dz;
} else {
t1 = (1.0-pz)/dz;
t2 = (-pz)/dz;
}
if( t2 < RAY_EPSILON ) {
return false;
}
if( t1 >= RAY_EPSILON ) {
vec3f p( r.at( t1 ) );
if( (p[0]*p[0] + p[1]*p[1]) <= 1.0 ) {
i.t = t1;
if( dz > 0.0 ) {
// Intersection with cap at z = 0.
i.N = vec3f( 0.0, 0.0, -1.0 );
} else {
i.N = vec3f( 0.0, 0.0, 1.0 );
}
return true;
}
}
vec3f p( r.at( t2 ) );
if( (p[0]*p[0] + p[1]*p[1]) <= 1.0 ) {
i.t = t2;
if( dz > 0.0 ) {
// Intersection with cap at z = 1.
i.N = vec3f( 0.0, 0.0, 1.0 );
} else {
i.N = vec3f( 0.0, 0.0, -1.0 );
}
return true;
}
return false;
}
// Apply the phong model to this point on the surface of the object, returning
// the color of that point.
Vec3d Material::shade(Scene *scene, const ray& r, const isect& i) const
{
const Material& m = i.getMaterial();
Vec3d I = m.ke(i) + prod(m.ka(i) ,scene->ambient());
Vec3d R = 2*(-r.getDirection() * i.N)*i.N +r.getDirection();
for ( vector<Light*>::const_iterator litr = scene->beginLights();
litr != scene->endLights();
++litr )
{
Vec3d atten = (*litr)->distanceAttenuation(r.at(i.t)) * (*litr)->shadowAttenuation(r,r.at(i.t));
I += prod(atten,(m.kd(i)*max((i.N * (*litr)->getDirection(r.at(i.t)) ), 0.0) + m.ks(i) * max(((scene->getCamera().getEye() - r.at(i.t)) *R),0.0)));
}
// You will need to call both the distanceAttenuation() and
// shadowAttenuation() methods for each light source in order to
// compute shadows and light falloff.
return I;
}
bool Metaball::intersectLocal(const ray& r, isect& i) const
{
bool inside = false;
if (calvalue(r.getPosition(), ball1pos, ball2pos)>threshold)inside = true;
//determine possible intersect range
double t11=0, t12=0, t21=0, t22=0;
double tmin, tmax;
bool i1, i2;
i1 = intersectCircle(r, t11, t12, ball1pos);
i2 = intersectCircle(r, t21, t22, ball2pos);
if (!i1 && !i2) return false;
else if (!i1 && i2)
{
tmin = t21;
tmax = t22;
}
else if (i1 && !i2)
{
tmin = t11;
tmax = t12;
}
else
{
tmin = min(t11, t21);
tmax = max(t12, t22);
}
for (double t = tmin; t < tmax; t += 0.001)
{
vec3f point = r.getPosition() + t * r.getDirection();
double value = calvalue(point, ball1pos, ball2pos);
if ((!inside && value > threshold) || (inside && value < threshold))
{
// prevent fake intersect
if (inside && t < 0.01)return false;
vec3f normal;
normal += 2 * (point - ball1pos) / ((point - ball1pos).length()*(point - ball1pos).length());
normal += 2 * (point - ball2pos) / ((point - ball2pos).length()*(point - ball2pos).length());
normal = normal.normalize();
i.t = t;
i.N = normal;
i.obj = this;
return true;
}
}
return false;
}
// Apply the phong model to this point on the surface of the object, returning
// the color of that point.
vec3f Material::shade( Scene *scene, const ray& r, const isect& i ) const
{
// YOUR CODE HERE
// For now, this method just returns the diffuse color of the object.
// This gives a single matte color for every distinct surface in the
// scene, and that's it. Simple, but enough to get you started.
// (It's also inconsistent with the phong model...)
// Your mission is to fill in this method with the rest of the phong
// shading model, including the contributions of all the light sources.
// You will need to call both distanceAttenuation() and shadowAttenuation()
// somewhere in your code in order to compute shadows and light falloff.
