Sprout/sprout/darkroom/objects/sphere.hpp

#ifndef SPROUT_DARKROOM_OBJECTS_SPHERE_HPP
#define SPROUT_DARKROOM_OBJECTS_SPHERE_HPP

#include <cstddef>
#include <type_traits>
#include <sprout/config.hpp>
#include <sprout/tuple/tuple.hpp>
#include <sprout/tuple/functions.hpp>
#include <sprout/math/constants.hpp>
#include <sprout/math/atan2.hpp>
#include <sprout/math/sqrt.hpp>
#include <sprout/darkroom/access/access.hpp>
#include <sprout/darkroom/coords/vector.hpp>
#include <sprout/darkroom/rays/ray.hpp>
#include <sprout/darkroom/materials/material.hpp>

namespace sprout {
	namespace darkroom {
		namespace objects {
			//
			// basic_sphere
			//
			template<typename Material, typename Position = sprout::darkroom::coords::vector3d>
			class basic_sphere {
			public:
				typedef Material material_type;
				typedef Position position_type;
				typedef typename sprout::darkroom::access::unit<position_type>::type unit_type;
				typedef unit_type radius_type;
			public:
				template<typename Ray>
				struct intersection {
					typedef sprout::tuples::tuple<
						bool,
						unit_type,
						position_type,
						position_type,
						decltype(sprout::darkroom::materials::calc_material(
							std::declval<material_type const&>(),
							std::declval<unit_type const&>(),
							std::declval<unit_type const&>()
							))
					> type;
				};
			private:
				typedef sprout::tuples::tuple<int, bool, unit_type> zwo_type;
				typedef sprout::tuples::tuple<position_type, position_type> drei_type;
				struct zw {
					SPROUT_STATIC_CONSTEXPR std::size_t hit_side = 0;
					SPROUT_STATIC_CONSTEXPR std::size_t does_intersect = 1;
					SPROUT_STATIC_CONSTEXPR std::size_t distance = 2;
				};
				struct dr {
					SPROUT_STATIC_CONSTEXPR std::size_t point_of_intersection = 0;
					SPROUT_STATIC_CONSTEXPR std::size_t normal = 1;
				};
			private:
				position_type pos_;
				radius_type rad_;
				material_type mat_;
			private:
				template<typename Ray>
				SPROUT_CONSTEXPR zwo_type zweitens_2(
					Ray const& ray,
					unit_type const& i1,
					unit_type const& i2,
					int hit_side,
					bool does_intersect
					) const
				{
					return zwo_type(
						hit_side,
						does_intersect,
						hit_side < 0 ? i2
							: hit_side > 0 ? i1
							: -1
						);
				}
				template<typename Ray>
				SPROUT_CONSTEXPR zwo_type zweitens_1(
					Ray const& ray,
					unit_type const& i1,
					unit_type const& i2
					) const
				{
					return zweitens_2(
						ray,
						i1,
						i2,
						i2 > 0
							? i1 < 0 ? -1 : 1
							: 0
							,
						i2 > 0
						);
				}
				template<typename Ray>
				SPROUT_CONSTEXPR zwo_type zweitens(
					Ray const& ray,
					bool neg,
					unit_type const& b,
					unit_type const& det
					) const
				{
					return neg
						? zweitens_1(ray, b - det, b + det)
						: zwo_type(0, false, -1)
						;
				}
				template<typename Ray>
				SPROUT_CONSTEXPR drei_type drittens_1(
					Ray const& ray,
					typename sprout::darkroom::access::unit<Ray>::type point_of_intersection
					) const
				{
					return drei_type(
						point_of_intersection,
						sprout::darkroom::coords::normalize(
							sprout::darkroom::coords::sub(point_of_intersection, pos_)
							)
						);
				}
				template<typename Ray>
				SPROUT_CONSTEXPR drei_type drittens(
					Ray const& ray,
					bool neg,
					unit_type const& distance
					) const
				{
					return neg
						? drittens_1(ray, sprout::darkroom::rays::point_of_intersection(ray, distance))
						: drei_type(
							sprout::tuples::make<position_type>(0, 0, 0),
							sprout::tuples::make<position_type>(1, 1, 1)
							)
						;
				}
