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+///////////////////////////////////////////////////////////////////////////////////
+/// OpenGL Mathematics (glm.g-truc.net)
+///
+/// Copyright (c) 2005 - 2015 G-Truc Creation (www.g-truc.net)
+/// Permission is hereby granted, free of charge, to any person obtaining a copy
+/// of this software and associated documentation files (the "Software"), to deal
+/// in the Software without restriction, including without limitation the rights
+/// to use, copy, modify, merge, publish, distribute, sublicense, and/or sell
+/// copies of the Software, and to permit persons to whom the Software is
+/// furnished to do so, subject to the following conditions:
+///
+/// The above copyright notice and this permission notice shall be included in
+/// all copies or substantial portions of the Software.
+///
+/// Restrictions:
+/// By making use of the Software for military purposes, you choose to make
+/// a Bunny unhappy.
+///
+/// THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
+/// IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
+/// FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE
+/// AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER
+/// LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM,
+/// OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN
+/// THE SOFTWARE.
+///
+/// @ref gtx_dual_quaternion
+/// @file glm/gtx/dual_quaternion.hpp
+/// @date 2013-02-10 / 2013-02-20
+/// @author Maksim Vorobiev (msomeone@gmail.com)
+///
+/// @see core (dependence)
+/// @see gtc_half_float (dependence)
+/// @see gtc_constants (dependence)
+/// @see gtc_quaternion (dependence)
+///
+/// @defgroup gtx_dual_quaternion GLM_GTX_dual_quaternion
+/// @ingroup gtx
+///
+/// @brief Defines a templated dual-quaternion type and several dual-quaternion operations.
+///
+/// <glm/gtx/dual_quaternion.hpp> need to be included to use these functionalities.
+///////////////////////////////////////////////////////////////////////////////////
+
+#pragma once
+
+// Dependency:
+#include "../glm.hpp"
+#include "../gtc/constants.hpp"
+#include "../gtc/quaternion.hpp"
+
+#if(defined(GLM_MESSAGES) && !defined(GLM_EXT_INCLUDED))
+# pragma message("GLM: GLM_GTX_dual_quaternion extension included")
+#endif
+
+namespace glm
+{
+ /// @addtogroup gtx_dual_quaternion
+ /// @{
+
+ template <typename T, precision P>
+ struct tdualquat
+ {
+ typedef T value_type;
+ typedef glm::tquat<T, P> part_type;
+
+ public:
+ glm::tquat<T, P> real, dual;
+
+ //////////////////////////////////////
+ // Component accesses
+
+# ifdef GLM_FORCE_SIZE_FUNC
+ typedef size_t size_type;
+ /// Return the count of components of a dual quaternion
+ GLM_FUNC_DECL GLM_CONSTEXPR size_type size() const;
+
+ GLM_FUNC_DECL part_type & operator[](size_type i);
+ GLM_FUNC_DECL part_type const & operator[](size_type i) const;
+# else
+ typedef length_t length_type;
+ /// Return the count of components of a dual quaternion
+ GLM_FUNC_DECL GLM_CONSTEXPR length_type length() const;
+
+ GLM_FUNC_DECL part_type & operator[](length_type i);
+ GLM_FUNC_DECL part_type const & operator[](length_type i) const;
+# endif//GLM_FORCE_SIZE_FUNC
+
+ //////////////////////////////////////
+ // Implicit basic constructors
+
+ GLM_FUNC_DECL tdualquat();
+ GLM_FUNC_DECL tdualquat(tdualquat<T, P> const & d);
+ template <precision Q>
+ GLM_FUNC_DECL tdualquat(tdualquat<T, Q> const & d);
+
+ //////////////////////////////////////
+ // Explicit basic constructors
+
+ GLM_FUNC_DECL explicit tdualquat(ctor);
+ GLM_FUNC_DECL explicit tdualquat(tquat<T, P> const & real);
+ GLM_FUNC_DECL tdualquat(tquat<T, P> const & orientation, tvec3<T, P> const & translation);
+ GLM_FUNC_DECL tdualquat(tquat<T, P> const & real, tquat<T, P> const & dual);
+