//intersection point
vec3f point = r.at(i.t);
bool istransmissive = abs(index - 1.0) > NORMAL_EPSILON || !kt.iszero();
vec3f rate = vec3f(1, 1, 1) - kt;
vec3f I = ke;
//ambient
if (istransmissive) I += scene->ambient.time(ka).time(rate).clamp();
else I += scene->ambient.time(ka).clamp();
list<Light*>::const_iterator begin = scene->beginLights();
list<Light*>::const_iterator end = scene->endLights();
while (begin != end)
{
vec3f atten = (*begin)->shadowAttenuation(point) * (*begin)->distanceAttenuation(point);
vec3f L = (*begin)->getDirection(point);
double NL = i.N.dot(L);
//diffuse
if (istransmissive) I += (atten * NL).time(kd).time(rate).clamp();
else I += (atten * NL).time(kd).clamp();
//specular
vec3f R = i.N * (2 * NL) - L;
double RV = -R.dot(r.getDirection());
//TODO: where is n£¿
double n = 64;
I += (atten * pow(RV, n)).time(ks).clamp();
begin++;
}
return I;
}
// if the ray hits the box, put the "t" value of the intersection
// closest to the origin in tMin and the "t" value of the far intersection
// in tMax and return true, else return false.
// Using Kay/Kajiya algorithm.
bool BoundingBox::intersect(const ray& r, double& tMin, double& tMax) const
{
vec3f R0 = r.getPosition();
vec3f Rd = r.getDirection();
tMin = -1.0e308; // 1.0e308 is close to infinity... close enough for us!
tMax = 1.0e308;
double ttemp;
for (int currentaxis = 0; currentaxis < 3; currentaxis++)
{
double vd = Rd[currentaxis];
// if the ray is parallel to the face's plane (=0.0)
if( vd > -RAY_EPSILON && vd < RAY_EPSILON ) {
if(R0[currentaxis] <= min[currentaxis] - RAY_EPSILON || R0[currentaxis] >= max[currentaxis] + RAY_EPSILON) {
return false;
}
else {
continue;
}
}
double v1 = min[currentaxis] - R0[currentaxis];
double v2 = max[currentaxis] - R0[currentaxis];
// two slab intersections
double t1 = v1/vd;
double t2 = v2/vd;
if ( t1 > t2 ) { // swap t1 & t2
ttemp = t1;
t1 = t2;
t2 = ttemp;
}
if (t1 > tMin)
tMin = t1;
if (t2 < tMax)
tMax = t2;
if (tMin > tMax) // box is missed
return false;
if (tMax < -RAY_EPSILON) // box is behind ray
return false;
}
return true; // it made it past all 3 axes.
}
bool Box::intersectLocal( const ray& r, isect& i ) const
{
BoundingBox bounds = ComputeLocalBoundingBox();
vec3f p = r.getPosition();
vec3f d = r.getDirection();
//find tmin and tmax
vec3f tmin;
vec3f tmax;
vec3f nmin(0, 0, 0);
vec3f nmax(0, 0, 0);
double min;
double max;
for(int j=0; j<3; j++) {
if(d[j]>=0) {
tmin[j] = (bounds.min[j] - p[j]) / d[j];
tmax[j] = (bounds.max[j] - p[j]) / d[j];
nmin[j] = -1;
nmax[j] = 1;
} else {
tmin[j] = (bounds.max[j] - p[j]) / d[j];
tmax[j] = (bounds.min[j] - p[j]) / d[j];
nmin[j] = 1;
nmax[j] = -1;
}
}
//min of tmax, max of tmin
max = std::min( std::min(tmax[0], tmax[1]), tmax[2]);
min = std::max( std::max(tmin[0], tmin[1]), tmin[2]);
if(min > max || max < RAY_EPSILON) return false;
i.obj = this;
vec3f N(0, 0, 0);
if(min >= RAY_EPSILON) {
i.t = min;
for(int i=0; i<3; i++) {
if(tmin[i] == min) { N[i] = nmin[i]; break; }
}
} else {
i.t = max;
for(int i=0; i<3; i++) {
if(tmax[i] == max) { N[i] = nmax[i]; break; }
}
}
i.N = N;
return true;
}
bool Geometry::intersect(const ray&r, isect&i) const {
double tmin, tmax;
if (hasBoundingBoxCapability() && !(bounds.intersect(r, tmin, tmax))) return false;
// Transform the ray into the object's local coordinate space
Vec3d pos = transform->globalToLocalCoords(r.getPosition());
Vec3d dir = transform->globalToLocalCoords(r.getPosition() + r.getDirection()) - pos;
double length = dir.length();
dir /= length;
ray localRay( pos, dir, r.type() );
if (intersectLocal(localRay, i)) {
// Transform the intersection point & normal returned back into global space.
i.N = transform->localToGlobalCoordsNormal(i.N);
i.t /= length;
return true;
} else return false;
}
bool Geometry::intersect(const ray&r, isect&i) const
{
// Transform the ray into the object's local coordinate space
vec3f pos = transform->globalToLocalCoords(r.getPosition());
vec3f dir = transform->globalToLocalCoords(r.getPosition() + r.getDirection()) - pos;
double length = dir.length();
dir /= length;
ray localRay( pos, dir );
if (intersectLocal(localRay, i)) {
// Transform the intersection point & normal returned back into global space.
