/// @ref gtx_dual_quaternion /// @file glm/gtx/dual_quaternion.inl #include "../geometric.hpp" #include <limits> namespace glm { // -- Component accesses -- template <typename T, precision P> GLM_FUNC_QUALIFIER typename tdualquat<T, P>::part_type & tdualquat<T, P>::operator[](typename tdualquat<T, P>::length_type i) { assert(i >= 0 && i < this->length()); return (&real)[i]; } template <typename T, precision P> GLM_FUNC_QUALIFIER typename tdualquat<T, P>::part_type const & tdualquat<T, P>::operator[](typename tdualquat<T, P>::length_type i) const { assert(i >= 0 && i < this->length()); return (&real)[i]; } // -- Implicit basic constructors -- # if !GLM_HAS_DEFAULTED_FUNCTIONS || !defined(GLM_FORCE_NO_CTOR_INIT) template <typename T, precision P> GLM_FUNC_QUALIFIER GLM_CONSTEXPR tdualquat<T, P>::tdualquat() # ifndef GLM_FORCE_NO_CTOR_INIT : real(tquat<T, P>()) , dual(tquat<T, P>(0, 0, 0, 0)) # endif {} # endif # if !GLM_HAS_DEFAULTED_FUNCTIONS template <typename T, precision P> GLM_FUNC_QUALIFIER GLM_CONSTEXPR tdualquat<T, P>::tdualquat(tdualquat<T, P> const & d) : real(d.real) , dual(d.dual) {} # endif//!GLM_HAS_DEFAULTED_FUNCTIONS template <typename T, precision P> template <precision Q> GLM_FUNC_QUALIFIER GLM_CONSTEXPR tdualquat<T, P>::tdualquat(tdualquat<T, Q> const & d) : real(d.real) , dual(d.dual) {} // -- Explicit basic constructors -- template <typename T, precision P> GLM_FUNC_QUALIFIER GLM_CONSTEXPR_CTOR tdualquat<T, P>::tdualquat(ctor) {} template <typename T, precision P> GLM_FUNC_QUALIFIER GLM_CONSTEXPR tdualquat<T, P>::tdualquat(tquat<T, P> const & r) : real(r), dual(tquat<T, P>(0, 0, 0, 0)) {} template <typename T, precision P> GLM_FUNC_QUALIFIER GLM_CONSTEXPR tdualquat<T, P>::tdualquat(tquat<T, P> const & q, tvec3<T, P> const& p) : real(q), dual( T(-0.5) * ( p.x*q.x + p.y*q.y + p.z*q.z), T(+0.5) * ( p.x*q.w + p.y*q.z - p.z*q.y), T(+0.5) * (-p.x*q.z + p.y*q.w + p.z*q.x), T(+0.5) * ( p.x*q.y - p.y*q.x + p.z*q.w)) {} template <typename T, precision P> GLM_FUNC_QUALIFIER GLM_CONSTEXPR tdualquat<T, P>::tdualquat(tquat<T, P> const & r, tquat<T, P> const & d) : real(r), dual(d) {} // -- Conversion constructors -- template <typename T, precision P> template <typename U, precision Q> GLM_FUNC_QUALIFIER GLM_CONSTEXPR tdualquat<T, P>::tdualquat(tdualquat<U, Q> const & q) : real(q.real) , dual(q.dual) {} template <typename T, precision P> GLM_FUNC_QUALIFIER tdualquat<T, P>::tdualquat(tmat2x4<T, P> const & m) { *this = dualquat_cast(m); } template <typename T, precision P> GLM_FUNC_QUALIFIER tdualquat<T, P>::tdualquat(tmat3x4<T, P> const & m) { *this = dualquat_cast(m); } // -- Unary arithmetic operators -- # if !GLM_HAS_DEFAULTED_FUNCTIONS template <typename T, precision P> GLM_FUNC_QUALIFIER tdualquat<T, P> & tdualquat<T, P>::operator=(tdualquat<T, P> const & q) { this->real = q.real; this->dual = q.dual; return *this; } # endif//!GLM_HAS_DEFAULTED_FUNCTIONS template <typename T, precision P> template <typename U> GLM_FUNC_QUALIFIER tdualquat<T, P> & tdualquat<T, P>::operator=(tdualquat<U, P> const & q) { this->real = q.real; this->dual = q.dual; return *this; } template <typename T, precision P> template <typename U> GLM_FUNC_QUALIFIER tdualquat<T, P> & tdualquat<T, P>::operator*=(U s) { this->real *= static_cast<T>(s); this->dual *= static_cast<T>(s); return *this; } template <typename T, precision P> template <typename U> GLM_FUNC_QUALIFIER tdualquat<T, P> & tdualquat<T, P>::operator/=(U s) { this->real /= static_cast<T>(s); this->dual /= static_cast<T>(s); return *this; } // -- Unary bit operators -- template <typename T, precision P> GLM_FUNC_QUALIFIER tdualquat<T, P> operator+(tdualquat<T, P> const & q) { return q; } template <typename T, precision P> GLM_FUNC_QUALIFIER tdualquat<T, P> operator-(tdualquat<T, P> const & q) { return tdualquat<T, P>(-q.real, -q.dual); } // -- Binary operators -- template <typename T, precision P> GLM_FUNC_QUALIFIER tdualquat<T, P> operator+(tdualquat<T, P> const & q, tdualquat<T, P> const & p) { return tdualquat<T, P>(q.real + p.real,q.dual + p.dual); } template <typename T, precision P> GLM_FUNC_QUALIFIER tdualquat<T, P> operator*(tdualquat<T, P> const & p, tdualquat<T, P> const & o) { return tdualquat<T, P>(p.real * o.real,p.real * o.dual + p.dual * o.real); } template <typename T, precision P> GLM_FUNC_QUALIFIER tvec3<T, P> operator*(tdualquat<T, P> const & q, tvec3<T, P> const & v) { tvec3<T, P> const real_v3(q.real.x,q.real.y,q.real.z); tvec3<T, P> const dual_v3(q.dual.x,q.dual.y,q.dual.z); return (cross(real_v3, cross(real_v3,v) + v * q.real.w + dual_v3) + dual_v3 * q.real.w - real_v3 * q.dual.w) * T(2) + v; } template <typename T, precision P> GLM_FUNC_QUALIFIER tvec3<T, P> operator*(tvec3<T, P> const & v, tdualquat<T, P> const & q) { return glm::inverse(q) * v; } template <typename T, precision P> GLM_FUNC_QUALIFIER tvec4<T, P> operator*(tdualquat<T, P> const & q, tvec4<T, P> const & v) { return tvec4<T, P>(q * tvec3<T, P>(v), v.w); } template <typename T, precision P> GLM_FUNC_QUALIFIER tvec4<T, P> operator*(tvec4<T, P> const & v, tdualquat<T, P> const & q) { return glm::inverse(q) * v; } template <typename T, precision P> GLM_FUNC_QUALIFIER tdualquat<T, P> operator*(tdualquat<T, P> const & q, T const & s) { return tdualquat<T, P>(q.real * s, q.dual * s); } template <typename T, precision P> GLM_FUNC_QUALIFIER tdualquat<T, P> operator*(T const & s, tdualquat<T, P> const & q) { return q * s; } template <typename T, precision P> GLM_FUNC_QUALIFIER tdualquat<T, P> operator/(tdualquat<T, P> const & q, T const & s) { return tdualquat<T, P>(q.real / s, q.dual / s); } // -- Boolean operators -- template <typename T, precision P> GLM_FUNC_QUALIFIER bool operator==(tdualquat<T, P> const & q1, tdualquat<T, P> const & q2) { return (q1.real == q2.real) && (q1.dual == q2.dual); } template <typename T, precision P> GLM_FUNC_QUALIFIER bool operator!=(tdualquat<T, P> const & q1, tdualquat<T, P> const & q2) { return (q1.real != q2.dual) || (q1.real != q2.dual); } // -- Operations -- template <typename T, precision P> GLM_FUNC_QUALIFIER tdualquat<T, P> normalize(tdualquat<T, P> const & q) { return q / length(q.real); } template <typename T, precision P> GLM_FUNC_QUALIFIER tdualquat<T, P> lerp(tdualquat<T, P> const & x, tdualquat<T, P> const & y, T const & a) { // Dual Quaternion Linear blend aka DLB: // Lerp is only defined in [0, 1] assert(a >= static_cast<T>(0)); assert(a <= static_cast<T>(1)); T const k = dot(x.real,y.real) < static_cast<T>(0) ? -a : a; T const one(1); return