intersect_line_sphere.hpp

#ifndef PASTELGEOMETRY_INTERSECT_LINE_SPHERE_HPP
#define PASTELGEOMETRY_INTERSECT_LINE_SPHERE_HPP

#include "pastel/geometry/shape/line.h"
#include "pastel/geometry/shape/sphere.h"

#include "pastel/sys/vector/vector_tools.h"
#include "pastel/sys/math_functions.h"

namespace Pastel
{

    template <typename Real, integer N>
        bool intersect(
            const Line<Real, N>& line,
            const Sphere<Real, N>& sphere,
            Vector<Real, 2>& hitList)
    {
        // Let
        // P = line position
        // D = line direction
        // S = sphere position
        // r = sphere radius
        //
        // R(t) = P + tD
        // dot(S - R(t), S - R(t)) = r^2
        // =>
        // dot((S - P) - tD, (S - P) - tD) - r^2 = 0
        // =>
        // dot(S - P, S - P) - 2 * t * dot(S - P, D) + t^2 * dot(D) - r^2 = 0
        // =>
        // at^2 + bt + c = 0
        // with
        // a = dot(D)
        // b = -2 * dot(S - P, D)
        // c = dot(S - P, S - P) - r^2

        Vector<Real, N> delta(
            sphere.position() - line.position());

        Real aCoeff =
            dot(line.direction());
        Real bCoeff =
            -2 * dot(line.direction(), delta);
        Real cCoeff = 
            dot(delta) -
            square(sphere.radius());

        Real t0(0);
        Real t1(0);

        if (!quadratic(aCoeff, bCoeff, cCoeff, t0, t1))
        {
            return false;
        }

        // t0 <= t1 from now on...

        hitList.set(t0, t1);

        return true;
    }

}

#endif