mirror of
https://github.com/bolero-MURAKAMI/Sprout.git
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add curve/bezier, curve/catmull_rom_sprine
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bolero-MURAKAMI
parent
3029507c05
commit
b55e74de78
5 changed files with 325 additions and 0 deletions
16
sprout/math/curve.hpp
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16
sprout/math/curve.hpp
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/*=============================================================================
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Copyright (c) 2011-2014 Bolero MURAKAMI
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https://github.com/bolero-MURAKAMI/Sprout
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Distributed under the Boost Software License, Version 1.0. (See accompanying
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file LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt)
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=============================================================================*/
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#ifndef SPROUT_MATH_CURVE_HPP
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#define SPROUT_MATH_CURVE_HPP
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#include <sprout/config.hpp>
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#include <sprout/math/curve/curve_point.hpp>
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#include <sprout/math/curve/bezier.hpp>
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#include <sprout/math/curve/catmull_rom_sprine.hpp>
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#endif // #ifndef SPROUT_MATH_CURVE_HPP
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144
sprout/math/curve/bezier.hpp
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144
sprout/math/curve/bezier.hpp
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/*=============================================================================
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Copyright (c) 2011-2015 Bolero MURAKAMI
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https://github.com/bolero-MURAKAMI/Sprout
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Distributed under the Boost Software License, Version 1.0. (See accompanying
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file LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt)
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=============================================================================*/
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#ifndef SPROUT_MATH_CURVE_BEZIER_HPP
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#define SPROUT_MATH_CURVE_BEZIER_HPP
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#include <sprout/config.hpp>
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#include <sprout/workaround/std/cstddef.hpp>
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#include <sprout/detail/pow.hpp>
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#include <sprout/tuple/tuple/get.hpp>
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#include <sprout/tuple/tuple/make_tuple.hpp>
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#include <sprout/math/curve/curve_point.hpp>
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namespace sprout {
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namespace math {
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namespace detail {
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template<typename Points, typename T, std::size_t N = sprout::tuple_size<Points>::value - 1>
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class bezier_impl;
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template<typename Points, typename T>
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class bezier_impl<Points, T, 2> {
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public:
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static SPROUT_CONSTEXPR typename sprout::math::curve_point_result<Points>::type
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call(Points const& p, T const& t) {
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using sprout::tuples::nested_get;
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using sprout::detail::pow2;
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return sprout::math::curve_point_traits<Points>::make(
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pow2(1 - t) * nested_get<0, 0>(p)
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+ 2 * t * (1 - t) * nested_get<1, 0>(p)
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+ pow2(t) * nested_get<2, 0>(p)
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,
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pow2(1 - t) * nested_get<0, 1>(p)
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+ 2 * t * (1 - t) * nested_get<1, 1>(p)
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+ pow2(t) * nested_get<2, 1>(p)
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);
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}
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};
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template<typename Points, typename T>
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class bezier_impl<Points, T, 3> {
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public:
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static SPROUT_CONSTEXPR typename sprout::math::curve_point_result<Points>::type
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call(Points const& p, T const& t) {
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using sprout::tuples::nested_get;
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using sprout::detail::pow2;
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using sprout::detail::pow3;
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return sprout::math::curve_point_traits<Points>::make(
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pow3(1 - t) * nested_get<0, 0>(p)
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+ 3 * t * pow2(1 - t) * nested_get<1, 0>(p)
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+ 3 * pow2(t) * (1 - t) * nested_get<2, 0>(p)
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+ pow3(t) * nested_get<3, 0>(p)
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,
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pow3(1 - t) * nested_get<0, 1>(p)
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+ 3 * t * pow2(1 - t) * nested_get<1, 1>(p)
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+ 3 * pow2(t) * (1 - t) * nested_get<2, 1>(p)
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+ pow3(t) * nested_get<3, 1>(p)
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);
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}
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};
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template<typename Points, typename T>
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class bezier_impl<Points, T, 4> {
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public:
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static SPROUT_CONSTEXPR typename sprout::math::curve_point_result<Points>::type
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call(Points const& p, T const& t) {
