std::vector<double> PolyBase::realRoots(const double epsilon)
/**
Get just the real roots
@param epsilon :: tolerance factor (-ve to use default)
@return vector of the real roots (if any)
*/
{
const double eps((epsilon > 0.0) ? epsilon : Eaccuracy);
std::vector<std::complex<double>> Croots = calcRoots(epsilon);
std::vector<double> Out;
std::vector<std::complex<double>>::const_iterator vc;
for (vc = Croots.begin(); vc != Croots.end(); ++vc) {
if (fabs(vc->imag()) < eps)
Out.push_back(vc->real());
}
return Out;
}
bool
Sphere::closestIntersectionModel(const Ray &ray, double maxLambda, RayIntersection& intersection) const
{
/*
A ray and a sphere intersect if and only if
(o + lambda * d - c)^2 = r^2
where
o is the origin of the ray
d is the direction vector of the ray
c is the center of the sphere
r is the radius of the sphere
Since o and d are known, c = O and r = 1, we have
a quadratic equation in lambda. We solve it using calcRoots()
which is a slightly modified version of the classical
quadratic formula (as described in [1]).
[1] http://wiki.delphigl.com/index.php/Tutorial_Raytracing_-_Grundlagen_I#Quadratische_Gleichungen
*/
// a, b and c are the constants in
// a * lambda^2 + b * lambda + c = 0.
double a = dot(ray.direction(), ray.direction());
double b = 2 * dot(ray.direction(), ray.origin());
double c = dot(ray.origin(), ray.origin()) - 1;
// t1 and t2 are the solutions of our quadratic equation.
// W.l.o.g. t1 <= t2 (calcRoots takes care of that)
// calcRoots return the number of roots it found (zero, one or two).
double t1, t2;
int roots = calcRoots(a, b, c, t1, t2);
bool doIntersect = false;
if (roots > 0) {
// There is a solution, we just need the (smallest) positve one.
double lambda = t1 >= 0 ? t1 : t2;
if (lambda >= 0.0 && lambda < maxLambda) {
doIntersect = true;
intersection = RayIntersection(ray, shared_from_this(), lambda, ray.pointOnRay(lambda), Vec3d(0,0,0));
}
}
return doIntersect;
}