1464 lines
39 KiB
C++
1464 lines
39 KiB
C++
// Copyright (C) 2024 Jérôme "SirLynix" Leclercq (lynix680@gmail.com)
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// This file is part of the "Nazara Engine - Math module"
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// For conditions of distribution and use, see copyright notice in Config.hpp
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#include <Nazara/Core/Algorithm.hpp>
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#include <Nazara/Core/Error.hpp>
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#include <Nazara/Core/Log.hpp>
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#include <Nazara/Math/Config.hpp>
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#include <Nazara/Math/EulerAngles.hpp>
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#include <Nazara/Math/Quaternion.hpp>
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#include <Nazara/Math/Vector2.hpp>
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#include <Nazara/Math/Vector3.hpp>
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#include <Nazara/Math/Vector4.hpp>
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#include <cstring>
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#include <limits>
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#include <sstream>
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#include <stdexcept>
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#include <Nazara/Core/Debug.hpp>
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namespace Nz
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{
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/*!
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* \ingroup math
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* \class Nz::Matrix4
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* \brief Math class that represents a transformation of the four dimensional vector space with the notion of projectivity
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*
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* \remark Matrix4 is said to be "row-major" and affine if last column is made of (0, 0, 0, 1)
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*/
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/*!
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* \brief Constructs a Matrix4 object from its components
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*
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* \param rIJ Matrix components at index(I, J)
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*/
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template<typename T>
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constexpr Matrix4<T>::Matrix4(T r11, T r12, T r13, T r14,
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T r21, T r22, T r23, T r24,
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T r31, T r32, T r33, T r34,
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T r41, T r42, T r43, T r44) :
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m11(r11),
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m12(r12),
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m13(r13),
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m14(r14),
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m21(r21),
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m22(r22),
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m23(r23),
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m24(r24),
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m31(r31),
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m32(r32),
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m33(r33),
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m34(r34),
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m41(r41),
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m42(r42),
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m43(r43),
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m44(r44)
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{
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}
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/*!
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* \brief Constructs a Matrix4 object from an array of sixteen elements
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*
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* \param matrix[16] Matrix components
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*/
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template<typename T>
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constexpr Matrix4<T>::Matrix4(const T matrix[16]) :
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Matrix4(matrix[ 0], matrix[ 1], matrix[ 2], matrix[ 3],
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matrix[ 4], matrix[ 5], matrix[ 6], matrix[ 7],
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matrix[ 8], matrix[ 9], matrix[10], matrix[11],
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matrix[12], matrix[13], matrix[14], matrix[15])
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{
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}
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/*!
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* \brief Constructs a Matrix4 object from another type of Matrix4
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*
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* \param matrix Matrix4 of type U to convert to type T
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*/
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template<typename T>
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template<typename U>
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constexpr Matrix4<T>::Matrix4(const Matrix4<U>& matrix) :
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m11(static_cast<T>(matrix.m11)),
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m12(static_cast<T>(matrix.m12)),
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m13(static_cast<T>(matrix.m13)),
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m14(static_cast<T>(matrix.m14)),
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m21(static_cast<T>(matrix.m21)),
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m22(static_cast<T>(matrix.m22)),
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m23(static_cast<T>(matrix.m23)),
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m24(static_cast<T>(matrix.m24)),
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m31(static_cast<T>(matrix.m31)),
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m32(static_cast<T>(matrix.m32)),
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m33(static_cast<T>(matrix.m33)),
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m34(static_cast<T>(matrix.m34)),
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m41(static_cast<T>(matrix.m41)),
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m42(static_cast<T>(matrix.m42)),
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m43(static_cast<T>(matrix.m43)),
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m44(static_cast<T>(matrix.m44))
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{
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}
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/*!
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* \brief Apply the rotation represented by the quaternion to this matrix
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* \return A reference to this matrix which has been rotated
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*
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* \param rotation Quaternion representing a rotation of space
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*/
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template<typename T>
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constexpr Matrix4<T>& Matrix4<T>::ApplyRotation(const Quaternion<T>& rotation)
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{
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return Concatenate(Matrix4<T>::Rotate(rotation));
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}
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/*!