tdualquat<T, P>(x * (one - a) + y * k); } template <typename T, precision P> GLM_FUNC_QUALIFIER tdualquat<T, P> inverse(tdualquat<T, P> const & q) { const glm::tquat<T, P> real = conjugate(q.real); const glm::tquat<T, P> dual = conjugate(q.dual); return tdualquat<T, P>(real, dual + (real * (-2.0f * dot(real,dual)))); } template <typename T, precision P> GLM_FUNC_QUALIFIER tmat2x4<T, P> mat2x4_cast(tdualquat<T, P> const & x) { return tmat2x4<T, P>( x[0].x, x[0].y, x[0].z, x[0].w, x[1].x, x[1].y, x[1].z, x[1].w ); } template <typename T, precision P> GLM_FUNC_QUALIFIER tmat3x4<T, P> mat3x4_cast(tdualquat<T, P> const & x) { tquat<T, P> r = x.real / length2(x.real); tquat<T, P> const rr(r.w * x.real.w, r.x * x.real.x, r.y * x.real.y, r.z * x.real.z); r *= static_cast<T>(2); T const xy = r.x * x.real.y; T const xz = r.x * x.real.z; T const yz = r.y * x.real.z; T const wx = r.w * x.real.x; T const wy = r.w * x.real.y; T const wz = r.w * x.real.z; tvec4<T, P> const a( rr.w + rr.x - rr.y - rr.z, xy - wz, xz + wy, -(x.dual.w * r.x - x.dual.x * r.w + x.dual.y * r.z - x.dual.z * r.y)); tvec4<T, P> const b( xy + wz, rr.w + rr.y - rr.x - rr.z, yz - wx, -(x.dual.w * r.y - x.dual.x * r.z - x.dual.y * r.w + x.dual.z * r.x)); tvec4<T, P> const c( xz - wy, yz + wx, rr.w + rr.z - rr.x - rr.y, -(x.dual.w * r.z + x.dual.x * r.y - x.dual.y * r.x - x.dual.z * r.w)); return tmat3x4<T, P>(a, b, c); } template <typename T, precision P> GLM_FUNC_QUALIFIER tdualquat<T, P> dualquat_cast(tmat2x4<T, P> const & x) { return tdualquat<T, P>( tquat<T, P>( x[0].w, x[0].x, x[0].y, x[0].z ), tquat<T, P>( x[1].w, x[1].x, x[1].y, x[1].z )); } template <typename T, precision P> GLM_FUNC_QUALIFIER tdualquat<T, P> dualquat_cast(tmat3x4<T, P> const & x) { tquat<T, P> real(uninitialize); T const trace = x[0].x + x[1].y + x[2].z; if(trace > static_cast<T>(0)) { T const r = sqrt(T(1) + trace); T const invr = static_cast<T>(0.5) / r; real.w = static_cast<T>(0.5) * r; real.x = (x[2].y - x[1].z) * invr; real.y = (x[0].z - x[2].x) * invr; real.z = (x[1].x - x[0].y) * invr; } else if(x[0].x > x[1].y && x[0].x > x[2].z) { T const r = sqrt(T(1) + x[0].x - x[1].y - x[2].z); T const invr = static_cast<T>(0.5) / r; real.x = static_cast<T>(0.5)*r; real.y = (x[1].x + x[0].y) * invr; real.z = (x[0].z + x[2].x) * invr; real.w = (x[2].y - x[1].z) * invr; } else if(x[1].y > x[2].z) { T const r = sqrt(T(1) + x[1].y - x[0].x - x[2].z); T const invr = static_cast<T>(0.5) / r; real.x = (x[1].x + x[0].y) * invr; real.y = static_cast<T>(0.5) * r; real.z = (x[2].y + x[1].z) * invr; real.w = (x[0].z - x[2].x) * invr; } else { T const r = sqrt(T(1) + x[2].z - x[0].x - x[1].y); T const invr = static_cast<T>(0.5) / r; real.x = (x[0].z + x[2].x) * invr; real.y = (x[2].y + x[1].z) * invr; real.z = static_cast<T>(0.5) * r; real.w = (x[1].x - x[0].y) * invr; } tquat<T, P> dual(uninitialize); dual.x = static_cast<T>(0.5) * ( x[0].w * real.w + x[1].w * real.z - x[2].w * real.y); dual.y = static_cast<T>(0.5) * (-x[0].w * real.z + x[1].w * real.w + x[2].w * real.x); dual.z = static_cast<T>(0.5) * ( x[0].w * real.y - x[1].w * real.x + x[2].w * real.w); dual.w = -static_cast<T>(0.5) * ( x[0].w * real.x + x[1].w * real.y + x[2].w * real.z); return tdualquat<T, P>(real, dual); } }//namespace glm