/*
 * Licensed under the Apache License, Version 2.0 (the "License");
 * you may not use this file except in compliance with the License.
 * You may obtain a copy of the License at
 *
 *     http://www.apache.org/licenses/LICENSE-2.0
 *
 * Unless required by applicable law or agreed to in writing, software
 * distributed under the License is distributed on an "AS IS" BASIS,
 * WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
 * See the License for the specific language governing permissions and
 * limitations under the License.
 *
 * Copyright 2015-2018 Danny Robson <danny@nerdcruft.net>
 */

#ifndef __UTIL_GEOM_SPHERE_HPP
#define __UTIL_GEOM_SPHERE_HPP

#include "../point.hpp"

#include "ray.hpp"


///////////////////////////////////////////////////////////////////////////////
namespace util::geom {
    template <size_t S, typename T>
    struct sphere {
        point<S,T> centre;
        T radius;
    };

    typedef sphere<2,float> sphere2f;
    typedef sphere<3,float> sphere3f;


    ///////////////////////////////////////////////////////////////////////////
    /// returns the smallest distance from a ray to a sphere intersection
    ///
    /// returns NaN on miss
    /// returns NaN if behind
    template <size_t S, typename T>
    constexpr T
    distance (const ray<S,T> r, const sphere<S,T> s)
    {
        const T b = dot (r.direction, r.origin - s.centre);
        const T c = dot (r.origin - s.centre, r.origin - s.centre) - s.radius * s.radius;

        const T D = b * b - c;

        // no intersection
        if (D < 0)
            return INFINITY;

        auto t_ = std::sqrt (D);
        auto t0 = -b + t_;
        auto t1 = -b - t_;

        return t1 >= 0 ? t1 :
               t0 >= 0 ? t0 :
               INFINITY;
    }
}

#endif