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diff --git a/external/include/glm/detail/func_geometric.inl b/external/include/glm/detail/func_geometric.inl
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+/// @ref core
+/// @file glm/detail/func_geometric.inl
+
+#include "func_exponential.hpp"
+#include "func_common.hpp"
+#include "type_vec2.hpp"
+#include "type_vec4.hpp"
+#include "type_float.hpp"
+
+namespace glm{
+namespace detail
+{
+ template <template <typename, precision> class vecType, typename T, precision P, bool Aligned>
+ struct compute_length
+ {
+ GLM_FUNC_QUALIFIER static T call(vecType<T, P> const & v)
+ {
+ return sqrt(dot(v, v));
+ }
+ };
+
+ template <template <typename, precision> class vecType, typename T, precision P, bool Aligned>
+ struct compute_distance
+ {
+ GLM_FUNC_QUALIFIER static T call(vecType<T, P> const & p0, vecType<T, P> const & p1)
+ {
+ return length(p1 - p0);
+ }
+ };
+
+ template <template <class, precision> class vecType, typename T, precision P, bool Aligned>
+ struct compute_dot{};
+
+ template <typename T, precision P, bool Aligned>
+ struct compute_dot<tvec1, T, P, Aligned>
+ {
+ GLM_FUNC_QUALIFIER static T call(tvec1<T, P> const & a, tvec1<T, P> const & b)
+ {
+ return a.x * b.x;
+ }
+ };
+
+ template <typename T, precision P, bool Aligned>
+ struct compute_dot<tvec2, T, P, Aligned>
+ {
+ GLM_FUNC_QUALIFIER static T call(tvec2<T, P> const & x, tvec2<T, P> const & y)
+ {
+ tvec2<T, P> tmp(x * y);
+ return tmp.x + tmp.y;
+ }
+ };
+
+ template <typename T, precision P, bool Aligned>
+ struct compute_dot<tvec3, T, P, Aligned>
+ {
+ GLM_FUNC_QUALIFIER static T call(tvec3<T, P> const & x, tvec3<T, P> const & y)
+ {
+ tvec3<T, P> tmp(x * y);
+ return tmp.x + tmp.y + tmp.z;
+ }
+ };
+
+ template <typename T, precision P, bool Aligned>
+ struct compute_dot<tvec4, T, P, Aligned>
+ {
+ GLM_FUNC_QUALIFIER static T call(tvec4<T, P> const & x, tvec4<T, P> const & y)
+ {
+ tvec4<T, P> tmp(x * y);
+ return (tmp.x + tmp.y) + (tmp.z + tmp.w);
+ }
+ };
+
+ template <typename T, precision P, bool Aligned>
+ struct compute_cross
+ {
+ GLM_FUNC_QUALIFIER static tvec3<T, P> call(tvec3<T, P> const & x, tvec3<T, P> const & y)
+ {
+ GLM_STATIC_ASSERT(std::numeric_limits<T>::is_iec559, "'cross' accepts only floating-point inputs");
+
+ return tvec3<T, P>(
+ x.y * y.z - y.y * x.z,
+ x.z * y.x - y.z * x.x,
+ x.x * y.y - y.x * x.y);
+ }
+ };
+
+ template <typename T, precision P, template <typename, precision> class vecType, bool Aligned>
+ struct compute_normalize
+ {
+ GLM_FUNC_QUALIFIER static vecType<T, P> call(vecType<T, P> const & v)
+ {
+ GLM_STATIC_ASSERT(std::numeric_limits<T>::is_iec559, "'normalize' accepts only floating-point inputs");
+
+ return v * inversesqrt(dot(v, v));
+ }
+ };
+
+ template <typename T, precision P, template <typename, precision> class vecType, bool Aligned>
+ struct compute_faceforward
+ {
+ GLM_FUNC_QUALIFIER static vecType<T, P> call(vecType<T, P> const & N, vecType<T, P> const & I, vecType<T, P> const & Nref)
+ {
+ GLM_STATIC_ASSERT(std::numeric_limits<T>::is_iec559, "'normalize' accepts only floating-point inputs");
+
+ return dot(Nref, I) < static_cast<T>(0) ? N : -N;
+ }
+ };
+
+ template <typename T, precision P, template <typename, precision> class vecType, bool Aligned>
+ struct compute_reflect
+ {
+ GLM_FUNC_QUALIFIER static vecType<T, P> call(vecType<T, P> const & I, vecType<T, P> const & N)
+ {
+ return I - N * dot(N, I) * static_cast<T>(2);
+ }
+ };
+
+ template <typename T, precision P, template <typename, precision> class vecType, bool Aligned>
+ struct compute_refract
+ {
+ GLM_FUNC_QUALIFIER static vecType<T, P> call(vecType<T, P> const & I, vecType<T, P> const & N, T eta)
+ {
+ T const dotValue(dot(N, I));
+ T const k(static_cast<T>(1) - eta * eta * (static_cast<T>(1) - dotValue * dotValue));
+ return (eta * I - (eta * dotValue + std::sqrt(k)) * N) * static_cast<T>(k >= static_cast<T>(0));
+ }
+ };
+}//namespace detail
+
+ // length
+ template <typename genType>
+ GLM_FUNC_QUALIFIER genType length(genType x)
+ {
+ GLM_STATIC_ASSERT(std::numeric_limits<genType>::is_iec559, "'length' accepts only floating-point inputs");
+
+ return abs(x);
+ }
+
+ template <typename T, precision P, template <typename, precision> class vecType>