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* \brief Apply the scale represented by the vector to this matrix
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* \return A reference to this matrix which has been scaled
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*
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* \param scale Vector3 representing the homothety
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*/
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template<typename T>
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constexpr Matrix4<T>& Matrix4<T>::ApplyScale(const Vector3<T>& scale)
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{
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m11 *= scale.x;
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m12 *= scale.x;
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m13 *= scale.x;
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m21 *= scale.y;
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m22 *= scale.y;
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m23 *= scale.y;
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m31 *= scale.z;
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m32 *= scale.z;
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m33 *= scale.z;
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return *this;
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}
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/*!
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* \brief Apply the translation represented by the vector to this matrix
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* \return A reference to this matrix which has been translated
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*
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* \param translation Vector3 representing the translation
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*/
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template<typename T>
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constexpr Matrix4<T>& Matrix4<T>::ApplyTranslation(const Vector3<T>& translation)
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{
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m41 += translation.x;
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m42 += translation.y;
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m43 += translation.z;
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return *this;
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}
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template<typename T>
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constexpr bool Matrix4<T>::ApproxEqual(const Matrix4& mat, T maxDifference) const
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{
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for (unsigned int i = 0; i < 16; ++i)
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if (!NumberEquals((&m11)[i], (&mat.m11)[i], maxDifference))
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return false;
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return true;
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}
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/*!
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* \brief Concatenates this matrix to other one
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* \return A reference to this matrix which is the product with other one
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*
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* \param matrix Matrix to multiply with
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*
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* \remark if NAZARA_MATH_MATRIX4_CHECK_TRANSFORM is defined, will print a message if both matrices are transform matrices (and will call ConcatenateTransform)
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*
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* \see ConcatenateTransform
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*/
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template<typename T>
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constexpr Matrix4<T>& Matrix4<T>::Concatenate(const Matrix4& matrix)
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{
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#if NAZARA_MATH_MATRIX4_CHECK_TRANSFORM
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if (IsTransformMatrix() && matrix.IsTransformMatrix())
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{
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NazaraDebug("Matrix4::Concatenate was called on transform matrices, use Matrix4::ConcatenateTransform");
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return ConcatenateTransform(matrix);
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}
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#endif
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return operator=(Matrix4(
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m11 * matrix.m11 + m12 * matrix.m21 + m13 * matrix.m31 + m14 * matrix.m41,
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m11 * matrix.m12 + m12 * matrix.m22 + m13 * matrix.m32 + m14 * matrix.m42,
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m11 * matrix.m13 + m12 * matrix.m23 + m13 * matrix.m33 + m14 * matrix.m43,
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m11 * matrix.m14 + m12 * matrix.m24 + m13 * matrix.m34 + m14 * matrix.m44,
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m21 * matrix.m11 + m22 * matrix.m21 + m23 * matrix.m31 + m24 * matrix.m41,
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m21 * matrix.m12 + m22 * matrix.m22 + m23 * matrix.m32 + m24 * matrix.m42,
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m21 * matrix.m13 + m22 * matrix.m23 + m23 * matrix.m33 + m24 * matrix.m43,
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m21 * matrix.m14 + m22 * matrix.m24 + m23 * matrix.m34 + m24 * matrix.m44,
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m31 * matrix.m11 + m32 * matrix.m21 + m33 * matrix.m31 + m34 * matrix.m41,
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m31 * matrix.m12 + m32 * matrix.m22 + m33 * matrix.m32 + m34 * matrix.m42,
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m31 * matrix.m13 + m32 * matrix.m23 + m33 * matrix.m33 + m34 * matrix.m43,
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m31 * matrix.m14 + m32 * matrix.m24 + m33 * matrix.m34 + m34 * matrix.m44,
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m41 * matrix.m11 + m42 * matrix.m21 + m43 * matrix.m31 + m44 * matrix.m41,
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m41 * matrix.m12 + m42 * matrix.m22 + m43 * matrix.m32 + m44 * matrix.m42,
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m41 * matrix.m13 + m42 * matrix.m23 + m43 * matrix.m33 + m44 * matrix.m43,
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m41 * matrix.m14 + m42 * matrix.m24 + m43 * matrix.m34 + m44 * matrix.m44
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));
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}
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/*!
