hypersphere.hpp

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/*
 * Copyright (C) 2023  Christopher J. Howard
 *
 * This file is part of Antkeeper source code.
 *
 * Antkeeper source code is free software: you can redistribute it and/or modify
 * it under the terms of the GNU General Public License as published by
 * the Free Software Foundation, either version 3 of the License, or
 * (at your option) any later version.
 *
 * Antkeeper source code is distributed in the hope that it will be useful,
 * but WITHOUT ANY WARRANTY; without even the implied warranty of
 * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
 * GNU General Public License for more details.
 *
 * You should have received a copy of the GNU General Public License
 * along with Antkeeper source code.  If not, see <http://www.gnu.org/licenses/>.
 */
 
#ifndef ANTKEEPER_GEOM_PRIMITIVES_HYPERSPHERE_HPP
#define ANTKEEPER_GEOM_PRIMITIVES_HYPERSPHERE_HPP
 
#include <engine/math/numbers.hpp>
#include <engine/math/vector.hpp>
 
namespace geom {
namespace primitives {
 
template <class T, std::size_t N>
struct hypersphere
{
    using vector_type = math::vector<T, N>;
    
    vector_type center;
    
    T radius;
    
    [[nodiscard]] inline constexpr bool contains(const vector_type& point) const noexcept
    {
        return math::sqr_distance(center, point) <= radius * radius;
    }
    
    [[nodiscard]] constexpr bool contains(const hypersphere& other) const noexcept
    {
        const T containment_radius = radius - other.radius;
        if (containment_radius < T{0})
        {
            return false;
        }
        
        return math::sqr_distance(center, other.center) <= containment_radius * containment_radius;
    }
    
    [[nodiscard]] inline T distance(const vector_type& point) const noexcept
    {
        const T d = math::sqr_distance(center, point);
        return (d ? std::sqrt(d) : d) - radius;
    }
    
    [[nodiscard]] constexpr bool intersects(const hypersphere& other) const noexcept
    {
        const T intersection_radius = radius + other.radius;
        return math::sqr_distance(center, other.center) <= intersection_radius * intersection_radius;
    }
    
    template <std::size_t M>
    [[nodiscard]] static constexpr T volume(T r) noexcept
    {
        return (math::two_pi<T> / static_cast<T>(M)) * r * r * volume<M - 2>(r);
    }
    
    template <>
    [[nodiscard]] static constexpr T volume<1>(T r) noexcept
    {
        return r * T{2};
    }
    
    template <>
    [[nodiscard]] static constexpr T volume<0>(T r) noexcept
    {
        return T{1};
    }
    
    [[nodiscard]] inline constexpr T volume() const noexcept
    {
        return volume<N>(radius);
    }
};
 
} // namespace primitives
 
using namespace primitives;
 
} // namespace geom
 
#endif // ANTKEEPER_GEOM_PRIMITIVES_HYPERSPHERE_HPP