From b55e74de78d2df7f242b6ae4efe6fcb7835eca4b Mon Sep 17 00:00:00 2001
From: bolero-MURAKAMI <bolero.murakami@gmail.com>
Date: Sat, 10 Jan 2015 19:30:09 +0900
Subject: [PATCH] add curve/bezier, curve/catmull_rom_sprine

---
 sprout/math/curve.hpp                    |  16 +++
 sprout/math/curve/bezier.hpp             | 144 +++++++++++++++++++++++
 sprout/math/curve/catmull_rom_sprine.hpp | 122 +++++++++++++++++++
 sprout/math/curve/curve_point.hpp        |  42 +++++++
 testspr/header_all.hpp                   |   1 +
 5 files changed, 325 insertions(+)
 create mode 100644 sprout/math/curve.hpp
 create mode 100644 sprout/math/curve/bezier.hpp
 create mode 100644 sprout/math/curve/catmull_rom_sprine.hpp
 create mode 100644 sprout/math/curve/curve_point.hpp

diff --git a/sprout/math/curve.hpp b/sprout/math/curve.hpp
new file mode 100644
index 00000000..e3da3d66
--- /dev/null
+++ b/sprout/math/curve.hpp
@@ -0,0 +1,16 @@
+/*=============================================================================
+  Copyright (c) 2011-2014 Bolero MURAKAMI
+  https://github.com/bolero-MURAKAMI/Sprout
+
+  Distributed under the Boost Software License, Version 1.0. (See accompanying
+  file LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt)
+=============================================================================*/
+#ifndef SPROUT_MATH_CURVE_HPP
+#define SPROUT_MATH_CURVE_HPP
+
+#include <sprout/config.hpp>
+#include <sprout/math/curve/curve_point.hpp>
+#include <sprout/math/curve/bezier.hpp>
+#include <sprout/math/curve/catmull_rom_sprine.hpp>
+
+#endif	// #ifndef SPROUT_MATH_CURVE_HPP
diff --git a/sprout/math/curve/bezier.hpp b/sprout/math/curve/bezier.hpp
new file mode 100644
index 00000000..87dafe1d
--- /dev/null
+++ b/sprout/math/curve/bezier.hpp
@@ -0,0 +1,144 @@
+/*=============================================================================
+  Copyright (c) 2011-2015 Bolero MURAKAMI
+  https://github.com/bolero-MURAKAMI/Sprout
+
+  Distributed under the Boost Software License, Version 1.0. (See accompanying
+  file LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt)
+=============================================================================*/
+#ifndef SPROUT_MATH_CURVE_BEZIER_HPP
+#define SPROUT_MATH_CURVE_BEZIER_HPP
+
+#include <sprout/config.hpp>
+#include <sprout/workaround/std/cstddef.hpp>
+#include <sprout/detail/pow.hpp>
+#include <sprout/tuple/tuple/get.hpp>
+#include <sprout/tuple/tuple/make_tuple.hpp>
+#include <sprout/math/curve/curve_point.hpp>
+
+namespace sprout {
+	namespace math {
+		namespace detail {
+			template<typename Points, typename T, std::size_t N = sprout::tuple_size<Points>::value - 1>
+			class bezier_impl;
+			template<typename Points, typename T>
+			class bezier_impl<Points, T, 2> {
+			public:
+				static SPROUT_CONSTEXPR typename sprout::math::curve_point_result<Points>::type
+				call(Points const& p, T const& t) {
+					using sprout::tuples::nested_get;
+					using sprout::detail::pow2;
+					return sprout::math::curve_point_traits<Points>::make(
+						pow2(1 - t) * nested_get<0, 0>(p)
+							+ 2 * t * (1 - t) * nested_get<1, 0>(p)
