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172 lines
5.8 KiB
172 lines
5.8 KiB
/////////////////////////////////////////////////////////////////////////////////// |
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/// OpenGL Mathematics (glm.g-truc.net) |
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/// |
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/// Copyright (c) 2005 - 2015 G-Truc Creation (www.g-truc.net) |
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/// Permission is hereby granted, free of charge, to any person obtaining a copy |
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/// of this software and associated documentation files (the "Software"), to deal |
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/// in the Software without restriction, including without limitation the rights |
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/// to use, copy, modify, merge, publish, distribute, sublicense, and/or sell |
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/// copies of the Software, and to permit persons to whom the Software is |
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/// furnished to do so, subject to the following conditions: |
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/// |
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/// The above copyright notice and this permission notice shall be included in |
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/// all copies or substantial portions of the Software. |
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/// |
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/// Restrictions: |
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/// By making use of the Software for military purposes, you choose to make |
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/// a Bunny unhappy. |
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/// |
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/// THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR |
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/// IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY, |
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/// FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE |
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/// AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER |
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/// LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM, |
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/// OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN |
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/// THE SOFTWARE. |
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/// |
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/// @ref gtx_fast_trigonometry |
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/// @file glm/gtx/fast_trigonometry.inl |
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/// @date 2006-01-08 / 2014-11-25 |
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/// @author Christophe Riccio |
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/////////////////////////////////////////////////////////////////////////////////////////////////// |
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namespace glm{ |
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namespace detail |
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{ |
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template <typename T, precision P, template <typename, precision> class vecType> |
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GLM_FUNC_QUALIFIER vecType<T, P> taylorCos(vecType<T, P> const & x) |
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{ |
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return static_cast<T>(1) |
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- (x * x) / 2.f |
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+ (x * x * x * x) / 24.f |
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- (x * x * x * x * x * x) / 720.f |
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+ (x * x * x * x * x * x * x * x) / 40320.f; |
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} |
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template <typename T> |
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GLM_FUNC_QUALIFIER T cos_52s(T x) |
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{ |
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T const xx(x * x); |
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return (T(0.9999932946) + xx * (T(-0.4999124376) + xx * (T(0.0414877472) + xx * T(-0.0012712095)))); |
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} |
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template <typename T, precision P, template <typename, precision> class vecType> |
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GLM_FUNC_QUALIFIER vecType<T, P> cos_52s(vecType<T, P> const & x) |
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{ |
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return detail::functor1<T, T, P, vecType>::call(cos_52s, x); |
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} |
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}//namespace detail |
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// wrapAngle |
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template <typename T> |
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GLM_FUNC_QUALIFIER T wrapAngle(T angle) |
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{ |
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return abs<T>(mod<T>(angle, two_pi<T>())); |
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} |
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template <typename T, precision P, template <typename, precision> class vecType> |
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GLM_FUNC_QUALIFIER vecType<T, P> wrapAngle(vecType<T, P> const & x) |
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{ |
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return detail::functor1<T, T, P, vecType>::call(wrapAngle, x); |
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} |
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// cos |
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template <typename T> |
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GLM_FUNC_QUALIFIER T fastCos(T x) |
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{ |
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T const angle(wrapAngle<T>(x)); |
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if(angle < half_pi<T>()) |
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return detail::cos_52s(angle); |
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if(angle < pi<T>()) |
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return -detail::cos_52s(pi<T>() - angle); |
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if(angle < (T(3) * half_pi<T>())) |
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return -detail::cos_52s(angle - pi<T>()); |
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return detail::cos_52s(two_pi<T>() - angle); |
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} |
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template <typename T, precision P, template <typename, precision> class vecType> |
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GLM_FUNC_QUALIFIER vecType<T, P> fastCos(vecType<T, P> const & x) |
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{ |
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return detail::functor1<T, T, P, vecType>::call(fastCos, x); |
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} |
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// sin |
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template <typename T> |
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GLM_FUNC_QUALIFIER T fastSin(T x) |
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{ |
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return fastCos<T>(half_pi<T>() - x); |
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} |
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template <typename T, precision P, template <typename, precision> class vecType> |
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GLM_FUNC_QUALIFIER vecType<T, P> fastSin(vecType<T, P> const & x) |
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{ |
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return detail::functor1<T, T, P, vecType>::call(fastSin, x); |
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} |
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// tan |
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template <typename T> |
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GLM_FUNC_QUALIFIER T fastTan(T x) |
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{ |
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return x + (x * x * x * T(0.3333333333)) + (x * x * x * x * x * T(0.1333333333333)) + (x * x * x * x * x * x * x * T(0.0539682539)); |
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} |
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template <typename T, precision P, template <typename, precision> class vecType> |
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GLM_FUNC_QUALIFIER vecType<T, P> fastTan(vecType<T, P> const & x) |
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{ |
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return detail::functor1<T, T, P, vecType>::call(fastTan, x); |
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} |
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// asin |
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template <typename T> |
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GLM_FUNC_QUALIFIER T fastAsin(T x) |
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{ |
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return x + (x * x * x * T(0.166666667)) + (x * x * x * x * x * T(0.075)) + (x * x * x * x * x * x * x * T(0.0446428571)) + (x * x * x * x * x * x * x * x * x * T(0.0303819444));// + (x * x * x * x * x * x * x * x * x * x * x * T(0.022372159)); |
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} |
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template <typename T, precision P, template <typename, precision> class vecType> |
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GLM_FUNC_QUALIFIER vecType<T, P> fastAsin(vecType<T, P> const & x) |
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{ |
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return detail::functor1<T, T, P, vecType>::call(fastAsin, x); |
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} |
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// acos |
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template <typename T> |
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GLM_FUNC_QUALIFIER T fastAcos(T x) |
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{ |
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return T(1.5707963267948966192313216916398) - fastAsin(x); //(PI / 2) |
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} |
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template <typename T, precision P, template <typename, precision> class vecType> |
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GLM_FUNC_QUALIFIER vecType<T, P> fastAcos(vecType<T, P> const & x) |
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{ |
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return detail::functor1<T, T, P, vecType>::call(fastAcos, x); |
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} |
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// atan |
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template <typename T> |
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GLM_FUNC_QUALIFIER T fastAtan(T y, T x) |
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{ |
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T sgn = sign(y) * sign(x); |
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return abs(fastAtan(y / x)) * sgn; |
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} |
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template <typename T, precision P, template <typename, precision> class vecType> |
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GLM_FUNC_QUALIFIER vecType<T, P> fastAtan(vecType<T, P> const & y, vecType<T, P> const & x) |
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{ |
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return detail::functor2<T, P, vecType>::call(fastAtan, y, x); |
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} |
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template <typename T> |
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GLM_FUNC_QUALIFIER T fastAtan(T x) |
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{ |
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return x - (x * x * x * T(0.333333333333)) + (x * x * x * x * x * T(0.2)) - (x * x * x * x * x * x * x * T(0.1428571429)) + (x * x * x * x * x * x * x * x * x * T(0.111111111111)) - (x * x * x * x * x * x * x * x * x * x * x * T(0.0909090909)); |
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} |
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template <typename T, precision P, template <typename, precision> class vecType> |
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GLM_FUNC_QUALIFIER vecType<T, P> fastAtan(vecType<T, P> const & x) |
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{ |
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return detail::functor1<T, T, P, vecType>::call(fastAtan, x); |
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} |
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}//namespace glm
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