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* \brief Concatenates this matrix to other one
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* \return A reference to this matrix which is the product with other one
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*
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* \param matrix Matrix to multiply with
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*
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* \remark if NAZARA_MATH_MATRIX4_CHECK_TRANSFORM is defined and matrices are not transform matrices, a NazaraWarning is produced and Concatenate is called
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*
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* \see Concatenate
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*/
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template<typename T>
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constexpr Matrix4<T>& Matrix4<T>::ConcatenateTransform(const Matrix4& matrix)
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{
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#if NAZARA_MATH_MATRIX4_CHECK_TRANSFORM
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if (!IsTransformMatrix())
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{
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NazaraDebug("Matrix4::ConcatenateTransform first matrix is not a transform matrix");
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return Concatenate(matrix);
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}
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if (!matrix.IsTransformMatrix())
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{
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NazaraDebug("Matrix4::ConcatenateTransform second matrix is not a transform matrix");
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return Concatenate(matrix);
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}
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#endif
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return operator=(Matrix4(
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m11*matrix.m11 + m12*matrix.m21 + m13*matrix.m31,
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m11*matrix.m12 + m12*matrix.m22 + m13*matrix.m32,
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m11*matrix.m13 + m12*matrix.m23 + m13*matrix.m33,
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T(0.0),
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m21*matrix.m11 + m22*matrix.m21 + m23*matrix.m31,
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m21*matrix.m12 + m22*matrix.m22 + m23*matrix.m32,
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m21*matrix.m13 + m22*matrix.m23 + m23*matrix.m33,
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T(0.0),
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m31*matrix.m11 + m32*matrix.m21 + m33*matrix.m31,
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m31*matrix.m12 + m32*matrix.m22 + m33*matrix.m32,
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m31*matrix.m13 + m32*matrix.m23 + m33*matrix.m33,
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T(0.0),
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m41*matrix.m11 + m42*matrix.m21 + m43*matrix.m31 + matrix.m41,
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m41*matrix.m12 + m42*matrix.m22 + m43*matrix.m32 + matrix.m42,
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m41*matrix.m13 + m42*matrix.m23 + m43*matrix.m33 + matrix.m43,
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T(1.0)
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));
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}
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/*!
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* \brief Gets the ith column of the matrix
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* \return Vector4 which is the transformation of this axis
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*
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* \param column Index of the column you want
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*/
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template<typename T>
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constexpr Vector4<T> Matrix4<T>::GetColumn(std::size_t column) const
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{
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NazaraAssert(column < 4, "column index out of range");
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const T* ptr = &m11 + column * 4;
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return Vector4<T>(ptr[0], ptr[1], ptr[2], ptr[3]);
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}
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/*!
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* \brief Computes the determinant of this matrix
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* \return The value of the determinant
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*
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* \remark if NAZARA_MATH_MATRIX4_CHECK_AFFINE is defined, GetDeterminantTransform is called
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*
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* \see GetDeterminantTransform
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*/
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template<typename T>
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constexpr T Matrix4<T>::GetDeterminant() const
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{
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#if NAZARA_MATH_MATRIX4_CHECK_TRANSFORM
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if (IsTransformMatrix())
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{
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NazaraDebug("Matrix4::GetDeterminant was called on a transform matrix, use Matrix4::GetDeterminantTransform");
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return GetDeterminantTransform();
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}
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#endif
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T A = m22*(m33*m44 - m43*m34) - m32*(m23*m44 - m43*m24) + m42*(m23*m34 - m33*m24);
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T B = m12*(m33*m44 - m43*m34) - m32*(m13*m44 - m43*m14) + m42*(m13*m34 - m33*m14);
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T C = m12*(m23*m44 - m43*m24) - m22*(m13*m44 - m43*m14) + m42*(m13*m24 - m23*m14);
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T D = m12*(m23*m34 - m33*m24) - m22*(m13*m34 - m33*m14) + m32*(m13*m24 - m23*m14);
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return m11*A - m21*B + m31*C - m41*D;
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}
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/*!