+ //////////////////////////////////////////////////////////////
+ // tdualquat conversions
+
+# ifdef GLM_FORCE_EXPLICIT_CTOR
+ template <typename U, precision Q>
+ GLM_FUNC_DECL explicit tdualquat(tdualquat<U, Q> const & q);
+# else
+ template <typename U, precision Q>
+ GLM_FUNC_DECL tdualquat(tdualquat<U, Q> const & q);
+# endif
+
+ GLM_FUNC_DECL explicit tdualquat(tmat2x4<T, P> const & holder_mat);
+ GLM_FUNC_DECL explicit tdualquat(tmat3x4<T, P> const & aug_mat);
+
+ // Operators
+ GLM_FUNC_DECL tdualquat<T, P> & operator=(tdualquat<T, P> const & m);
+
+ template <typename U>
+ GLM_FUNC_DECL tdualquat<T, P> & operator=(tdualquat<U, P> const & m);
+ template <typename U>
+ GLM_FUNC_DECL tdualquat<T, P> & operator*=(U s);
+ template <typename U>
+ GLM_FUNC_DECL tdualquat<T, P> & operator/=(U s);
+ };
+
+ template <typename T, precision P>
+ GLM_FUNC_DECL tquat<T, P> operator- (
+ tquat<T, P> const & q);
+
+ template <typename T, precision P>
+ GLM_FUNC_DECL tdualquat<T, P> operator+ (
+ tdualquat<T, P> const & q,
+ tdualquat<T, P> const & p);
+
+ template <typename T, precision P>
+ GLM_FUNC_DECL tdualquat<T, P> operator* (
+ tdualquat<T, P> const & q,
+ tdualquat<T, P> const & p);
+
+ template <typename T, precision P>
+ GLM_FUNC_DECL tvec3<T, P> operator* (
+ tquat<T, P> const & q,
+ tvec3<T, P> const & v);
+
+ template <typename T, precision P>
+ GLM_FUNC_DECL tvec3<T, P> operator* (
+ tvec3<T, P> const & v,
+ tquat<T, P> const & q);
+
+ template <typename T, precision P>
+ GLM_FUNC_DECL tvec4<T, P> operator* (
+ tquat<T, P> const & q,
+ tvec4<T, P> const & v);
+
+ template <typename T, precision P>
+ GLM_FUNC_DECL tvec4<T, P> operator* (
+ tvec4<T, P> const & v,
+ tquat<T, P> const & q);
+
+ template <typename T, precision P>
+ GLM_FUNC_DECL tdualquat<T, P> operator* (
+ tdualquat<T, P> const & q,
+ T const & s);
+
+ template <typename T, precision P>
+ GLM_FUNC_DECL tdualquat<T, P> operator* (
+ T const & s,
+ tdualquat<T, P> const & q);
+
+ template <typename T, precision P>
+ GLM_FUNC_DECL tdualquat<T, P> operator/ (
+ tdualquat<T, P> const & q,
+ T const & s);
+
+ /// Returns the normalized quaternion.
+ ///
+ /// @see gtx_dual_quaternion
+ template <typename T, precision P>
+ GLM_FUNC_DECL tdualquat<T, P> normalize(
+ tdualquat<T, P> const & q);
+
+ /// Returns the linear interpolation of two dual quaternion.
+ ///
+ /// @see gtc_dual_quaternion
+ template <typename T, precision P>
+ GLM_FUNC_DECL tdualquat<T, P> lerp(
+ tdualquat<T, P> const & x,
+ tdualquat<T, P> const & y,
+ T const & a);
+
+ /// Returns the q inverse.
+ ///
+ /// @see gtx_dual_quaternion
+ template <typename T, precision P>
+ GLM_FUNC_DECL tdualquat<T, P> inverse(
+ tdualquat<T, P> const & q);
+
+ /// Converts a quaternion to a 2 * 4 matrix.
+ ///
+ /// @see gtx_dual_quaternion
+ template <typename T, precision P>
+ GLM_FUNC_DECL tmat2x4<T, P> mat2x4_cast(
+ tdualquat<T, P> const & x);
+
+ /// Converts a quaternion to a 3 * 4 matrix.
+ ///
+ /// @see gtx_dual_quaternion
+ template <typename T, precision P>
+ GLM_FUNC_DECL tmat3x4<T, P> mat3x4_cast(
+ tdualquat<T, P> const & x);
+
+ /// Converts a 2 * 4 matrix (matrix which holds real and dual parts) to a quaternion.
+ ///
+ /// @see gtx_dual_quaternion
+ template <typename T, precision P>
+ GLM_FUNC_DECL tdualquat<T, P> dualquat_cast(
+ tmat2x4<T, P> const & x);
+
+ /// Converts a 3 * 4 matrix (augmented matrix rotation + translation) to a quaternion.
+ ///
+ /// @see gtx_dual_quaternion
+ template <typename T, precision P>
+ GLM_FUNC_DECL tdualquat<T, P> dualquat_cast(
+ tmat3x4<T, P> const & x);
+
+
+ /// Dual-quaternion of low single-precision floating-point numbers.
+ ///
+ /// @see gtx_dual_quaternion
+ typedef tdualquat<float, lowp> lowp_dualquat;
+
+ /// Dual-quaternion of medium single-precision floating-point numbers.
