intersection.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_INTERSECTION_HPP
#define ANTKEEPER_GEOM_INTERSECTION_HPP
 
#include <engine/geom/primitives/hyperplane.hpp>
#include <engine/geom/primitives/hyperrectangle.hpp>
#include <engine/geom/primitives/hypersphere.hpp>
#include <engine/geom/primitives/ray.hpp>
#include <algorithm>
#include <optional>
 
namespace geom {
 
template <class T, std::size_t N>
[[nodiscard]] constexpr std::optional<T> intersection(const ray<T, N>& ray, const hyperplane<T, N>& hyperplane) noexcept
{
    const T cos_theta = math::dot(ray.direction, hyperplane.normal);
    if (cos_theta != T{0})
    {
        const T t = -hyperplane.distance(ray.origin) / cos_theta;
        if (t >= T{0})
        {
            return t;
        }
    }
    
    return std::nullopt;
}
 
template <class T, std::size_t N>
[[nodiscard]] inline constexpr std::optional<T> intersection(const hyperplane<T, N>& hyperplane, const ray<T, N>& ray) noexcept
{
    return intersection<T, N>(ray, hyperplane);
}
 
template <class T, std::size_t N>
[[nodiscard]] constexpr std::optional<std::tuple<T, T>> intersection(const ray<T, N>& ray, const hyperrectangle<T, N>& hyperrectangle) noexcept
{
    T t0 = -std::numeric_limits<T>::infinity();
    T t1 = std::numeric_limits<T>::infinity();
    
    for (std::size_t i = 0; i < N; ++i)
    {
        if (!ray.direction[i])
        {
            if (ray.origin[i] < hyperrectangle.min[i] || ray.origin[i] > hyperrectangle.max[i])
            {
                return std::nullopt;
            }
        }
        else
        {
            T min = (hyperrectangle.min[i] - ray.origin[i]) / ray.direction[i];
            T max = (hyperrectangle.max[i] - ray.origin[i]) / ray.direction[i];
            t0 = std::max(t0, std::min(min, max));
            t1 = std::min(t1, std::max(min, max));
        }
    }
    
    if (t0 > t1 || t1 < T{0})
    {
        return std::nullopt;
    }
    
    return std::tuple<T, T>{t0, t1};
}
 
template <class T, std::size_t N>
[[nodiscard]] inline constexpr std::optional<std::tuple<T, T>> intersection(const hyperrectangle<T, N>& hyperrectangle, const ray<T, N>& ray) noexcept
{
    return intersection<T, N>(ray, hyperrectangle);
}
 
template <class T, std::size_t N>
[[nodiscard]] std::optional<std::tuple<T, T>> intersection(const ray<T, N>& ray, const hypersphere<T, N>& hypersphere) noexcept
{
    const math::vector<T, N> d = ray.origin - hypersphere.center;
    const T b = math::dot(d, ray.direction);
    const math::vector<T, N> qc = d - ray.direction * b;
    const T h = hypersphere.radius * hypersphere.radius - math::dot(qc, qc);
    
    if (h < T{0})
    {
        return std::nullopt;
    }
    
    const T sqrt_h = std::sqrt(h);
    return std::tuple<T, T>{-b - sqrt_h, -b + sqrt_h};
}
 
template <class T>
[[nodiscard]] constexpr std::optional<std::tuple<T, T, T>> intersection(const ray<T, 3>& ray, const math::vec3<T>& a, const math::vec3<T>& b, const math::vec3<T>& c) noexcept
{
    // Find edges
    const math::vec3<T> edge_ab = b - a;
    const math::vec3<T> edge_ac = c - a;
    
    // Calculate determinant
    const math::vec3<T> pv = math::cross(ray.direction, edge_ac);
    const T det = math::dot(edge_ab, pv);
    if (!det)
    {
        return std::nullopt;
    }
    
    const T inverse_det = T{1} / det;
    
    // Calculate u
    const math::vec3<T> tv = ray.origin - a;
    const T u = math::dot(tv, pv) * inverse_det;
    if (u < T{0} || u > T{1})
    {
        return std::nullopt;
    }
    
    // Calculate v
    const math::vec3<T> qv = math::cross(tv, edge_ab);
    const T v = math::dot(ray.direction, qv) * inverse_det;
    if (v < T{0} || u + v > T{1})
    {
        return std::nullopt;
    }
    
    // Calculate t
    const T t = math::dot(edge_ac, qv) * inverse_det;
    if (t < T{0})
    {
        return std::nullopt;
    }
    
    return std::tuple<T, T, T>{t, u, v};
}
template <class T>
[[nodiscard]] inline constexpr std::optional<std::tuple<T, T, T>> intersection(const math::vec3<T>& a, const math::vec3<T>& b, const math::vec3<T>& c, const ray<T, 3>& ray) noexcept
{
    return intersection(ray, a, b, c);
}
 
template <class T, std::size_t N>
[[nodiscard]] inline constexpr bool intersection(const hyperrectangle<T, N>& a, const hyperrectangle<T, N>& b) noexcept
{
    return a.intersects(b);
}
 
template <class T, std::size_t N>
[[nodiscard]] constexpr bool intersection(const hyperrectangle<T, N>& hyperrectangle, const hypersphere<T, N>& hypersphere) noexcept
{
    T sqr_distance{0};
    for (std::size_t i = 0; i < N; ++i)
    {
        if (hypersphere.center[i] < hyperrectangle.min[i])
        {
            const T difference = hyperrectangle.min[i] - hypersphere.center[i];
            sqr_distance += difference * difference;
        }
        else if (hypersphere.center[i] > hyperrectangle.max[i])
        {
            const T difference = hypersphere.center[i] - hyperrectangle.max[i];
            sqr_distance += difference * difference;
        }
    }
    
    return sqr_distance <= hypersphere.radius * hypersphere.radius;
}
 
template <class T, std::size_t N>
[[nodiscard]] inline constexpr bool intersection(const hypersphere<T, N>& hypersphere, const hyperrectangle<T, N>& hyperrectangle) noexcept
{
    return intersection<T, N>(hyperrectangle, hypersphere);
}
 
template <class T, std::size_t N>
[[nodiscard]] inline constexpr bool intersection(const hypersphere<T, N>& a, const hypersphere<T, N>& b) noexcept
{
    return a.intersects(b);
}
 
} // namespace geom
 
#endif // ANTKEEPER_GEOM_INTERSECTION_HPP