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* \brief Computes the determinant of this matrix
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* \return The value of the determinant
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*
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* \remark if NAZARA_DEBUG is defined and matrix is not affine, a NazaraWarning is produced and GetDeterminant is called
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*
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* \see GetDeterminant
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*/
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template<typename T>
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constexpr T Matrix4<T>::GetDeterminantTransform() const
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{
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#if NAZARA_MATH_MATRIX4_CHECK_TRANSFORM
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if (!IsTransformMatrix())
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{
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NazaraDebug("matrix is not a transform matrix");
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return GetDeterminant();
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}
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#endif
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T A = m22*m33 - m32*m23;
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T B = m12*m33 - m32*m13;
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T C = m12*m23 - m22*m13;
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return m11*A - m21*B + m31*C;
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}
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/*!
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* \brief Gets the inverse of this matrix
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* \return true if matrix can be inverted
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*
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* \param dest Matrix to put the result
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*
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* \remark You can call this method on the same object
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* \remark if NAZARA_MATH_MATRIX4_CHECK_AFFINE is defined, GetInverseAffine is called
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* \remark if NAZARA_DEBUG is defined, a NazaraError is produced if dest is null and false is returned
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*
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* \see GetInverseAffine
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*/
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template<typename T>
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constexpr bool Matrix4<T>::GetInverse(Matrix4* dest) const
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{
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NazaraAssert(dest, "destination matrix must be valid");
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#if NAZARA_MATH_MATRIX4_CHECK_TRANSFORM
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if (IsTransformMatrix())
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{
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NazaraDebug("Matrix4::GetInverse was called on a transform matrix, use Matrix4::GetInverseTransform");
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return GetInverseTransform(dest);
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}
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#endif
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T det = GetDeterminant();
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if (det == T(0.0))
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return false;
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// http://stackoverflow.com/questions/1148309/inverting-a-4x4-matrix
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T inv[16];
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inv[0] = m22 * m33 * m44 -
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m22 * m34 * m43 -
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m32 * m23 * m44 +
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m32 * m24 * m43 +
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m42 * m23 * m34 -
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m42 * m24 * m33;
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inv[1] = -m12 * m33 * m44 +
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m12 * m34 * m43 +
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m32 * m13 * m44 -
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m32 * m14 * m43 -
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m42 * m13 * m34 +