i.N = transform->localToGlobalCoordsNormal(i.N);
i.t /= length;
return true;
} else {
return false;
}
}
//Test
// now the object is in the local coordinate rather than the global
bool Square::intersectLocal( const ray& r, isect& i ) const
{
// get the parameters of the ray
Vec3d p = r.getPosition();
Vec3d d = r.getDirection();
// if the ray is perpendicular to the z-axis
if( d[2] == 0.0 ) {
return false;
}
// calculate the value of t
double t = -p[2]/d[2];
// if the intersection is too close to the source
// then we don't count that as a intersection
if( t <= RAY_EPSILON ) {
return false;
}
Vec3d P = r.at( t );
if( P[0] < -0.5 || P[0] > 0.5 ) {
return false;
}
if( P[1] < -0.5 || P[1] > 0.5 ) {
return false;
}
i.obj = this;
i.t = t;
if( d[2] > 0.0 ) {
i.N = Vec3d( 0.0, 0.0, -1.0 );
} else {
i.N = Vec3d( 0.0, 0.0, 1.0 );
}
i.setUVCoordinates( Vec2d(P[0] + 0.5, P[1] + 0.5) );
return true;
}
vec3f PointLight::_shadowAttenuation(const vec3f& P, const ray& r) const
{
double distance = (position - P).length();
vec3f d = r.getDirection();
vec3f result = getColor(P);
vec3f curP = r.getPosition();
isect isecP;
ray newr(curP, d);
while (scene->intersect(newr, isecP))
{
//prevent going beyond this light
if ((distance -= isecP.t) < RAY_EPSILON) return result;
//if not transparent return black
if (isecP.getMaterial().kt.iszero()) return vec3f(0, 0, 0);
//use current intersection point as new light source
curP = r.at(isecP.t);
newr = ray(curP, d);
result = prod(result, isecP.getMaterial().kt);
}
return result;
}
//Test
bool Square::intersectLocal(ray& r, isect& i) const
{
Vec3d p = r.getPosition();
Vec3d d = r.getDirection();
if( d[2] == 0.0 ) {
return false;
}
double t = -p[2]/d[2];
if( t <= RAY_EPSILON ) {
return false;
}
Vec3d P = r.at( t );
if( P[0] < -0.5 || P[0] > 0.5 ) {
return false;
}
if( P[1] < -0.5 || P[1] > 0.5 ) {
return false;
}
i.obj = this;
i.setMaterial(this->getMaterial());
i.t = t;
if( d[2] > 0.0 ) {
i.N = Vec3d( 0.0, 0.0, -1.0 );
} else {
i.N = Vec3d( 0.0, 0.0, 1.0 );
}
i.setUVCoordinates( Vec2d(P[0] + 0.5, P[1] + 0.5) );
return true;
}
bool Cone::intersectCaps( const ray& r, isect& i ) const
{
if( !capped ) {
return false;
}
double pz = r.getPosition()[2];
double dz = r.getDirection()[2];
if( 0.0 == dz ) {
return false;
}
double t1;
double t2;
double r1;
double r2;
if( dz > 0.0 ) {
t1 = (-pz)/dz;
t2 = (height-pz)/dz;
r1 = b_radius;
r2 = t_radius;
} else {
t1 = (height-pz)/dz;
t2 = (-pz)/dz;
r1 = t_radius;
r2 = b_radius;
}
if( t2 < RAY_EPSILON ) {
return false;
}
if( t1 >= RAY_EPSILON ) {
vec3f p( r.at( t1 ) );
if( (p[0]*p[0] + p[1]*p[1]) <= r1 * r1 ) {
i.t = t1;
if( dz > 0.0 ) {
// Intersection with cap at z = 0.
i.N = vec3f( 0.0, 0.0, -1.0 );
} else {
i.N = vec3f( 0.0, 0.0, 1.0 );
}
return true;
}
}
vec3f p( r.at( t2 ) );
if( (p[0]*p[0] + p[1]*p[1]) <= r2 * r2 ) {
i.t = t2;
if( dz > 0.0 ) {
// Intersection with interior of cap at z = 1.
i.N = vec3f( 0.0, 0.0, 1.0 );
} else {
i.N = vec3f( 0.0, 0.0, -1.0 );
}
return true;
}
return false;
}
// Do recursive ray tracing! You'll want to insert a lot of code here
// (or places called from here) to handle reflection, refraction, etc etc.