+ ///
+ /// @see gtx_dual_quaternion
+ typedef tdualquat<float, mediump> mediump_dualquat;
+
+ /// Dual-quaternion of high single-precision floating-point numbers.
+ ///
+ /// @see gtx_dual_quaternion
+ typedef tdualquat<float, highp> highp_dualquat;
+
+
+ /// Dual-quaternion of low single-precision floating-point numbers.
+ ///
+ /// @see gtx_dual_quaternion
+ typedef tdualquat<float, lowp> lowp_fdualquat;
+
+ /// Dual-quaternion of medium single-precision floating-point numbers.
+ ///
+ /// @see gtx_dual_quaternion
+ typedef tdualquat<float, mediump> mediump_fdualquat;
+
+ /// Dual-quaternion of high single-precision floating-point numbers.
+ ///
+ /// @see gtx_dual_quaternion
+ typedef tdualquat<float, highp> highp_fdualquat;
+
+
+ /// Dual-quaternion of low double-precision floating-point numbers.
+ ///
+ /// @see gtx_dual_quaternion
+ typedef tdualquat<double, lowp> lowp_ddualquat;
+
+ /// Dual-quaternion of medium double-precision floating-point numbers.
+ ///
+ /// @see gtx_dual_quaternion
+ typedef tdualquat<double, mediump> mediump_ddualquat;
+
+ /// Dual-quaternion of high double-precision floating-point numbers.
+ ///
+ /// @see gtx_dual_quaternion
+ typedef tdualquat<double, highp> highp_ddualquat;
+
+
+#if(!defined(GLM_PRECISION_HIGHP_FLOAT) && !defined(GLM_PRECISION_MEDIUMP_FLOAT) && !defined(GLM_PRECISION_LOWP_FLOAT))
+ /// Dual-quaternion of floating-point numbers.
+ ///
+ /// @see gtx_dual_quaternion
+ typedef highp_fdualquat dualquat;
+
+ /// Dual-quaternion of single-precision floating-point numbers.
+ ///
+ /// @see gtx_dual_quaternion
+ typedef highp_fdualquat fdualquat;
+#elif(defined(GLM_PRECISION_HIGHP_FLOAT) && !defined(GLM_PRECISION_MEDIUMP_FLOAT) && !defined(GLM_PRECISION_LOWP_FLOAT))
+ typedef highp_fdualquat dualquat;
+ typedef highp_fdualquat fdualquat;
+#elif(!defined(GLM_PRECISION_HIGHP_FLOAT) && defined(GLM_PRECISION_MEDIUMP_FLOAT) && !defined(GLM_PRECISION_LOWP_FLOAT))
+ typedef mediump_fdualquat dualquat;
+ typedef mediump_fdualquat fdualquat;
+#elif(!defined(GLM_PRECISION_HIGHP_FLOAT) && !defined(GLM_PRECISION_MEDIUMP_FLOAT) && defined(GLM_PRECISION_LOWP_FLOAT))
+ typedef lowp_fdualquat dualquat;
+ typedef lowp_fdualquat fdualquat;
+#else
+# error "GLM error: multiple default precision requested for single-precision floating-point types"
+#endif
+
+
+#if(!defined(GLM_PRECISION_HIGHP_DOUBLE) && !defined(GLM_PRECISION_MEDIUMP_DOUBLE) && !defined(GLM_PRECISION_LOWP_DOUBLE))
+ /// Dual-quaternion of default double-precision floating-point numbers.
+ ///
+ /// @see gtx_dual_quaternion
+ typedef highp_ddualquat ddualquat;
+#elif(defined(GLM_PRECISION_HIGHP_DOUBLE) && !defined(GLM_PRECISION_MEDIUMP_DOUBLE) && !defined(GLM_PRECISION_LOWP_DOUBLE))
+ typedef highp_ddualquat ddualquat;
+#elif(!defined(GLM_PRECISION_HIGHP_DOUBLE) && defined(GLM_PRECISION_MEDIUMP_DOUBLE) && !defined(GLM_PRECISION_LOWP_DOUBLE))
+ typedef mediump_ddualquat ddualquat;
+#elif(!defined(GLM_PRECISION_HIGHP_DOUBLE) && !defined(GLM_PRECISION_MEDIUMP_DOUBLE) && defined(GLM_PRECISION_LOWP_DOUBLE))
+ typedef lowp_ddualquat ddualquat;
+#else
+# error "GLM error: Multiple default precision requested for double-precision floating-point types"
+#endif
+
+ /// @}
+} //namespace glm
+
+#include "dual_quaternion.inl"