brep2sdf/code/pre_processing/ParametricSample/Mathematics/IntrRay3Sphere3.h

// David Eberly, Geometric Tools, Redmond WA 98052
// Copyright (c) 1998-2021
// Distributed under the Boost Software License, Version 1.0.
// https://www.boost.org/LICENSE_1_0.txt
// https://www.geometrictools.com/License/Boost/LICENSE_1_0.txt
// Version: 4.0.2021.02.10

#pragma once

#include <Mathematics/IntrIntervals.h>
#include <Mathematics/IntrLine3Sphere3.h>
#include <Mathematics/Ray.h>

namespace gte
{
    template <typename Real>
    class TIQuery<Real, Ray3<Real>, Sphere3<Real>>
    {
    public:
        struct Result
        {
            Result()
                :
                intersect(false)
            {
            }

            bool intersect;
        };

        Result operator()(Ray3<Real> const& ray, Sphere3<Real> const& sphere)
        {
            // The sphere is (X-C)^T*(X-C)-1 = 0 and the line is X = P+t*D.
            // Substitute the line equation into the sphere equation to
            // obtain a quadratic equation Q(t) = t^2 + 2*a1*t + a0 = 0, where
            // a1 = D^T*(P-C) and a0 = (P-C)^T*(P-C)-1.
            Real constexpr zero = 0;
            Result result{};

            Vector3<Real> diff = ray.origin - sphere.center;
            Real a0 = Dot(diff, diff) - sphere.radius * sphere.radius;
            if (a0 <= zero)
            {
                // P is inside the sphere.
                result.intersect = true;
                return result;
            }
            // else: P is outside the sphere

            Real a1 = Dot(ray.direction, diff);
            if (a1 >= zero)
            {
                result.intersect = false;
                return result;
            }

            // Intersection occurs when Q(t) has real roots.
            Real discr = a1 * a1 - a0;
            result.intersect = (discr >= zero);
            return result;
        }
    };

    template <typename Real>
    class FIQuery<Real, Ray3<Real>, Sphere3<Real>>
        :
        public FIQuery<Real, Line3<Real>, Sphere3<Real>>
    {
    public:
        struct Result
            :
            public FIQuery<Real, Line3<Real>, Sphere3<Real>>::Result
        {
            // No additional information to compute.
        };

        Result operator()(Ray3<Real> const& ray, Sphere3<Real> const& sphere)
        {
            Result result{};
            DoQuery(ray.origin, ray.direction, sphere, result);
            for (int i = 0; i < result.numIntersections; ++i)
            {
                result.point[i] = ray.origin + result.parameter[i] * ray.direction;
            }
            return result;
        }

    protected:
        void DoQuery(Vector3<Real> const& rayOrigin,
            Vector3<Real> const& rayDirection, Sphere3<Real> const& sphere,
            Result& result)
        {
            FIQuery<Real, Line3<Real>, Sphere3<Real>>::DoQuery(rayOrigin,
                rayDirection, sphere, result);

            if (result.intersect)
            {
                // The line containing the ray intersects the sphere; the
                // t-interval is [t0,t1].  The ray intersects the sphere as
                // long as [t0,t1] overlaps the ray t-interval [0,+infinity).
                Real constexpr zero = 0;
                Real constexpr rmax = std::numeric_limits<Real>::max();
                std::array<Real, 2> rayInterval = { zero, rmax };
                FIQuery<Real, std::array<Real, 2>, std::array<Real, 2>> iiQuery;
                auto iiResult = iiQuery(result.parameter, rayInterval);
                if (iiResult.intersect)
                {
                    result.numIntersections = iiResult.numIntersections;
                    result.parameter = iiResult.overlap;
                }
                else
                {
                    result.intersect = false;
                    result.numIntersections = 0;
                }
            }
        }
    };
}