Vec3d RayTracer::traceRay( const ray& r,
const Vec3d& thresh, int depth )
{
isect i;
if( scene->intersect( r, i ) ) {
// YOUR CODE HERE
// An intersection occured! We've got work to do. For now,
// this code gets the material for the surface that was intersected,
// and asks that material to provide a color for the ray.
// This is a great place to insert code for recursive ray tracing.
// Instead of just returning the result of shade(), add some
// more steps: add in the contributions from reflected and refracted
// rays.
const Material& m = i.getMaterial();
Vec3d ret = m.shade(scene, r, i);
if (depth == traceUI->getDepth())
return ret;
Vec3d d = r.getDirection();
double n;
Vec3d NN = i.N;
if (i.N * (-d) >= 0)
{
// entering the object
n = 1.0 / m.index(i);
}
else
{
// leaving
n = m.index(i);
NN = -NN;
}
double c1 = -(NN * d);
Vec3d Rl = d + 2 * NN * c1;
ray reflection = ray(r.at(i.t), Rl, r.REFLECTION);
ret += prod(m.kr(i), traceRay(reflection, thresh, depth+1));
double c2 = 1 - n*n * (1 - c1*c1);
if (c2 >= 0)
{
// not total internal reflection
c2 = sqrt(c2);
Vec3d Rr = (n * d) + (n * c1 - c2) * NN;
ray refraction = ray(r.at(i.t), Rr, r.REFRACTION);
ret += prod(m.kt(i), traceRay(refraction, thresh, depth+1));
}
return ret;
} else {
// No intersection. This ray travels to infinity, so we color
// it according to the background color, which in this (simple) case
// is just black.
return Vec3d( 0.0, 0.0, 0.0 );
}
}
vec3f RayTracer::traceRay( Scene *scene, const ray& r,
const vec3f& thresh, int depth, isect& i, vector<const SceneObject*>& stack )
{
if( depth>=0
&& thresh[0] > threshold - RAY_EPSILON && thresh[1] > threshold - RAY_EPSILON && thresh[2] > threshold - RAY_EPSILON
&& scene->intersect( r, i ) ) {
// YOUR CODE HERE
// An intersection occured! We've got work to do. For now,
// this code gets the material for the surface that was intersected,
// and asks that material to provide a color for the ray.
// This is a great place to insert code for recursive ray tracing.
// Instead of just returning the result of shade(), add some
// more steps: add in the contributions from reflected and refracted
// rays.
const Material& m = i.getMaterial();
vec3f color = m.shade(scene, r, i);
//calculate the reflected ray
vec3f d = r.getDirection();
vec3f position = r.at(i.t);
vec3f direction = d - 2 * i.N * d.dot(i.N);
ray newray(position, direction);
if(!m.kr.iszero()) {
vec3f reflect = m.kr.multiply(traceRay(scene, newray, thresh.multiply(m.kr), depth-1, stack).clamp());
color += reflect;
}
//calculate the refracted ray
double ref_ratio;
double sin_ang = d.cross(i.N).length();
vec3f N = i.N;
//Decide going in or out
const SceneObject *mi = NULL, *mt = NULL;
int stack_idx = -1;
vector<const SceneObject*>::reverse_iterator itr;
//1 use the normal to decide whether to go in or out
//0: travel through, 1: in, 2: out
char travel = 0;
if(i.N.dot(d) <= -RAY_EPSILON) {
//from outer surface in
//test whether the object has two face
ray test_ray(r.at(i.t) + d * 2 * RAY_EPSILON, -d);
isect test_i;
if(i.obj->intersect(r, test_i) && test_i.N.dot(N) > -RAY_EPSILON) {
//has interior
travel = 1;
}
}
else {
travel = 2;
}
if(travel == 1) {
if(!stack.empty()) {
mi = stack.back();
}
mt = i.obj;
stack.push_back(mt);
}
else if(travel == 2) {
//if it is in our stack, then we must pop it
for(itr = stack.rbegin(); itr != stack.rend(); ++itr) {
if(*itr == i.obj) {
mi = *itr;
vector<const SceneObject*>::iterator ii = itr.base() - 1;
stack_idx = ii - stack.begin();
stack.erase(ii);
break;
}
}
if(!stack.empty()) {
mt = stack.back();
}
}
if(N.dot(d) >= RAY_EPSILON) {
N = -N;
}
ref_ratio = (mi?(mi->getMaterial().index):1.0) / (mt?(mt->getMaterial().index):1.0);
if(!m.kt.iszero() && (ref_ratio < 1.0 + RAY_EPSILON || sin_ang < 1.0 / ref_ratio + RAY_EPSILON)) {
//No total internal reflection
//We do refraction now
double c = N.dot(-d);
direction = (ref_ratio * c - sqrt(1 - ref_ratio * ref_ratio * (1 - c * c))) * N + ref_ratio * d;
newray = ray(position, direction);
vec3f refraction = m.kt.multiply(traceRay(scene, newray, thresh.multiply(m.kt), depth-1, stack).clamp());
color += refraction;
}
if(travel == 1) {
stack.pop_back();
}
else if(travel == 2) {
if(mi) {
stack.insert(stack.begin() + stack_idx, mi);
}
}
return color;
} else {
// No intersection. This ray travels to infinity, so we color
// it according to the background color, which in this (simple) case
// is just black.