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using sprout::tuples::nested_get;
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using sprout::detail::pow2;
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using sprout::detail::pow3;
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using sprout::detail::pow4;
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return sprout::math::curve_point_traits<Points>::make(
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pow4(1 - t) * nested_get<0, 0>(p)
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+ 4 * t * pow3(1 - t) * nested_get<1, 0>(p)
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+ 6 * pow2(t) * pow2(1 - t) * nested_get<2, 0>(p)
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+ 4 * pow3(t) * (1 - t) * nested_get<3, 0>(p)
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+ pow4(t) * nested_get<4, 0>(p)
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,
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pow4(1 - t) * nested_get<0, 1>(p)
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+ 4 * t * pow3(1 - t) * nested_get<1, 1>(p)
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+ 6 * pow2(t) * pow2(1 - t) * nested_get<2, 1>(p)
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+ 4 * pow3(t) * (1 - t) * nested_get<3, 1>(p)
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+ pow4(t) * nested_get<4, 1>(p)
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);
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}
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};
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template<typename Points, typename T>
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class bezier_impl<Points, T, 5> {
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public:
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static SPROUT_CONSTEXPR typename sprout::math::curve_point_result<Points>::type
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call(Points const& p, T const& t) {
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using sprout::tuples::nested_get;
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using sprout::detail::pow2;
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using sprout::detail::pow3;
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using sprout::detail::pow4;
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using sprout::detail::pow5;
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return sprout::math::curve_point_traits<Points>::make(
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pow5(1 - t) * nested_get<0, 0>(p)
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+ 5 * t * pow4(1 - t) * nested_get<1, 0>(p)
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+ 10 * pow2(t) * pow3(1 - t) * nested_get<2, 0>(p)
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+ 10 * pow3(t) * pow2(1 - t) * nested_get<3, 0>(p)
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+ 5 * pow4(t) * (1 - t) * nested_get<4, 0>(p)
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+ pow5(t) * nested_get<5, 0>(p)
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,
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pow5(1 - t) * nested_get<0, 1>(p)
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+ 5 * t * pow4(1 - t) * nested_get<1, 1>(p)
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+ 10 * pow2(t) * pow3(1 - t) * nested_get<2, 1>(p)
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+ 10 * pow3(t) * pow2(1 - t) * nested_get<3, 1>(p)
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+ 5 * pow4(t) * (1 - t) * nested_get<4, 1>(p)
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+ pow5(t) * nested_get<5, 1>(p)
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);
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}
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};
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} // namespace detail
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//
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// bezier
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//
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template<typename Points, typename T>
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inline SPROUT_CONSTEXPR typename sprout::math::curve_point_result<Points>::type
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bezier(T const& t, Points const& p) {
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return sprout::math::detail::bezier_impl<Points, T>::call(p, t);
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}
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template<std::size_t N, typename Points, typename T>
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inline SPROUT_CONSTEXPR typename sprout::math::curve_point_result<Points>::type
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bezier(T const& t, Points const& p) {
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return sprout::math::detail::bezier_impl<Points, T, N>::call(p, t);
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}
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template<typename P0, typename P1, typename P2, typename... PTail, typename T>
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inline SPROUT_CONSTEXPR typename sprout::math::curve_point_result<sprout::tuples::tuple<P0 const&, P1 const&, P2 const&, PTail const&...> >::type
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bezier(T const& t, P0 const& p0, P1 const& p1, P2 const& p2, PTail const&... p) {
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return sprout::math::bezier(sprout::tuples::forward_as_tuple(p0, p1, p2, p...), t);
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}
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template<std::size_t N, typename P0, typename P1, typename P2, typename... PTail, typename T>
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inline SPROUT_CONSTEXPR typename sprout::math::curve_point_result<sprout::tuples::tuple<P0 const&, P1 const&, P2 const&, PTail const&...> >::type
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bezier(T const& t, P0 const& p0, P1 const& p1, P2 const& p2, PTail const&... p) {
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return sprout::math::bezier<N>(sprout::tuples::forward_as_tuple(p0, p1, p2, p...), t);
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}
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} // namespace math
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using sprout::math::bezier;
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} // namespace sprout
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#endif // #ifndef SPROUT_MATH_CURVE_BEZIER_HPP
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122
sprout/math/curve/catmull_rom_sprine.hpp
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122
sprout/math/curve/catmull_rom_sprine.hpp
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@ -0,0 +1,122 @@
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/*=============================================================================
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Copyright (c) 2011-2015 Bolero MURAKAMI
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https://github.com/bolero-MURAKAMI/Sprout