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m42 * m14 * m33;
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inv[2] = m12 * m23 * m44 -
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m12 * m24 * m43 -
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m22 * m13 * m44 +
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m22 * m14 * m43 +
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m42 * m13 * m24 -
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m42 * m14 * m23;
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inv[3] = -m12 * m23 * m34 +
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m12 * m24 * m33 +
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m22 * m13 * m34 -
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m22 * m14 * m33 -
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m32 * m13 * m24 +
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m32 * m14 * m23;
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inv[4] = -m21 * m33 * m44 +
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m21 * m34 * m43 +
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m31 * m23 * m44 -
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m31 * m24 * m43 -
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m41 * m23 * m34 +
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m41 * m24 * m33;
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inv[5] = m11 * m33 * m44 -
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m11 * m34 * m43 -
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m31 * m13 * m44 +
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m31 * m14 * m43 +
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m41 * m13 * m34 -
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m41 * m14 * m33;
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inv[6] = -m11 * m23 * m44 +
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m11 * m24 * m43 +
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m21 * m13 * m44 -
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m21 * m14 * m43 -
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m41 * m13 * m24 +
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m41 * m14 * m23;
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inv[7] = m11 * m23 * m34 -
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m11 * m24 * m33 -
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m21 * m13 * m34 +
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m21 * m14 * m33 +
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m31 * m13 * m24 -
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m31 * m14 * m23;
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inv[8] = m21 * m32 * m44 -
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m21 * m34 * m42 -
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m31 * m22 * m44 +
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m31 * m24 * m42 +
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m41 * m22 * m34 -
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m41 * m24 * m32;
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inv[9] = -m11 * m32 * m44 +
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m11 * m34 * m42 +
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m31 * m12 * m44 -
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m31 * m14 * m42 -
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m41 * m12 * m34 +
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m41 * m14 * m32;
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inv[10] = m11 * m22 * m44 -
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m11 * m24 * m42 -
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m21 * m12 * m44 +
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m21 * m14 * m42 +
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m41 * m12 * m24 -
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m41 * m14 * m22;
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inv[11] = -m11 * m22 * m34 +
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m11 * m24 * m32 +
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m21 * m12 * m34 -
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m21 * m14 * m32 -
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m31 * m12 * m24 +
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m31 * m14 * m22;
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inv[12] = -m21 * m32 * m43 +
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m21 * m33 * m42 +
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m31 * m22 * m43 -
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m31 * m23 * m42 -
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m41 * m22 * m33 +
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m41 * m23 * m32;
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inv[13] = m11 * m32 * m43 -