if(m_bBackground && bg) {
double u, v;
angleToSphere(r.getDirection(), u, v);
//Scale to [0, 1];
u /= 2 * M_PI;
v /= M_PI;
int tx = int(u * bg_width), ty = bg_height - int(v * bg_height);
return vec3f(bg[3 * (ty * bg_width + tx)] / 255.0, bg[3 * (ty * bg_width + tx) + 1] / 255.0, bg[3 * (ty * bg_width + tx) + 2] / 255.0);
}
else {
return vec3f( 0.0, 0.0, 0.0 );
}
}
}
bool Box::intersectLocal( const ray& r, isect& i ) const
{
Vec3d p = r.getPosition();
Vec3d d = r.getDirection();
int it;
double x, y, t, bestT;
int mod0, mod1, mod2, bestIndex;
bestT = HUGE_DOUBLE;
bestIndex = -1;
for(it=0; it<6; it++){
mod0 = it%3;
if(d[mod0] == 0){
continue;
}
t = ((it/3) - 0.5 - p[mod0]) / d[mod0];
if(t < RAY_EPSILON || t > bestT){
continue;
}
mod1 = (it+1)%3;
mod2 = (it+2)%3;
x = p[mod1]+t*d[mod1];
y = p[mod2]+t*d[mod2];
if( x<=0.5 && x>=-0.5 &&
y<=0.5 && y>=-0.5)
{
if(bestT > t){
bestT = t;
bestIndex = it;
}
}
}
if(bestIndex < 0) return false;
i.setT(bestT);
i.setObject(this);
Vec3d intersect_point = r.at(i.t);
int i1 = (bestIndex + 1) % 3;
int i2 = (bestIndex + 2) % 3;
if(bestIndex < 3)
{
i.setN(Vec3d(-double(bestIndex == 0), -double(bestIndex == 1), -double(bestIndex == 2)));
i.setUVCoordinates( Vec2d( 0.5 - intersect_point[ min(i1, i2) ],
0.5 + intersect_point[ max(i1, i2) ] ) );
}
else
{
i.setN(Vec3d(double(bestIndex==3), double(bestIndex == 4), double(bestIndex == 5)));
i.setUVCoordinates( Vec2d( 0.5 + intersect_point[ min(i1, i2) ],
0.5 + intersect_point[ max(i1, i2) ] ) );
}
return true;
}
// Do recursive ray tracing! You'll want to insert a lot of code here
// (or places called from here) to handle reflection, refraction, etc etc.
Vec3d RayTracer::traceRay( const ray& r, const Vec3d& thresh, int depth )
{
if (depth > traceUI->getDepth())
return Vec3d( 0.0, 0.0, 0.0 );
++depth;
isect i;
if( scene->intersect( r, i ) ) {
// YOUR CODE HERE
// An intersection occured! We've got work to do. For now,
// this code gets the material for the surface that was intersected,
// and asks that material to provide a color for the ray.
// This is a great place to insert code for recursive ray tracing.
// Instead of just returning the result of shade(), add some
// more steps: add in the contributions from reflected and refracted
// rays.
