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add curve/bezier, curve/catmull_rom_sprine
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bolero-MURAKAMI
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5 changed files with 325 additions and 0 deletions
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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