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m11 * m33 * m42 -
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m31 * m12 * m43 +
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m31 * m13 * m42 +
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m41 * m12 * m33 -
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m41 * m13 * m32;
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inv[14] = -m11 * m22 * m43 +
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m11 * m23 * m42 +
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m21 * m12 * m43 -
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m21 * m13 * m42 -
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m41 * m12 * m23 +
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m41 * m13 * m22;
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inv[15] = m11 * m22 * m33 -
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m11 * m23 * m32 -
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m21 * m12 * m33 +
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m21 * m13 * m32 +
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m31 * m12 * m23 -
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m31 * m13 * m22;
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T invDet = T(1.0) / det;
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for (unsigned int i = 0; i < 16; ++i)
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inv[i] *= invDet;
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*dest = inv;
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|
return true;
|
|
}
|
|
|
|
/*!
|
|
* \brief Gets the inverse of this matrix
|
|
* \return true if matrix can be inverted
|
|
*
|
|
* \param dest Matrix to put the result
|
|
*
|
|
* \remark You can call this method on the same object
|
|
* \remark if NAZARA_DEBUG is defined and matrix is not affine, a NazaraWarning is produced and GetInverse is called
|
|
* \remark if NAZARA_DEBUG is defined, a NazaraError is produced if dest is null and false is returned
|
|
*
|
|
* \see GetInverse
|
|
*/
|
|
template<typename T>
|
|
constexpr bool Matrix4<T>::GetInverseTransform(Matrix4* dest) const
|
|
{
|
|
NazaraAssert(dest, "destination matrix must be valid");
|
|
|
|
#if NAZARA_MATH_MATRIX4_CHECK_TRANSFORM
|
|
if (!IsTransformMatrix())
|
|
{
|
|
NazaraDebug("matrix is not a transform matrix");
|
|
return GetInverse(dest);
|
|
}
|
|
#endif
|
|
|
|
T det = GetDeterminantTransform();
|
|
if (det == T(0.0))
|
|
return false;
|
|
|
|
|
|
// http://stackoverflow.com/questions/1148309/inverting-a-4x4-matrix
|
|
T inv[16];
|
|
inv[0] = m22 * m33 -
|
|
m32 * m23;
|
|
|
|
inv[1] = -m12 * m33 +
|
|
m32 * m13;
|
|
|
|
inv[2] = m12 * m23 -
|
|
m22 * m13;
|
|
|
|
inv[3] = T(0.0);
|
|
|
|
inv[4] = -m21 * m33 +
|
|
m31 * m23;
|
|
|
|
inv[5] = m11 * m33 -
|
|
m31 * m13;
|
|
|
|
inv[6] = -m11 * m23 +
|
|
m21 * m13;
|
|
|
|
inv[7] = T(0.0);
|
|
|
|
inv[8] = m21 * m32 -
|
|
m31 * m22;
|
|
|
|
inv[9] = -m11 * m32 +
|
|
m31 * m12;
|
|
|
|
inv[10] = m11 * m22 -
|
|
m21 * m12;
|
|
|
|
inv[11] = T(0.0);
|
|
|
|
inv[12] = -m21 * m32 * m43 +
|
|
m21 * m33 * m42 +
|
|
m31 * m22 * m43 -
|
|
m31 * m23 * m42 -
|
|
m41 * m22 * m33 +
|
|
m41 * m23 * m32;
|
|
|
|
inv[13] = m11 * m32 * m43 -
|
|
m11 * m33 * m42 -
|
|
m31 * m12 * m43 +
|
|
m31 * m13 * m42 +
|
|
m41 * m12 * m33 -
|
|
m41 * m13 * m32;
|
|
|
|
inv[14] = -m11 * m22 * m43 +
|
|
m11 * m23 * m42 +
|
|
m21 * m12 * m43 -
|
|
m21 * m13 * m42 -
|
|
m41 * m12 * m23 +
|
|
m41 * m13 * m22;
|
|
|
|
T invDet = T(1.0) / det;
|
|
for (unsigned int i = 0; i < 16; ++i)
|
|
inv[i] *= invDet;
|
|
|
|
inv[15] = T(1.0);
|
|
|
|
*dest = inv;
|
|
return true;
|
|
}
|
|
|
|
/*!
|
|
* \brief Gets the rotation from this matrix
|
|
* \return Quaternion which is the representation of the rotation in this matrix
|
|
*/
|
|
template<typename T>
|
|
Quaternion<T> Matrix4<T>::GetRotation() const
|
|
{
|
|
// http://www.euclideanspace.com/maths/geometry/rotations/conversions/matrixToQuaternion/
|
|
Quaternion<T> quat;
|
|
|
|
T trace = m11 + m22 + m33;
|
|
if (trace > T(0.0))
|
|
{
|
|
T s = T(0.5) / std::sqrt(trace + T(1.0));
|
|
quat.w = T(0.25) / s;
|
|
quat.x = (m23 - m32) * s;
|
|
quat.y = (m31 - m13) * s;
|
|
quat.z = (m12 - m21) * s;
|
|
}
|
|
else
|
|
{
|
|
if (m11 > m22 && m11 > m33)
|
|
{
|
|
T s = T(2.0) * std::sqrt(T(1.0) + m11 - m22 - m33);
|
|
|
|
quat.w = (m23 - m32) / s;
|
|
quat.x = T(0.25) * s;
|
|
quat.y = (m21 + m12) / s;
|
|
quat.z = (m31 + m13) / s;
|
|
}
|
|
else if (m22 > m33)
|
|
{
|
|
T s = T(2.0) * std::sqrt(T(1.0) + m22 - m11 - m33);
|
|
|
|
quat.w = (m31 - m13) / s;
|
|
quat.x = (m21 + m12) / s;
|
|
quat.y = T(0.25) * s;
|
|
quat.z = (m32 + m23) / s;
|
|
}
|
|
else
|
|
{
|
|
T s = T(2.0) * std::sqrt(T(1.0) + m33 - m11 - m22);
|
|
|
|
quat.w = (m12 - m21) / s;
|
|
quat.x = (m31 + m13) / s;
|
|
quat.y = (m32 + m23) / s;
|
|
quat.z = T(0.25) * s;
|
|
}
|
|
}
|
|
|
|
return quat;
|
|
}
|
|
|
|
/*!
