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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_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 GLM_MESSAGES == GLM_MESSAGES_ENABLED && !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 = defaultp>
+ struct tdualquat
+ {
+ // -- Implementation detail --
+
+ typedef T value_type;
+ typedef glm::tquat<T, P> part_type;
+
+ // -- Data --
+
+ glm::tquat<T, P> real, dual;
+
+ // -- Component accesses --
+
+ typedef length_t length_type;
+ /// Return the count of components of a dual quaternion
+ GLM_FUNC_DECL static 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_CTOR;
+ GLM_FUNC_DECL GLM_CONSTEXPR tdualquat(tdualquat<T, P> const & d) GLM_DEFAULT;
+ template <precision Q>
+ GLM_FUNC_DECL GLM_CONSTEXPR tdualquat(tdualquat<T, Q> const & d);
+
+ // -- Explicit basic constructors --
+
+ GLM_FUNC_DECL GLM_CONSTEXPR_CTOR explicit tdualquat(ctor);
+ GLM_FUNC_DECL GLM_CONSTEXPR tdualquat(tquat<T, P> const & real);
+ GLM_FUNC_DECL GLM_CONSTEXPR tdualquat(tquat<T, P> const & orientation, tvec3<T, P> const & translation);
+ GLM_FUNC_DECL GLM_CONSTEXPR tdualquat(tquat<T, P> const & real, tquat<T, P> const & dual);
+
+ // -- Conversion constructors --
+
+ template <typename U, precision Q>
+ GLM_FUNC_DECL GLM_CONSTEXPR GLM_EXPLICIT tdualquat(tdualquat<U, Q> const & q);
+
+ GLM_FUNC_DECL GLM_EXPLICIT tdualquat(tmat2x4<T, P> const & holder_mat);
+ GLM_FUNC_DECL GLM_EXPLICIT tdualquat(tmat3x4<T, P> const & aug_mat);
+
+ // -- Unary arithmetic operators --
+
+ GLM_FUNC_DECL tdualquat<T, P> & operator=(tdualquat<T, P> const & m) GLM_DEFAULT;
+
+ 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);
+ };
+
+ // -- Unary bit operators --
+
+ template <typename T, precision P>
+ GLM_FUNC_DECL tdualquat<T, P> operator+(tdualquat<T, P> const & q);
+
+ template <typename T, precision P>
+ GLM_FUNC_DECL tdualquat<T, P> operator-(tdualquat<T, P> const & q);
+
+ // -- Binary operators --
+
+ 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*(tdualquat<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, tdualquat<T, P> const & q);
+
+ template <typename T, precision P>
+ GLM_FUNC_DECL tvec4<T, P> operator*(tdualquat<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, 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);
+
+ 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);
+
+ // -- Boolean operators --
+
+ template <typename T, precision P>
+ GLM_FUNC_DECL bool operator==(tdualquat<T, P> const & q1, tdualquat<T, P> const & q2);
+
+ template <typename T, precision P>
+ GLM_FUNC_DECL bool operator!=(tdualquat<T, P> const & q1, tdualquat<T, P> const & q2);
+
+ /// 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"