source/src/geom/primitive/intersection.hpp

/*
 * Copyright (C) 2021  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_PRIMITIVE_INTERSECTION_HPP
#define ANTKEEPER_GEOM_PRIMITIVE_INTERSECTION_HPP

#include "geom/primitive/hyperplane.hpp"
#include "geom/primitive/hyperrectangle.hpp"
#include "geom/primitive/hypersphere.hpp"
#include "geom/primitive/ray.hpp"
#include <algorithm>
#include <optional>

namespace geom {
namespace primitive {

/**
 * Ray-hyperplane intersection test.
 *
 * @param ray Ray.
 * @param hyperplane Hyperplane.
 *
 * @return Distance along the ray to the point of intersection, or `std::nullopt` if no intersection occurred.
 */
/// @{
template <class T, std::size_t N>
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>
constexpr inline std::optional<T> intersection(const hyperplane<T, N>& hyperplane, const ray<T, N>& ray) noexcept
{
	return intersection<T, N>(ray, hyperplane);
}
/// @}

/**
 * Ray-hyperrectangle intersection test.
 *
 * @param ray Ray.
 * @param hyperrectangle Hyperrectangle.
 *
 * @return Tuple containing the distances along the ray to the first and second points of intersection, or `std::nullopt` if no intersection occurred.
 */
/// @{
template <class T, std::size_t N>
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 {t0, t1};
}

template <class T, std::size_t N>
constexpr inline std::optional<std::tuple<T, T>> intersection(const hyperrectangle<T, N>& hyperrectangle, const ray<T, N>& ray) noexcept
{
	return intersection<T, N>(ray, hyperrectangle);
}
/// @}

/**
 * Ray-hypersphere intersection test.
 *
 * @param ray Ray.
 * @param hypersphere Hypersphere.
 *
 * @return Tuple containing the distances along the ray to the first and second points of intersection, or `std::nullopt` if no intersection occurred.
 */
template <class T, std::size_t N>
std::optional<std::tuple<T, T>> intersection(const ray<T, N>& ray, const hypersphere<T, N>& hypersphere) noexcept
{
	const math::vector<T, N> displacement = ray.origin - hypersphere.center;
	const T b = math::dot(displacement, ray.direction);
	const T c = math::length_squared(displacement) - hypersphere.radius * hypersphere.radius;
	T h = b * b - c;
	
	if (h < T{0})
		return std::nullopt;
	
	h = std::sqrt(h);
	
	return std::tuple<float, float>{-b - h, -b + h};
}

/**
 * Hyperrectangle-hyperrectangle intersection test.
 *
 * @param a First hyperrectangle.
 * @param b Second hyperrectangle.
 *
 * @return `true` if an intersection occurred, `false` otherwise.
 */
template <class T, std::size_t N>
constexpr inline bool intersection(const hyperrectangle<T, N>& a, const hyperrectangle<T, N>& b) noexcept
{
	return a.intersects(b);
}

/**
 * Hyperrectangle-hypersphere intersection test.
 *
 * @param hyperrectangle Hyperrectangle.
 * @param hypersphere Hypersphere.
 *
 * @return `true` if an intersection occurred, `false` otherwise.
 */
/// @{
template <class T, std::size_t N>
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>
constexpr inline bool intersection(const hypersphere<T, N>& hypersphere, const hyperrectangle<T, N>& hyperrectangle) noexcept
{
	return intersection<T, N>(hyperrectangle, hypersphere);
}
/// @}

/**
 * Hypersphere-hypersphere intersection test.
 *
 * @param a First hypersphere.
 * @param b Second hypersphere.
 *
 * @return `true` if an intersection occurred, `false` otherwise.
 */
template <class T, std::size_t N>
constexpr inline bool intersection(const hypersphere<T, N>& a, const hypersphere<T, N>& b) noexcept
{
	return a.intersects(b);
}

} // namespace primitive
} // namespace geom

#endif // ANTKEEPER_GEOM_PRIMITIVE_INTERSECTION_HPP