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+/// @ref gtx_dual_quaternion
+/// @file glm/gtx/dual_quaternion.hpp
+/// @author Maksim Vorobiev (msomeone@gmail.com)
+///
+/// @see core (dependence)
+/// @see gtc_constants (dependence)
+/// @see gtc_quaternion (dependence)
+///
+/// @defgroup gtx_dual_quaternion GLM_GTX_dual_quaternion
+/// @ingroup gtx
+///
+/// Include <glm/gtx/dual_quaternion.hpp> to use the features of this extension.
+///
+/// Defines a templated dual-quaternion type and several dual-quaternion operations.
+
+#pragma once
+
+// Dependency:
+#include "../glm.hpp"
+#include "../gtc/constants.hpp"
+#include "../gtc/quaternion.hpp"
+
+#if GLM_MESSAGES == GLM_ENABLE && !defined(GLM_EXT_INCLUDED)
+# ifndef GLM_ENABLE_EXPERIMENTAL
+# pragma message("GLM: GLM_GTX_dual_quaternion is an experimental extension and may change in the future. Use #define GLM_ENABLE_EXPERIMENTAL before including it, if you really want to use it.")
+# else
+# pragma message("GLM: GLM_GTX_dual_quaternion extension included")
+# endif
+#endif
+
+namespace glm
+{
+ /// @addtogroup gtx_dual_quaternion
+ /// @{
+
+ template<typename T, qualifier Q = defaultp>
+ struct tdualquat
+ {
+ // -- Implementation detail --
+
+ typedef T value_type;
+ typedef qua<T, Q> part_type;
+
+ // -- Data --
+
+ qua<T, Q> real, dual;
+
+ // -- Component accesses --
+
+ typedef length_t length_type;
+ /// Return the count of components of a dual quaternion
+ GLM_FUNC_DECL static GLM_CONSTEXPR length_type length(){return 2;}
+
+ GLM_FUNC_DECL part_type & operator[](length_type i);
+ GLM_FUNC_DECL part_type const& operator[](length_type i) const;
+
+ // -- Implicit basic constructors --
+
+ GLM_FUNC_DECL GLM_CONSTEXPR tdualquat() GLM_DEFAULT;
+ GLM_FUNC_DECL GLM_CONSTEXPR tdualquat(tdualquat<T, Q> const& d) GLM_DEFAULT;
+ template<qualifier P>
+ GLM_FUNC_DECL GLM_CONSTEXPR tdualquat(tdualquat<T, P> const& d);
+
+ // -- Explicit basic constructors --
+
+ GLM_FUNC_DECL GLM_CONSTEXPR tdualquat(qua<T, Q> const& real);
+ GLM_FUNC_DECL GLM_CONSTEXPR tdualquat(qua<T, Q> const& orientation, vec<3, T, Q> const& translation);
+ GLM_FUNC_DECL GLM_CONSTEXPR tdualquat(qua<T, Q> const& real, qua<T, Q> const& dual);
+
+ // -- Conversion constructors --
+
+ template<typename U, qualifier P>
+ GLM_FUNC_DECL GLM_CONSTEXPR GLM_EXPLICIT tdualquat(tdualquat<U, P> const& q);
+
+ GLM_FUNC_DECL GLM_EXPLICIT GLM_CONSTEXPR tdualquat(mat<2, 4, T, Q> const& holder_mat);
+ GLM_FUNC_DECL GLM_EXPLICIT GLM_CONSTEXPR tdualquat(mat<3, 4, T, Q> const& aug_mat);
+
+ // -- Unary arithmetic operators --
+
+ GLM_FUNC_DECL tdualquat<T, Q> & operator=(tdualquat<T, Q> const& m) GLM_DEFAULT;
+
+ template<typename U>
+ GLM_FUNC_DECL tdualquat<T, Q> & operator=(tdualquat<U, Q> const& m);
+ template<typename U>
+ GLM_FUNC_DECL tdualquat<T, Q> & operator*=(U s);
+ template<typename U>
+ GLM_FUNC_DECL tdualquat<T, Q> & operator/=(U s);
+ };
+
+ // -- Unary bit operators --
+
+ template<typename T, qualifier Q>
+ GLM_FUNC_DECL tdualquat<T, Q> operator+(tdualquat<T, Q> const& q);
+
+ template<typename T, qualifier Q>
+ GLM_FUNC_DECL tdualquat<T, Q> operator-(tdualquat<T, Q> const& q);
+
+ // -- Binary operators --
+
+ template<typename T, qualifier Q>
+ GLM_FUNC_DECL tdualquat<T, Q> operator+(tdualquat<T, Q> const& q, tdualquat<T, Q> const& p);
+
+ template<typename T, qualifier Q>
+ GLM_FUNC_DECL tdualquat<T, Q> operator*(tdualquat<T, Q> const& q, tdualquat<T, Q> const& p);
+
+ template<typename T, qualifier Q>
+ GLM_FUNC_DECL vec<3, T, Q> operator*(tdualquat<T, Q> const& q, vec<3, T, Q> const& v);
+
+ template<typename T, qualifier Q>
+ GLM_FUNC_DECL vec<3, T, Q> operator*(vec<3, T, Q> const& v, tdualquat<T, Q> const& q);
+
+ template<typename T, qualifier Q>
+ GLM_FUNC_DECL vec<4, T, Q> operator*(tdualquat<T, Q> const& q, vec<4, T, Q> const& v);
+
+ template<typename T, qualifier Q>
+ GLM_FUNC_DECL vec<4, T, Q> operator*(vec<4, T, Q> const& v, tdualquat<T, Q> const& q);
+
+ template<typename T, qualifier Q>
+ GLM_FUNC_DECL tdualquat<T, Q> operator*(tdualquat<T, Q> const& q, T const& s);
+
+ template<typename T, qualifier Q>
+ GLM_FUNC_DECL tdualquat<T, Q> operator*(T const& s, tdualquat<T, Q> const& q);
+
+ template<typename T, qualifier Q>
+ GLM_FUNC_DECL tdualquat<T, Q> operator/(tdualquat<T, Q> const& q, T const& s);
+
+ // -- Boolean operators --
+
+ template<typename T, qualifier Q>
+ GLM_FUNC_DECL bool operator==(tdualquat<T, Q> const& q1, tdualquat<T, Q> const& q2);
+
+ template<typename T, qualifier Q>
+ GLM_FUNC_DECL bool operator!=(tdualquat<T, Q> const& q1, tdualquat<T, Q> const& q2);
+
+ /// Creates an identity dual quaternion.