|
|
* \brief Gets the ith row of the matrix
|
|
* \return Vector4 which is the ith row of the matrix
|
|
*
|
|
* \param row Index of the row you want
|
|
*
|
|
* \remark Produce a NazaraError if you try to access index greater than 3 with NAZARA_MATH_SAFE defined
|
|
* \throw std::out_of_range if NAZARA_MATH_SAFE is defined and if you try to access index greater than 3
|
|
*/
|
|
template<typename T>
|
|
constexpr Vector4<T> Matrix4<T>::GetRow(std::size_t row) const
|
|
{
|
|
NazaraAssert(row < 4, "row index out of range");
|
|
|
|
const T* ptr = &m11;
|
|
return Vector4<T>(ptr[row], ptr[row+4], ptr[row+8], ptr[row+12]);
|
|
}
|
|
|
|
/*!
|
|
* \brief Gets the scale from this matrix
|
|
* \return Vector3 which is the representation of the scale in this matrix
|
|
*
|
|
* \see GetSquaredScale
|
|
*/
|
|
template<typename T>
|
|
constexpr Vector3<T> Matrix4<T>::GetScale() const
|
|
{
|
|
Vector3<T> squaredScale = GetSquaredScale();
|
|
return Vector3<T>(std::sqrt(squaredScale.x), std::sqrt(squaredScale.y), std::sqrt(squaredScale.z));
|
|
}
|
|
|
|
/*!
|
|
* \brief Gets the squared scale from this matrix
|
|
* \return Vector3 which is the representation of the squared scale in this matrix
|
|
*
|
|
* \see GetScale
|
|
*/
|
|
template<typename T>
|
|
constexpr Vector3<T> Matrix4<T>::GetSquaredScale() const
|
|
{
|
|
return Vector3<T>(m11 * m11 + m12 * m12 + m13 * m13,
|
|
m21 * m21 + m22 * m22 + m23 * m23,
|
|
m31 * m31 + m32 * m32 + m33 * m33);
|
|
}
|
|
|
|
/*!
|
|
* \brief Gets the translation from this matrix
|
|
* \return Vector3 which is the representation of the translation in this matrix
|
|
*/
|
|
template<typename T>
|
|
constexpr Vector3<T> Matrix4<T>::GetTranslation() const
|
|
{
|
|
return Vector3<T>(m41, m42, m43);
|
|
}
|
|
|
|
/*!
|
|
* \brief Gets the transposed of this matrix
|
|
*
|
|
* \param dest Matrix to put the result
|
|
*
|
|
* \remark You can call this method on the same object
|
|
* \remark if NAZARA_DEBUG is defined, a NazaraError is produced if dest is null and dest is not changed
|
|
*
|
|
* \see Transpose
|
|
*/
|
|
template<typename T>
|
|
constexpr void Matrix4<T>::GetTransposed(Matrix4* dest) const
|
|
{
|
|
#ifdef NAZARA_DEBUG
|
|
if (!dest)
|
|
{
|
|
NazaraError("destination matrix must be valid");
|
|
return;
|
|
}
|
|
#endif
|
|
|
|
(*dest) = Matrix4f(
|
|
m11, m21, m31, m41,
|
|
m12, m22, m32, m42,
|
|
m13, m23, m33, m43,
|
|
m14, m24, m34, m44
|
|
);
|
|
}
|
|
|
|
/*!
|
|
* \brief Checks whetever matrix has negative scale
|
|
* \return true if determinant is negative
|
|
*
|
|
* \see GetDeterminant
|
|
*/
|
|
template<typename T>
|
|
constexpr bool Matrix4<T>::HasNegativeScale() const
|
|
{
|
|
return GetDeterminant() < T(0.0);
|
|
}
|
|
|
|
/*!
|
|
* \brief Checks whetever matrix has scale
|
|
* \return true if determinant has scale
|
|
*
|
|
* \see HasNegativeScale
|
|
*/
|
|
template<typename T>
|
|
constexpr bool Matrix4<T>::HasScale() const
|
|
{
|
|
T t = m11*m11 + m21*m21 + m31*m31;
|
|
if (!NumberEquals(t, T(1.0)))
|
|
return true;
|
|
|
|
t = m12*m12 + m22*m22 + m32*m32;
|
|
if (!NumberEquals(t, T(1.0)))
|
|
return true;
|
|
|
|
t = m13*m13 + m23*m23 + m33*m33;
|
|
if (!NumberEquals(t, T(1.0)))
|
|
return true;
|
|
|
|
return false;
|
|
}
|
|
|
|
/*!