const Material& m = i.getMaterial();
Vec3d iPoint = r.at(i.t); // point of intersection
/*
// --Shadows--
Vec3d shadow = Vec3d(1.0, 1.0, 1.0);
//for (vector<Light*>::const_iterator litr = scene->beginLights();
// litr != scene->endLights(); ++litr )
//{
vector<Light*>::const_iterator litr = scene->beginLights();
Light* pLight = *litr;
Vec3d shadowDir = pLight->getDirection(iPoint);
isect aux;
ray shadow_ray (iPoint,shadowDir,ray::SHADOW);
if(scene->intersect(shadow_ray, aux)) {
const Material& mm = aux.getMaterial();
shadow = prod(shadow, mm.kt(aux));
}
//}
*/
// --Reflection--
Vec3d reflection = Vec3d(0.0,0.0,0.0);
if (m.kr(i) != Vec3d(0.0,0.0,0.0)) {
Vec3d reflecDir = 2*((-1*r.getDirection()*i.N)*i.N) + r.getDirection();
reflecDir.normalize();
ray ReflRay (iPoint, reflecDir, ray::REFLECTION);
reflection = traceRay(ReflRay, Vec3d(1.0,1.0,1.0), depth);
// use threshold
for(int i=0; i < 3; i++){
if(reflection[i] > thresh[i]){
reflection[i] = 1;
}
}
}
// --Refraction--
Vec3d refraction = Vec3d(0.0,0.0,0.0);
if (m.kt(i) != Vec3d(0.0,0.0,0.0)) {
double IofR = 1.0 / m.index(i); // the index of refraction
Vec3d inorm = i.N;
Vec3d d = -1.0*r.getDirection(); // reverse the ray direction for calculations
double cos_i = inorm*d;
// if the ray is inside of the object
if (cos_i < 0.0) {
IofR = m.index(i);
cos_i *= -1.0;
inorm *= -1.0;
}
double cos_t = 1.0 - (IofR*IofR)*(1.0 - (cos_i*cos_i));
// if not Total Internal Reflection
if (cos_t >= 0.0) {
Vec3d refractDir = (IofR*cos_i - sqrt(cos_t))*inorm - IofR*d;
refractDir.normalize();
ray RefrRay (iPoint, refractDir, ray::REFRACTION);
refraction = traceRay(RefrRay, Vec3d(1.0,1.0,1.0), depth);
// use threshold
for(int i=0; i < 3; i++){
if(refraction[i] > thresh[i]){
refraction[i] = 1;
}
}
}
}
return m.shade(scene, r, i) + prod(m.kr(i), reflection) + prod(m.kt(i), refraction);
} else {
// No intersection. This ray travels to infinity, so we color
// it according to the background color, which in this (simple) case
// is just black.
return Vec3d( 0.0, 0.0, 0.0 );
}
}
Vec3d CubeMap::getColor(ray r) const {
int axis, front, left, right, top, bottom;
double u,v;
Vec3d dir = r.getDirection();
if (fabs(dir[0]) > fabs(dir[1]))
if (fabs(dir[0]) > fabs(dir[2])) {
axis = 0;
bottom = 3;
top = 2;
if (dir[0] > 0.0) {
front = 0;
left = 4;
right = 5;
}
else {
front = 1;
left = 5;
right = 4;
}
}
else {
axis = 2;
bottom = 3;
top = 2;
if (dir[2] > 0.0) {
front = 5;
left = 0;
right = 1;
}
else {
front = 4;
left = 1;
right = 0;
}
}
else
if (fabs(dir[1]) > fabs(dir[2])) {
axis = 1;
left = 1;
right = 0;
if (dir[1] > 0.0) {
front = 2;
bottom = 4;
top = 5;
}
else {
front = 3;
bottom = 5;
top = 4;
}
}
else {
axis = 2;
bottom = 3;
top = 2;
if (dir[2] > 0.0) {
front = 5;
left = 0;
right = 1;
}
else {
front = 4;
left = 1;
right = 0;
}
}
if (axis == 0) {
u = dir[2]/dir[0];
if (dir[0] > 0.0) v = dir[1]/dir[0];
else v = -dir[1]/dir[0];
}
else if (axis == 1) {
if (dir[1] > 0.0) u = dir[0]/dir[1];
else u = -dir[0]/dir[1];
v = dir[2]/dir[1];
}
else if (axis == 2) {
u = -dir[0]/dir[2];
if (dir[2] > 0.0) v = dir[1]/dir[2];
else v = -dir[1]/dir[2];
}
u = (u + 1.0)/2.0;
v = (v + 1.0)/2.0;
int filterwidth = traceUI->getFilterWidth();
if (filterwidth == 1) return tMap[front]->getMappedValue(Vec2d(u, v)); // Why even bother with expensive computation when we can grab straight from the image?
