private static Intersection getIntersection(Ray ray, SphereObject obj, Model model) {
RealMatrix transform = obj.getTransform();
final RealMatrix transformInverse = obj.getTransformInverse();
ray = ray.transform(transformInverse);
Vector3D c = VectorUtils.toVector3D(obj.getCenter());
Vector3D p0 = VectorUtils.toVector3D(ray.getP0());
Vector3D p1 = VectorUtils.toVector3D(ray.getP1());
float a = (float) p1.dotProduct(p1);
Vector3D p0c = p0.subtract(c);
float b = (float) p1.dotProduct(p0c) * 2.0f;
float cc = (float) (p0c.dotProduct(p0c)) - obj.getSize() * obj.getSize();
Double t = quadraticEquationRoot1(a, b, cc);
if (t == null || t < EPSILON) {
return new Intersection(false);
}
Intersection result = new Intersection(true);
result.setObject(obj);
final Vector3D p = p0.add(p1.scalarMultiply(t));
RealVector pv = VectorUtils.toRealVector(p);
pv.setEntry(3, 1.0);
RealVector pt = transform.preMultiply(pv);
result.setP(VectorUtils.toVector3D(pt));
RealVector nv = pv.subtract(obj.getCenter());
final RealVector nvt = transformInverse.transpose().preMultiply(nv);
result.setN(VectorUtils.toVector3D(nvt).normalize());
result.setDistance(t);
return result;
}
private static Ray rayThruPixel(Camera cam, int xi, int yi) {
Ray result = new Ray();
float x = xi + .5f;
float y = yi + .5f;
final int halfW = cam.getHalfW();
float alpha = (float) (cam.getTanHalfFovX()) * ((x - halfW) / halfW);
final int halfH = cam.getHalfH();
float beta = (float) (cam.getTanHalfFovY() * (halfH - y) / halfH);
Vector3D p13 =
cam.getU().scalarMultiply(alpha).add(cam.getV().scalarMultiply(beta)).subtract(cam.getW());
result.setP0(cam.getFrom());
result.setP1(VectorUtils.toRealVector(p13));
return result;
}