+							+ pow2(t) * nested_get<2, 0>(p)
+							,
+						pow2(1 - t) * nested_get<0, 1>(p)
+							+ 2 * t * (1 - t) * nested_get<1, 1>(p)
+							+ pow2(t) * nested_get<2, 1>(p)
+						);
+				}
+			};
+			template<typename Points, typename T>
+			class bezier_impl<Points, T, 3> {
+			public:
+				static SPROUT_CONSTEXPR typename sprout::math::curve_point_result<Points>::type
+				call(Points const& p, T const& t) {
+					using sprout::tuples::nested_get;
+					using sprout::detail::pow2;
+					using sprout::detail::pow3;
+					return sprout::math::curve_point_traits<Points>::make(
+						pow3(1 - t) * nested_get<0, 0>(p)
+							+ 3 * t * pow2(1 - t) * nested_get<1, 0>(p)
+							+ 3 * pow2(t) * (1 - t) * nested_get<2, 0>(p)
+							+ pow3(t) * nested_get<3, 0>(p)
+							,
+						pow3(1 - t) * nested_get<0, 1>(p)
+							+ 3 * t * pow2(1 - t) * nested_get<1, 1>(p)
+							+ 3 * pow2(t) * (1 - t) * nested_get<2, 1>(p)
+							+ pow3(t) * nested_get<3, 1>(p)
+						);
+				}
+			};
+			template<typename Points, typename T>
+			class bezier_impl<Points, T, 4> {
+			public:
+				static SPROUT_CONSTEXPR typename sprout::math::curve_point_result<Points>::type
+				call(Points const& p, T const& t) {
+					using sprout::tuples::nested_get;
+					using sprout::detail::pow2;
+					using sprout::detail::pow3;
+					using sprout::detail::pow4;
+					return sprout::math::curve_point_traits<Points>::make(
+						pow4(1 - t) * nested_get<0, 0>(p)
+							+ 4 * t * pow3(1 - t) * nested_get<1, 0>(p)
+							+ 6 * pow2(t) * pow2(1 - t) * nested_get<2, 0>(p)
+							+ 4 * pow3(t) * (1 - t) * nested_get<3, 0>(p)
+							+ pow4(t) * nested_get<4, 0>(p)
+							,
+						pow4(1 - t) * nested_get<0, 1>(p)
+							+ 4 * t * pow3(1 - t) * nested_get<1, 1>(p)
+							+ 6 * pow2(t) * pow2(1 - t) * nested_get<2, 1>(p)
+							+ 4 * pow3(t) * (1 - t) * nested_get<3, 1>(p)
+							+ pow4(t) * nested_get<4, 1>(p)
+						);
+				}
+			};
+			template<typename Points, typename T>
+			class bezier_impl<Points, T, 5> {
+			public:
+				static SPROUT_CONSTEXPR typename sprout::math::curve_point_result<Points>::type
+				call(Points const& p, T const& t) {
+					using sprout::tuples::nested_get;
+					using sprout::detail::pow2;
+					using sprout::detail::pow3;
+					using sprout::detail::pow4;
+					using sprout::detail::pow5;
+					return sprout::math::curve_point_traits<Points>::make(
+						pow5(1 - t) * nested_get<0, 0>(p)
+							+ 5 * t * pow4(1 - t) * nested_get<1, 0>(p)
+							+ 10 * pow2(t) * pow3(1 - t) * nested_get<2, 0>(p)
+							+ 10 * pow3(t) * pow2(1 - t) * nested_get<3, 0>(p)
+							+ 5 * pow4(t) * (1 - t) * nested_get<4, 0>(p)
+							+ pow5(t) * nested_get<5, 0>(p)
+							,
+						pow5(1 - t) * nested_get<0, 1>(p)
+							+ 5 * t * pow4(1 - t) * nested_get<1, 1>(p)
+							+ 10 * pow2(t) * pow3(1 - t) * nested_get<2, 1>(p)
+							+ 10 * pow3(t) * pow2(1 - t) * nested_get<3, 1>(p)
+							+ 5 * pow4(t) * (1 - t) * nested_get<4, 1>(p)
+							+ pow5(t) * nested_get<5, 1>(p)
+						);
+				}
+			};
+		}	// namespace detail
+
+		//
+		// bezier
+		//
+		template<typename Points, typename T>