int fw = (filterwidth + 1)/2 - 1;
int rm = filterwidth - fw;
int width = tMap[front]->getWidth();
int height = tMap[front]->getHeight();
double delu = 1.0/width;
double delv = 1.0/height;
int x = floor(0.5 + u * (width - 1));
int y = floor(0.5 + v * (height - 1));
double startu = delu * (x - fw);
double startv = delv * (y - fw);
double nextu = startu;
double nextv = startv;
double xslope = 1.0/(((double)filterwidth + 1) / 2.0 * delu);
double yslope = 1.0/(((double)filterwidth + 1) / 2.0 * delv);
double correct = 0.0;
Vec3d thePixel = Vec3d(0.0, 0.0, 0.0);
for (int jj = -fw; jj < rm; jj++) {
for (int ii = -fw; ii < rm; ii++) {
int xindex = x + ii;
int yindex = y + jj;
if (xindex < 0 && yindex < 0) continue;
if (xindex >= width && yindex >= height) continue;
if (xindex >= width && yindex < 0) continue;
if (xindex < 0 && yindex >= height) continue;
int theMap = front;
if (yindex < 0) {
theMap = bottom;
if (axis == 0)
if (dir[0] > 0) {
yindex = height - 1 - xindex;
xindex = width + jj;
}
else {
yindex = xindex;
xindex = -1 - jj;
}
else if (axis == 1)
if (dir[1] > 0) yindex = height + jj;
else {
yindex = -1 - jj;
xindex = width - 1 - xindex;
}
else if (axis == 2)
if (dir[2] > 0) {
yindex = -1 - jj;
xindex = width - 1 - xindex;
}
else yindex = height + jj;
}
else if (yindex >= height) {
theMap = top;
if (axis == 0)
if (dir[0] > 0) {
yindex = xindex;
xindex = width - jj;
}
else {
yindex = height - 1 - xindex;
xindex = jj - 1;
}
else if (axis == 1)
if (dir[1] > 0) {
yindex = height - jj;
xindex = width - 1 - xindex;
}
else yindex = jj - 1;
else if (axis == 2)
if (dir[2] > 0) {
yindex = height - jj;
xindex = width - 1 - xindex;
}
else yindex = jj - 1;
}
else if (xindex < 0) {
theMap = left;
if (axis == 0 || axis == 2) xindex = width + ii;
else if (axis == 1)
if (dir[1] > 0) {
xindex = width - 1 - yindex;
yindex = height + ii;
}
else {
xindex = yindex;
yindex = -1 - ii;
}
}
else if (xindex >= width) {
theMap = right;
if (axis == 0 || axis == 2) xindex = ii - 1;
else if (axis == 1)
if (dir[1] > 0) {
xindex = yindex;
yindex = height - ii;
}
else {
xindex = width - 1 - yindex;
yindex = ii - 1;
}
}
double du = u - nextu;
double dv = v - nextv;
double weight = (1.0 - fabs(du * xslope)) * (1.0 - fabs(dv * yslope));
nextu += delu;
correct += weight;
thePixel += tMap[theMap]->getPixelAt(xindex, yindex) * weight;
}
nextu = startu;
nextv += delv;
}
thePixel /= correct;
return thePixel;
}
// Apply the phong model to this point on the surface of the object, returning
// the color of that point.
Vec3d Material::shade( Scene *scene, const ray& r, const isect& i ) const
{
// YOUR CODE HERE
// For now, this method just returns the diffuse color of the object.
// This gives a single matte color for every distinct surface in the
// scene, and that's it. Simple, but enough to get you started.
// (It's also inconsistent with the phong model...)
// Your mission is to fill in this method with the rest of the phong
// shading model, including the contributions of all the light sources.
// You will need to call both distanceAttenuation() and shadowAttenuation()
// somewhere in your code in order to compute shadows and light falloff.