+ ///
+ /// @see gtx_dual_quaternion
+ template <typename T, qualifier Q>
+ GLM_FUNC_DECL tdualquat<T, Q> dual_quat_identity();
+
+ /// Returns the normalized quaternion.
+ ///
+ /// @see gtx_dual_quaternion
+ template<typename T, qualifier Q>
+ GLM_FUNC_DECL tdualquat<T, Q> normalize(tdualquat<T, Q> const& q);
+
+ /// Returns the linear interpolation of two dual quaternion.
+ ///
+ /// @see gtc_dual_quaternion
+ template<typename T, qualifier Q>
+ GLM_FUNC_DECL tdualquat<T, Q> lerp(tdualquat<T, Q> const& x, tdualquat<T, Q> const& y, T const& a);
+
+ /// Returns the q inverse.
+ ///
+ /// @see gtx_dual_quaternion
+ template<typename T, qualifier Q>
+ GLM_FUNC_DECL tdualquat<T, Q> inverse(tdualquat<T, Q> const& q);
+
+ /// Converts a quaternion to a 2 * 4 matrix.
+ ///
+ /// @see gtx_dual_quaternion
+ template<typename T, qualifier Q>
+ GLM_FUNC_DECL mat<2, 4, T, Q> mat2x4_cast(tdualquat<T, Q> const& x);
+
+ /// Converts a quaternion to a 3 * 4 matrix.
+ ///
+ /// @see gtx_dual_quaternion
+ template<typename T, qualifier Q>
+ GLM_FUNC_DECL mat<3, 4, T, Q> mat3x4_cast(tdualquat<T, Q> const& x);
+
+ /// Converts a 2 * 4 matrix (matrix which holds real and dual parts) to a quaternion.
+ ///
+ /// @see gtx_dual_quaternion
+ template<typename T, qualifier Q>
+ GLM_FUNC_DECL tdualquat<T, Q> dualquat_cast(mat<2, 4, T, Q> const& x);
+
+ /// Converts a 3 * 4 matrix (augmented matrix rotation + translation) to a quaternion.
+ ///
+ /// @see gtx_dual_quaternion
+ template<typename T, qualifier Q>
+ GLM_FUNC_DECL tdualquat<T, Q> dualquat_cast(mat<3, 4, T, Q> const& x);
+
+
+ /// Dual-quaternion of low single-qualifier floating-point numbers.
+ ///
+ /// @see gtx_dual_quaternion
+ typedef tdualquat<float, lowp> lowp_dualquat;
+
+ /// Dual-quaternion of medium single-qualifier floating-point numbers.
+ ///
+ /// @see gtx_dual_quaternion
+ typedef tdualquat<float, mediump> mediump_dualquat;
+
+ /// Dual-quaternion of high single-qualifier floating-point numbers.
+ ///
+ /// @see gtx_dual_quaternion
+ typedef tdualquat<float, highp> highp_dualquat;
+
+
+ /// Dual-quaternion of low single-qualifier floating-point numbers.
+ ///
+ /// @see gtx_dual_quaternion
+ typedef tdualquat<float, lowp> lowp_fdualquat;
+
+ /// Dual-quaternion of medium single-qualifier floating-point numbers.
+ ///
+ /// @see gtx_dual_quaternion
+ typedef tdualquat<float, mediump> mediump_fdualquat;
+
+ /// Dual-quaternion of high single-qualifier floating-point numbers.
+ ///
+ /// @see gtx_dual_quaternion
+ typedef tdualquat<float, highp> highp_fdualquat;
+
+
+ /// Dual-quaternion of low double-qualifier floating-point numbers.
+ ///
+ /// @see gtx_dual_quaternion
+ typedef tdualquat<double, lowp> lowp_ddualquat;
+
+ /// Dual-quaternion of medium double-qualifier floating-point numbers.
+ ///
+ /// @see gtx_dual_quaternion
+ typedef tdualquat<double, mediump> mediump_ddualquat;
+
+ /// Dual-quaternion of high double-qualifier 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-qualifier 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-qualifier 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"