+		inline SPROUT_CONSTEXPR typename sprout::math::curve_point_result<Points>::type
+		bezier(T const& t, Points const& p) {
+			return sprout::math::detail::bezier_impl<Points, T>::call(p, t);
+		}
+		template<std::size_t N, typename Points, typename T>
+		inline SPROUT_CONSTEXPR typename sprout::math::curve_point_result<Points>::type
+		bezier(T const& t, Points const& p) {
+			return sprout::math::detail::bezier_impl<Points, T, N>::call(p, t);
+		}
+
+		template<typename P0, typename P1, typename P2, typename... PTail, typename T>
+		inline SPROUT_CONSTEXPR typename sprout::math::curve_point_result<sprout::tuples::tuple<P0 const&, P1 const&, P2 const&, PTail const&...> >::type
+		bezier(T const& t, P0 const& p0, P1 const& p1, P2 const& p2, PTail const&... p) {
+			return sprout::math::bezier(sprout::tuples::forward_as_tuple(p0, p1, p2, p...), t);
+		}
+		template<std::size_t N, typename P0, typename P1, typename P2, typename... PTail, typename T>
+		inline SPROUT_CONSTEXPR typename sprout::math::curve_point_result<sprout::tuples::tuple<P0 const&, P1 const&, P2 const&, PTail const&...> >::type
+		bezier(T const& t, P0 const& p0, P1 const& p1, P2 const& p2, PTail const&... p) {
+			return sprout::math::bezier<N>(sprout::tuples::forward_as_tuple(p0, p1, p2, p...), t);
+		}
+	}	// namespace math
+
+	using sprout::math::bezier;
+}	// namespace sprout
+
+#endif	// #ifndef SPROUT_MATH_CURVE_BEZIER_HPP
diff --git a/sprout/math/curve/catmull_rom_sprine.hpp b/sprout/math/curve/catmull_rom_sprine.hpp
new file mode 100644
index 00000000..1b9faf29
--- /dev/null
+++ b/sprout/math/curve/catmull_rom_sprine.hpp
@@ -0,0 +1,122 @@
+/*=============================================================================
+  Copyright (c) 2011-2015 Bolero MURAKAMI
+  https://github.com/bolero-MURAKAMI/Sprout
+
+  Distributed under the Boost Software License, Version 1.0. (See accompanying
+  file LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt)
+=============================================================================*/
+#ifndef SPROUT_MATH_CURVE_CATMULL_ROM_SPRINE_HPP
+#define SPROUT_MATH_CURVE_CATMULL_ROM_SPRINE_HPP
+
+#include <sprout/config.hpp>
+#include <sprout/detail/pow.hpp>
+#include <sprout/tuple/tuple/get.hpp>
+#include <sprout/tuple/tuple/make_tuple.hpp>
+#include <sprout/math/curve/curve_point.hpp>
+
+namespace sprout {
+	namespace math {
+		namespace detail {
+			template<typename Points, typename T>
+			class catmull_rom_sprine_impl {
+			public:
+				static SPROUT_CONSTEXPR typename sprout::math::curve_point_result<Points>::type
+				call(Points const& p, T const& t) {
+					using sprout::tuples::nested_get;
+					using sprout::detail::pow2;
+					using sprout::detail::pow3;
+					return sprout::math::curve_point_traits<Points>::make(
+						(-nested_get<0, 0>(p) + 3 * nested_get<1, 0>(p) - 3 * nested_get<2, 0>(p) + nested_get<3, 0>(p)) / 2 * pow3(t)
+							+ (2 * nested_get<0, 0>(p) - 5 * nested_get<1, 0>(p) + 4 * nested_get<2, 0>(p) - nested_get<3, 0>(p)) / 2 * pow2(t)
+							+ (-nested_get<0, 0>(p) + nested_get<2, 0>(p)) / 2 * t
+							+ nested_get<1, 0>(p)
+							,