				template<typename Ray, typename Vec>
				SPROUT_CONSTEXPR typename intersection<Ray>::type intersect_6(
					Ray const& ray,
					zwo_type const& zwo,
					drei_type const& drei,
					Vec const& normal
					) const
				{
					using sprout::atan2;
					using sprout::sqrt;
					return typename intersection<Ray>::type(
						sprout::tuples::get<zw::does_intersect>(zwo),
						sprout::tuples::get<zw::distance>(zwo),
						sprout::tuples::get<dr::point_of_intersection>(drei),
						sprout::tuples::get<dr::normal>(drei),
						sprout::darkroom::materials::calc_material(	// ! Spherical
							mat_,
							atan2(
								sprout::darkroom::coords::z(normal),
								sprout::darkroom::coords::x(normal)
								)
								/ sprout::math::pi<unit_type>()
								,
							atan2(
								sprout::darkroom::coords::y(normal),
								sqrt(
									sprout::darkroom::coords::x(normal) * sprout::darkroom::coords::x(normal)
										+ sprout::darkroom::coords::z(normal) * sprout::darkroom::coords::z(normal)
									)
								)
								/ sprout::math::half_pi<unit_type>()
							)
						);
				}
				template<typename Ray>
				SPROUT_CONSTEXPR typename intersection<Ray>::type intersect_5(
					Ray const& ray,
					zwo_type const& zwo,
					drei_type const& drei
					) const
				{
					return intersect_6(
						ray,
						zwo,
						drei,
						sprout::tuples::get<dr::normal>(drei)
						);
				}
				template<typename Ray>
				SPROUT_CONSTEXPR typename intersection<Ray>::type intersect_4(
					Ray const& ray,
					zwo_type const& zwo
					) const
				{
					return intersect_5(
						ray,
						zwo,
						drittens(
							ray,
							sprout::tuples::get<zw::does_intersect>(zwo),
							sprout::tuples::get<zw::distance>(zwo)
							)
						);
				}
				template<typename Ray>
				SPROUT_CONSTEXPR typename intersection<Ray>::type intersect_3(
					Ray const& ray,
					unit_type const& b,
					unit_type const& det_sq
					) const
				{
					using sprout::sqrt;
					return intersect_4(
						ray,
						zweitens(
							ray,
							det_sq > 0,
							b,
							sqrt(det_sq)
							)
						);
				}
				template<typename Ray>
				SPROUT_CONSTEXPR typename intersection<Ray>::type intersect_2(
					Ray const& ray,
					position_type const& v,
					unit_type const& b
					) const
				{
					return intersect_3(
						ray,
						b,
						b * b - sprout::darkroom::coords::length_sq(v) + rad_ * rad_
						);
				}
				template<typename Ray>
				SPROUT_CONSTEXPR typename intersection<Ray>::type intersect_1(
					Ray const& ray,
					position_type const& v
					) const
				{
					return intersect_2(
						ray,
						v,
						-sprout::darkroom::coords::dot(v, sprout::darkroom::rays::direction(ray))
						);
				}
			public:
				SPROUT_CONSTEXPR basic_sphere(
					position_type const& pos,
					radius_type rad,
					material_type const& mat
					)
					: pos_(pos)
					, rad_(rad)
					, mat_(mat)
				{};
				template<typename Ray>
				SPROUT_CONSTEXPR typename intersection<Ray>::type intersect(Ray const& ray) const {
					return intersect_1(
						ray,
						sprout::darkroom::coords::sub(sprout::darkroom::rays::position(ray), pos_)
						);
				}
			};
			//
			// make_sphere
			//
			template<typename Material, typename Position, typename Radius>
			inline SPROUT_CONSTEXPR sprout::darkroom::objects::basic_sphere<Material, Position>
			make_sphere(Position const& pos, Radius const& rad, Material const& mat) {
				return sprout::darkroom::objects::basic_sphere<Material, Position>(pos, rad, mat);
			}
		}	// namespace objects
	}	// namespace darkroom
}	// namespace sprout

#endif	// #ifndef SPROUT_DARKROOM_OBJECTS_SPHERE_HPP