// 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;
}
bool Sphere::intersectLocal(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;
i.setMaterial(this->getMaterial());
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;
}
//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::intersectLocal(ray& r, isect& i) const
{
bool ret = false;
const int x = 0, y = 1, z = 2; // For the dumb array indexes for the vectors
Vec3d normal;
Vec3d R0 = r.getPosition();
Vec3d Rd = r.getDirection();
double pz = R0[2];
double dz = Rd[2];
double a = Rd[x]*Rd[x] + Rd[y]*Rd[y] - beta_squared * Rd[z]*Rd[z];
if( a == 0.0) return false; // We're in the x-y plane, no intersection
double b = 2 * (R0[x]*Rd[x] + R0[y]*Rd[y] - beta_squared * ((R0[z] + gamma) * Rd[z]));
double c = -beta_squared*(gamma + R0[z])*(gamma + R0[z]) + R0[x] * R0[x] + R0[y] * R0[y];
double discriminant = b * b - 4 * a * c;
double farRoot, nearRoot, theRoot = RAY_EPSILON;
bool farGood, nearGood;
if(discriminant <= 0) return false; // No intersection
discriminant = sqrt(discriminant);
// We have two roots, so calculate them
nearRoot = (-b + discriminant) / ( 2 * a );
farRoot = (-b - discriminant) / ( 2 * a );
// This is confusing, but it figures out which
// root is closer and puts into theRoot
nearGood = isGoodRoot(r.at(nearRoot));
if(nearGood && (nearRoot > theRoot))
{
theRoot = nearRoot;
normal = Vec3d((r.at(theRoot))[x], (r.at(theRoot))[y], -2.0 * beta_squared * (r.at(theRoot)[z] + gamma));
}
farGood = isGoodRoot(r.at(farRoot));
if(farGood && ( (nearGood && farRoot < theRoot) || farRoot > RAY_EPSILON) )
{
theRoot = farRoot;
normal = Vec3d((r.at(theRoot))[x], (r.at(theRoot))[y], -2.0 * beta_squared * (r.at(theRoot)[z] + gamma));
}
// 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 && (normal * r.getDirection()) > 0 )
normal = -normal;
// These are to help with finding caps
double t1 = (-pz)/dz;
double t2 = (height-pz)/dz;
Vec3d p( r.at( t1 ) );
if(capped) {
if( p[0]*p[0] + p[1]*p[1] <= b_radius*b_radius)
{
if(t1 < theRoot && t1 > RAY_EPSILON)
{
theRoot = t1;
if( dz > 0.0 ) {
// Intersection with cap at z = 0.
normal = Vec3d( 0.0, 0.0, -1.0 );
} else {
normal = Vec3d( 0.0, 0.0, 1.0 );
}
}
}
Vec3d q( r.at( t2 ) );
if( q[0]*q[0] + q[1]*q[1] <= t_radius*t_radius)
{
if(t2 < theRoot && t2 > RAY_EPSILON)
{
theRoot = t2;
if( dz > 0.0 ) {
// Intersection with interior of cap at z = 1.
normal = Vec3d( 0.0, 0.0, 1.0 );
} else {
normal = Vec3d( 0.0, 0.0, -1.0 );
}
}
}
}
if(theRoot <= RAY_EPSILON) return false;
i.setT(theRoot);
normal.normalize();
i.setN(normal);
i.obj = this;
i.setMaterial(this->getMaterial());
return true;
return ret;
}