+						(-nested_get<0, 1>(p) + 3 * nested_get<1, 1>(p) - 3 * nested_get<2, 1>(p) + nested_get<3, 1>(p)) / 2 * pow3(t)
+							+ (2 * nested_get<0, 1>(p) - 5 * nested_get<1, 1>(p) + 4 * nested_get<2, 1>(p) - nested_get<3, 1>(p)) / 2 * pow2(t)
+							+ (-nested_get<0, 1>(p) + nested_get<2, 1>(p)) / 2 * t
+							+ nested_get<1, 1>(p)
+						);
+				}
+			};
+			template<typename Points, typename T>
+			class catmull_rom_sprine_start_impl {
+			public:
+				static SPROUT_CONSTEXPR typename sprout::math::curve_point_result<Points>::type
+				call(Points const& p, T const& t) {
+					using sprout::tuples::nested_get;
+					using sprout::detail::pow2;
+					return sprout::math::curve_point_traits<Points>::make(
+						(nested_get<0, 0>(p) - 2 * nested_get<1, 0>(p) + nested_get<2, 0>(p)) / 2 * pow2(t)
+							+ (-3 * nested_get<0, 0>(p) + 4 * nested_get<1, 0>(p) - nested_get<2, 0>(p)) / 2 * t
+							+ nested_get<0, 0>(p)
+							,
+						(nested_get<0, 1>(p) - 2 * nested_get<1, 1>(p) + nested_get<2, 1>(p)) / 2 * pow2(t)
+							+ (-3 * nested_get<0, 1>(p) + 4 * nested_get<1, 1>(p) - nested_get<2, 1>(p)) / 2 * t
+							+ nested_get<0, 1>(p)
+						);
+				}
+			};
+			template<typename Points, typename T>
+			class catmull_rom_sprine_end_impl {
+			public:
+				static SPROUT_CONSTEXPR typename sprout::math::curve_point_result<Points>::type
+				call(Points const& p, T const& t) {
+					using sprout::tuples::nested_get;
+					using sprout::detail::pow2;
+					return sprout::math::curve_point_traits<Points>::make(
+						(nested_get<0, 0>(p) - 2 * nested_get<1, 0>(p) + nested_get<2, 0>(p)) / 2 * pow2(t)
+							+ (-nested_get<0, 0>(p) + nested_get<2, 0>(p)) / 2 * t
+							+ nested_get<1, 0>(p)
+							,
+						(nested_get<0, 1>(p) - 2 * nested_get<1, 1>(p) + nested_get<2, 1>(p)) / 2 * pow2(t)
+							+ (-nested_get<0, 1>(p) + nested_get<2, 1>(p)) / 2 * t
+							+ nested_get<1, 1>(p)
+						);
+				}
+			};
+		}	// namespace detail
+
+		//
+		// catmull_rom_sprine
+		// catmull_rom_sprine_start
+		// catmull_rom_sprine_end
+		//
+		template<typename Points, typename T>
+		inline SPROUT_CONSTEXPR typename sprout::math::curve_point_result<Points>::type
+		catmull_rom_sprine(T const& t, Points const& p) {
+			return sprout::math::detail::catmull_rom_sprine_impl<Points, T>::call(p, t);
+		}
+		template<typename Points, typename T>
+		inline SPROUT_CONSTEXPR typename sprout::math::curve_point_result<Points>::type
+		catmull_rom_sprine_start(T const& t, Points const& p) {
+			return sprout::math::detail::catmull_rom_sprine_start_impl<Points, T>::call(p, t);
+		}
+		template<typename Points, typename T>
+		inline SPROUT_CONSTEXPR typename sprout::math::curve_point_result<Points>::type
+		catmull_rom_sprine_end(T const& t, Points const& p) {
+			return sprout::math::detail::catmull_rom_sprine_end_impl<Points, T>::call(p, t);
+		}
+
+		template<typename P0, typename P1, typename P2, typename P3, typename T>
+		inline SPROUT_CONSTEXPR typename sprout::math::curve_point_result<sprout::tuples::tuple<P0 const&, P1 const&, P2 const&, P3 const&> >::type
+		catmull_rom_sprine(T const& t, P0 const& p0, P1 const& p1, P2 const& p2, P3 const& p3) {