+ GLM_FUNC_QUALIFIER T length(vecType<T, P> const & v)
+ {
+ GLM_STATIC_ASSERT(std::numeric_limits<T>::is_iec559, "'length' accepts only floating-point inputs");
+
+ return detail::compute_length<vecType, T, P, detail::is_aligned<P>::value>::call(v);
+ }
+
+ // distance
+ template <typename genType>
+ GLM_FUNC_QUALIFIER genType distance(genType const & p0, genType const & p1)
+ {
+ GLM_STATIC_ASSERT(std::numeric_limits<genType>::is_iec559, "'distance' accepts only floating-point inputs");
+
+ return length(p1 - p0);
+ }
+
+ template <typename T, precision P, template <typename, precision> class vecType>
+ GLM_FUNC_QUALIFIER T distance(vecType<T, P> const & p0, vecType<T, P> const & p1)
+ {
+ return detail::compute_distance<vecType, T, P, detail::is_aligned<P>::value>::call(p0, p1);
+ }
+
+ // dot
+ template <typename T>
+ GLM_FUNC_QUALIFIER T dot(T x, T y)
+ {
+ GLM_STATIC_ASSERT(std::numeric_limits<T>::is_iec559, "'dot' accepts only floating-point inputs");
+ return x * y;
+ }
+
+ template <typename T, precision P, template <typename, precision> class vecType>
+ GLM_FUNC_QUALIFIER T dot(vecType<T, P> const & x, vecType<T, P> const & y)
+ {
+ GLM_STATIC_ASSERT(std::numeric_limits<T>::is_iec559, "'dot' accepts only floating-point inputs");
+ return detail::compute_dot<vecType, T, P, detail::is_aligned<P>::value>::call(x, y);
+ }
+
+ // cross
+ template <typename T, precision P>
+ GLM_FUNC_QUALIFIER tvec3<T, P> cross(tvec3<T, P> const & x, tvec3<T, P> const & y)
+ {
+ return detail::compute_cross<T, P, detail::is_aligned<P>::value>::call(x, y);
+ }
+
+ // normalize
+ template <typename genType>
+ GLM_FUNC_QUALIFIER genType normalize(genType const & x)
+ {
+ GLM_STATIC_ASSERT(std::numeric_limits<genType>::is_iec559, "'normalize' accepts only floating-point inputs");
+
+ return x < genType(0) ? genType(-1) : genType(1);
+ }
+
+ template <typename T, precision P, template <typename, precision> class vecType>
+ GLM_FUNC_QUALIFIER vecType<T, P> normalize(vecType<T, P> const & x)
+ {
+ GLM_STATIC_ASSERT(std::numeric_limits<T>::is_iec559, "'normalize' accepts only floating-point inputs");
+
+ return detail::compute_normalize<T, P, vecType, detail::is_aligned<P>::value>::call(x);
+ }
+
+ // faceforward
+ template <typename genType>
+ GLM_FUNC_QUALIFIER genType faceforward(genType const & N, genType const & I, genType const & Nref)
+ {
+ return dot(Nref, I) < static_cast<genType>(0) ? N : -N;
+ }
+
+ template <typename T, precision P, template <typename, precision> class vecType>
+ GLM_FUNC_QUALIFIER vecType<T, P> faceforward(vecType<T, P> const & N, vecType<T, P> const & I, vecType<T, P> const & Nref)
+ {
+ return detail::compute_faceforward<T, P, vecType, detail::is_aligned<P>::value>::call(N, I, Nref);
+ }
+
+ // reflect
+ template <typename genType>
+ GLM_FUNC_QUALIFIER genType reflect(genType const & I, genType const & N)
+ {
+ return I - N * dot(N, I) * genType(2);
+ }
+
+ template <typename T, precision P, template <typename, precision> class vecType>
+ GLM_FUNC_QUALIFIER vecType<T, P> reflect(vecType<T, P> const & I, vecType<T, P> const & N)
+ {
+ return detail::compute_reflect<T, P, vecType, detail::is_aligned<P>::value>::call(I, N);
+ }
+
+ // refract
+ template <typename genType>
+ GLM_FUNC_QUALIFIER genType refract(genType const & I, genType const & N, genType eta)
+ {
+ GLM_STATIC_ASSERT(std::numeric_limits<genType>::is_iec559, "'refract' accepts only floating-point inputs");
+ genType const dotValue(dot(N, I));
+ genType const k(static_cast<genType>(1) - eta * eta * (static_cast<genType>(1) - dotValue * dotValue));
+ return (eta * I - (eta * dotValue + sqrt(k)) * N) * static_cast<genType>(k >= static_cast<genType>(0));
+ }
+
+ template <typename T, precision P, template <typename, precision> class vecType>
+ GLM_FUNC_QUALIFIER vecType<T, P> refract(vecType<T, P> const & I, vecType<T, P> const & N, T eta)
+ {
+ GLM_STATIC_ASSERT(std::numeric_limits<T>::is_iec559, "'refract' accepts only floating-point inputs");
+ return detail::compute_refract<T, P, vecType, detail::is_aligned<P>::value>::call(I, N, eta);
+ }
+}//namespace glm
+
+#if GLM_ARCH != GLM_ARCH_PURE && GLM_HAS_UNRESTRICTED_UNIONS
+# include "func_geometric_simd.inl"
+#endif