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Distributed under the Boost Software License, Version 1.0. (See accompanying
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file LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt)
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=============================================================================*/
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#ifndef SPROUT_MATH_CURVE_CATMULL_ROM_SPRINE_HPP
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#define SPROUT_MATH_CURVE_CATMULL_ROM_SPRINE_HPP
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#include <sprout/config.hpp>
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#include <sprout/detail/pow.hpp>
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#include <sprout/tuple/tuple/get.hpp>
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#include <sprout/tuple/tuple/make_tuple.hpp>
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#include <sprout/math/curve/curve_point.hpp>
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namespace sprout {
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namespace math {
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namespace detail {
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template<typename Points, typename T>
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class catmull_rom_sprine_impl {
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public:
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static SPROUT_CONSTEXPR typename sprout::math::curve_point_result<Points>::type
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call(Points const& p, T const& t) {
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using sprout::tuples::nested_get;
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using sprout::detail::pow2;
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using sprout::detail::pow3;
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return sprout::math::curve_point_traits<Points>::make(
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(-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)
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+ (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)
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+ (-nested_get<0, 0>(p) + nested_get<2, 0>(p)) / 2 * t
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+ nested_get<1, 0>(p)
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,
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(-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)
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+ (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)
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+ (-nested_get<0, 1>(p) + nested_get<2, 1>(p)) / 2 * t
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+ nested_get<1, 1>(p)
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);
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}
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};
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template<typename Points, typename T>
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class catmull_rom_sprine_start_impl {
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public:
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static SPROUT_CONSTEXPR typename sprout::math::curve_point_result<Points>::type
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call(Points const& p, T const& t) {
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using sprout::tuples::nested_get;
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using sprout::detail::pow2;
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return sprout::math::curve_point_traits<Points>::make(
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(nested_get<0, 0>(p) - 2 * nested_get<1, 0>(p) + nested_get<2, 0>(p)) / 2 * pow2(t)
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+ (-3 * nested_get<0, 0>(p) + 4 * nested_get<1, 0>(p) - nested_get<2, 0>(p)) / 2 * t
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+ nested_get<0, 0>(p)
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,
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(nested_get<0, 1>(p) - 2 * nested_get<1, 1>(p) + nested_get<2, 1>(p)) / 2 * pow2(t)
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+ (-3 * nested_get<0, 1>(p) + 4 * nested_get<1, 1>(p) - nested_get<2, 1>(p)) / 2 * t
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+ nested_get<0, 1>(p)
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);
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}
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};
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template<typename Points, typename T>
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class catmull_rom_sprine_end_impl {
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public:
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static SPROUT_CONSTEXPR typename sprout::math::curve_point_result<Points>::type
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call(Points const& p, T const& t) {
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using sprout::tuples::nested_get;
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using sprout::detail::pow2;
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return sprout::math::curve_point_traits<Points>::make(
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(nested_get<0, 0>(p) - 2 * nested_get<1, 0>(p) + nested_get<2, 0>(p)) / 2 * pow2(t)
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+ (-nested_get<0, 0>(p) + nested_get<2, 0>(p)) / 2 * t
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+ nested_get<1, 0>(p)
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,
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(nested_get<0, 1>(p) - 2 * nested_get<1, 1>(p) + nested_get<2, 1>(p)) / 2 * pow2(t)
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+ (-nested_get<0, 1>(p) + nested_get<2, 1>(p)) / 2 * t
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+ nested_get<1, 1>(p)
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);
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}
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};
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} // namespace detail
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//
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// catmull_rom_sprine
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// catmull_rom_sprine_start
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// catmull_rom_sprine_end
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//
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template<typename Points, typename T>
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inline SPROUT_CONSTEXPR typename sprout::math::curve_point_result<Points>::type
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catmull_rom_sprine(T const& t, Points const& p) {
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return sprout::math::detail::catmull_rom_sprine_impl<Points, T>::call(p, t);
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}
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template<typename Points, typename T>
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inline SPROUT_CONSTEXPR typename sprout::math::curve_point_result<Points>::type