+			return sprout::math::catmull_rom_sprine(sprout::tuples::forward_as_tuple(p0, p1, p2, p3), t);
+		}
+		template<typename P0, typename P1, typename P2, typename T>
+		inline SPROUT_CONSTEXPR typename sprout::math::curve_point_result<sprout::tuples::tuple<P0 const&, P1 const&, P2 const&> >::type
+		catmull_rom_sprine_start(T const& t, P0 const& p0, P1 const& p1, P2 const& p2) {
+			return sprout::math::catmull_rom_sprine_start(sprout::tuples::forward_as_tuple(p0, p1, p2), t);
+		}
+		template<typename P0, typename P1, typename P2, typename T>
+		inline SPROUT_CONSTEXPR typename sprout::math::curve_point_result<sprout::tuples::tuple<P0 const&, P1 const&, P2 const&> >::type
+		catmull_rom_sprine_end(T const& t, P0 const& p0, P1 const& p1, P2 const& p2) {
+			return sprout::math::catmull_rom_sprine_end(sprout::tuples::forward_as_tuple(p0, p1, p2), t);
+		}
+	}	// namespace math
+
+	using sprout::math::catmull_rom_sprine;
+	using sprout::math::catmull_rom_sprine_start;
+	using sprout::math::catmull_rom_sprine_end;
+}	// namespace sprout
+
+#endif	// #ifndef SPROUT_MATH_CURVE_CATMULL_ROM_SPRINE_HPP
diff --git a/sprout/math/curve/curve_point.hpp b/sprout/math/curve/curve_point.hpp
new file mode 100644
index 00000000..53a65b01
--- /dev/null
+++ b/sprout/math/curve/curve_point.hpp
@@ -0,0 +1,42 @@
+/*=============================================================================
+  Copyright (c) 2011-2015 Bolero MURAKAMI
+  https://github.com/bolero-MURAKAMI/Sprout
+
+  Distributed under the Boost Software License, Version 1.0. (See accompanying
+  file LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt)
+=============================================================================*/
+#ifndef SPROUT_MATH_CURVE_CURVE_POINT_HPP
+#define SPROUT_MATH_CURVE_CURVE_POINT_HPP
+
+#include <utility>
+#include <sprout/config.hpp>
+#include <sprout/tuple/traits.hpp>
+#include <sprout/type_traits/identity.hpp>
+#include <sprout/type_traits/remove_cvref.hpp>
+#include <sprout/tuple/traits.hpp>
+
+namespace sprout {
+	namespace math {
+		//
+		// curve_point
+		// curve_point_traits
+		// curve_point_result
+		//
+		template<typename Points>
+		struct curve_point
+			: public sprout::remove_cvref<decltype(sprout::tuples::nested_get<0>(std::declval<Points const&>()))>
+		{};
+		template<typename Points>
+		struct curve_point_traits
+			: public sprout::tuples::tuple_construct_traits<typename sprout::math::curve_point<Points>::type>
+		{};
+		template<typename Points>
+		struct curve_point_result
+			: public sprout::identity<
+				typename sprout::math::curve_point_traits<Points>::copied_type
+			>
+		{};
+	}	// namespace math
+}	// namespace sprout
+
+#endif	// #ifndef SPROUT_MATH_CURVE_CURVE_POINT_HPP
diff --git a/testspr/header_all.hpp b/testspr/header_all.hpp
index 3a0f78e7..8a00b533 100644
--- a/testspr/header_all.hpp
+++ b/testspr/header_all.hpp
@@ -48,6 +48,7 @@
 #include <sprout/limits.hpp>
 #include <sprout/logic.hpp>
 #include <sprout/math.hpp>
+#include <sprout/math/curve.hpp>
 #include <sprout/memory.hpp>
 #include <sprout/net.hpp>
 #include <sprout/none.hpp>