if( debugMode )
std::cout << "Debugging Phong code..." << std::endl;
Vec3d intensity(0.0f,0.0f,0.0f);
Vec3d emmisiveIntensity = ke(i);
Vec3d ambientIntensity = ka(i);
ambientIntensity %= scene->ambient();
// When you're iterating through the lights,
// you'll want to use code that looks something
// like this:
//
const Vec3d intersectionPoint = r.at(i.t);
const Vec3d blue(0.0f,0.0f,0.4f);
const Vec3d yellow(0.4f,0.4f,0.0f);
double alpha = 0.2f;
double beta = 0.6f;
bool bNonRealism = traceUI->nonRealism();
for ( vector<Light*>::const_iterator litr = scene->beginLights(); litr != scene->endLights(); ++litr ){
Light* pLight = *litr;
Vec3d lightDirection = pLight->getDirection(intersectionPoint);
Vec3d surfaceNormal = i.N;
surfaceNormal.normalize();
double aLightToNormal = surfaceNormal * lightDirection;
Vec3d lightReflectedDirectionCi = (lightDirection*surfaceNormal)*surfaceNormal;
Vec3d lightReflectedDirectionSi = lightReflectedDirectionCi - lightDirection;
Vec3d lightReflectedDirection = lightReflectedDirectionCi + lightReflectedDirectionSi;
lightReflectedDirection.normalize();
double aRayToLight = (-1 * r.getDirection()) * lightReflectedDirection;
Vec3d shadowLight(1.0f,1.0f,1.0f);
if(bNonRealism){
if(bump(i)[0]!= 2.0f){
Vec3d perturbed = 2.0f*bump(i)-1.0f;
perturbed[0] *= traceUI->getBumpScale();
perturbed[1] *= traceUI->getBumpScale();
perturbed %=surfaceNormal;
perturbed.normalize();
aLightToNormal = perturbed * lightDirection;}
double coolFac = (1.0f+ (-1.0f)* aLightToNormal)/2.0f;
double warmFac = 1.0f - coolFac;
Vec3d diffuseIntensity = (coolFac * ( blue + kd(i) * alpha)) + (warmFac * ( yellow + kd(i) * beta));
//Vec3d specularIntensity = ks(i) * pLight->getColor(intersectionPoint);
shadowLight %= diffuseIntensity; //+ specularIntensity * std::pow(std::max(aRayToLight,0.0),shininess(i)));
} else {
if(bump(i)[0]!= 2.0f){
Vec3d perturbed = 2.0f*bump(i)-1.0f;
perturbed[0] *= traceUI->getBumpScale();
perturbed[1] *= traceUI->getBumpScale();
perturbed %=surfaceNormal;
perturbed.normalize();
aLightToNormal = perturbed * lightDirection;}
Vec3d diffuseIntensity = kd(i);
Vec3d specularIntensity = ks(i);
diffuseIntensity%=pLight->getColor(intersectionPoint);
specularIntensity%=pLight->getColor(intersectionPoint);
shadowLight = pLight->shadowAttenuation(intersectionPoint);
shadowLight %= (diffuseIntensity * std::max(aLightToNormal, 0.0) + specularIntensity * std::pow(std::max(aRayToLight,0.0),shininess(i)));
}
intensity += shadowLight*pLight->distanceAttenuation(intersectionPoint);
}
return intensity + emmisiveIntensity + ambientIntensity;
}
// Apply the Phong model to this point on the surface of the object, returning
// the color of that point.
Vec3d Material::shade( Scene *scene, const ray& r, const isect& i, bool isInAir ) const
{
// YOUR CODE HERE
// For now, this method just returns the diffuse color of the object.
// This gives a single matte color for every distinct surface in the
// scene, and that's it. Simple, but enough to get you started.
// (It's also inconsistent with the Phong model...)
// Your mission is to fill in this method with the rest of the phong
// shading model, including the contributions of all the light sources.
// You will need to call both distanceAttenuation() and shadowAttenuation()
// somewhere in your code in order to compute shadows and light falloff.
// When you're iterating through the lights,
// you'll want to use code that looks something
// like this:
//
// for ( vector<Light*>::const_iterator litr = scene->beginLights();
// litr != scene->endLights();
// ++litr )
// {
// Light* pLight = *litr;
// .
// .
// .
// }
const Vec3d point = r.at(i.t);
// Start with emitted light.
Vec3d shade = ke(i);
// Add ambient light effects.
Vec3d ambient = prod(ka(i), scene->ambient());
if (!isInAir)
{
// If shading a point inside an object, ambient light had to pass through the object first.
// So apply the transmission factor to the ambient light to account for object's affect on light.
ambient = prod(kt(i), ambient);
}
shade += ambient;
// For each light source...
for (vector<Light*>::const_iterator literator = scene->beginLights(); literator != scene->endLights(); ++literator)
{
const Light* light = *literator;
const Vec3d lightDirection = light->getDirection(point);
const Vec3d shadowAttenuation = light->shadowAttenuation(point);
const double distanceAttenuation = light->distanceAttenuation(point);
const Vec3d intensity = prod(light->getColor(point), shadowAttenuation * distanceAttenuation);
if (debugMode) cerr << "Shadow: " << shadowAttenuation << ", Distance: " << distanceAttenuation << endl;
// Calculate diffuse term.
const Vec3d diffuseTerm = kd(i) * max(0.0, i.N * lightDirection);
// Calculate specular term.
const Vec3d reflectionDir = 2.0 * (lightDirection * i.N) * i.N - lightDirection;
const Vec3d viewingDir = -r.getDirection();
const Vec3d specularTerm = ks(i) * pow(max(0.0, viewingDir * reflectionDir), shininess(i));
// Apply diffuse and specular terms to light source.
shade += prod(intensity, diffuseTerm + specularTerm);
if (debugMode) cerr << "Diffuse: " << diffuseTerm << ", Specular: " << specularTerm << endl;
}
return shade;
}