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catmull_rom_sprine_start(T const& t, Points const& p) {
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return sprout::math::detail::catmull_rom_sprine_start_impl<Points, T>::call(p, t);
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}
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template<typename Points, typename T>
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inline SPROUT_CONSTEXPR typename sprout::math::curve_point_result<Points>::type
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catmull_rom_sprine_end(T const& t, Points const& p) {
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return sprout::math::detail::catmull_rom_sprine_end_impl<Points, T>::call(p, t);
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}
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template<typename P0, typename P1, typename P2, typename P3, typename T>
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inline SPROUT_CONSTEXPR typename sprout::math::curve_point_result<sprout::tuples::tuple<P0 const&, P1 const&, P2 const&, P3 const&> >::type
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catmull_rom_sprine(T const& t, P0 const& p0, P1 const& p1, P2 const& p2, P3 const& p3) {
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return sprout::math::catmull_rom_sprine(sprout::tuples::forward_as_tuple(p0, p1, p2, p3), t);
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}
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template<typename P0, typename P1, typename P2, typename T>
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inline SPROUT_CONSTEXPR typename sprout::math::curve_point_result<sprout::tuples::tuple<P0 const&, P1 const&, P2 const&> >::type
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catmull_rom_sprine_start(T const& t, P0 const& p0, P1 const& p1, P2 const& p2) {
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return sprout::math::catmull_rom_sprine_start(sprout::tuples::forward_as_tuple(p0, p1, p2), t);
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}
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template<typename P0, typename P1, typename P2, typename T>
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inline SPROUT_CONSTEXPR typename sprout::math::curve_point_result<sprout::tuples::tuple<P0 const&, P1 const&, P2 const&> >::type
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catmull_rom_sprine_end(T const& t, P0 const& p0, P1 const& p1, P2 const& p2) {
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return sprout::math::catmull_rom_sprine_end(sprout::tuples::forward_as_tuple(p0, p1, p2), t);
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}
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} // namespace math
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using sprout::math::catmull_rom_sprine;
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using sprout::math::catmull_rom_sprine_start;
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using sprout::math::catmull_rom_sprine_end;
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} // namespace sprout
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#endif // #ifndef SPROUT_MATH_CURVE_CATMULL_ROM_SPRINE_HPP
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42
sprout/math/curve/curve_point.hpp
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42
sprout/math/curve/curve_point.hpp
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/*=============================================================================
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Copyright (c) 2011-2015 Bolero MURAKAMI
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https://github.com/bolero-MURAKAMI/Sprout
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Distributed under the Boost Software License, Version 1.0. (See accompanying
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file LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt)
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=============================================================================*/
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#ifndef SPROUT_MATH_CURVE_CURVE_POINT_HPP
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#define SPROUT_MATH_CURVE_CURVE_POINT_HPP
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#include <utility>
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#include <sprout/config.hpp>
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#include <sprout/tuple/traits.hpp>
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#include <sprout/type_traits/identity.hpp>
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#include <sprout/type_traits/remove_cvref.hpp>
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#include <sprout/tuple/traits.hpp>
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namespace sprout {
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namespace math {
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//
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// curve_point
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// curve_point_traits
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// curve_point_result
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//
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template<typename Points>
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struct curve_point
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: public sprout::remove_cvref<decltype(sprout::tuples::nested_get<0>(std::declval<Points const&>()))>
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{};
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template<typename Points>
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struct curve_point_traits
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: public sprout::tuples::tuple_construct_traits<typename sprout::math::curve_point<Points>::type>
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{};
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template<typename Points>
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struct curve_point_result
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: public sprout::identity<
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typename sprout::math::curve_point_traits<Points>::copied_type
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>
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{};
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} // namespace math
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} // namespace sprout
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#endif // #ifndef SPROUT_MATH_CURVE_CURVE_POINT_HPP
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@ -48,6 +48,7 @@
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#include <sprout/limits.hpp>
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#include <sprout/logic.hpp>
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#include <sprout/math.hpp>
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#include <sprout/math/curve.hpp>
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#include <sprout/memory.hpp>
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#include <sprout/net.hpp>
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#include <sprout/none.hpp>
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