|
|
* \brief Inverts this matrix
|
|
* \return A reference to this matrix inverted
|
|
*
|
|
* \param succeeded Optional argument to know if matrix has been successfully inverted
|
|
*
|
|
* \see InverseTransform
|
|
*/
|
|
template<typename T>
|
|
constexpr Matrix4<T>& Matrix4<T>::Inverse(bool* succeeded)
|
|
{
|
|
bool result = GetInverse(this);
|
|
if (succeeded)
|
|
*succeeded = result;
|
|
|
|
return *this;
|
|
}
|
|
|
|
/*!
|
|
* \brief Inverts this matrix
|
|
* \return A reference to this matrix inverted
|
|
*
|
|
* \param succeeded Optional argument to know if matrix has been successfully inverted
|
|
*
|
|
* \see Inverse
|
|
*/
|
|
template<typename T>
|
|
constexpr Matrix4<T>& Matrix4<T>::InverseTransform(bool* succeeded)
|
|
{
|
|
bool result = GetInverseTransform(this);
|
|
if (succeeded)
|
|
*succeeded = result;
|
|
|
|
return *this;
|
|
}
|
|
|
|
/*!
|
|
* \brief Checks whether the matrix is affine
|
|
* \return true if matrix is affine
|
|
*/
|
|
template<typename T>
|
|
constexpr bool Matrix4<T>::IsTransformMatrix() const
|
|
{
|
|
return NumberEquals(m14, T(0.0)) && NumberEquals(m24, T(0.0)) && NumberEquals(m34, T(0.0)) && NumberEquals(m44, T(1.0));
|
|
}
|
|
|
|
/*!
|
|
* \brief Checks whether the matrix is identity
|
|
* \return true if matrix is identity
|
|
*/
|
|
template<typename T>
|
|
constexpr bool Matrix4<T>::IsIdentity() const
|
|
{
|
|
return (NumberEquals(m11, T(1.0)) && NumberEquals(m12, T(0.0)) && NumberEquals(m13, T(0.0)) && NumberEquals(m14, T(0.0)) &&
|
|
NumberEquals(m21, T(0.0)) && NumberEquals(m22, T(1.0)) && NumberEquals(m23, T(0.0)) && NumberEquals(m24, T(0.0)) &&
|
|
NumberEquals(m31, T(0.0)) && NumberEquals(m32, T(0.0)) && NumberEquals(m33, T(1.0)) && NumberEquals(m34, T(0.0)) &&
|
|
NumberEquals(m41, T(0.0)) && NumberEquals(m42, T(0.0)) && NumberEquals(m43, T(0.0)) && NumberEquals(m44, T(1.0)));
|
|
}
|
|
|
|
/*!
|
|
* \brief Sets the components of the matrix from a quaternion
|
|
* \return A reference to this matrix which is the rotation of the quaternion
|
|
*
|
|
* \param rotation Quaternion representing a rotation of space
|
|
*
|
|
* \remark 3rd column and row are unchanged. Scale is removed.
|
|
*/
|
|
template<typename T>
|
|
constexpr Matrix4<T>& Matrix4<T>::SetRotation(const Quaternion<T>& rotation)
|
|
{
|
|
T qw = rotation.w;
|
|
T qx = rotation.x;
|
|
T qy = rotation.y;
|
|
T qz = rotation.z;
|
|
|
|
T qx2 = qx * qx;
|
|
T qy2 = qy * qy;
|
|
T qz2 = qz * qz;
|
|
|
|
m11 = T(1.0) - T(2.0) * qy2 - T(2.0) * qz2;
|
|
m21 = T(2.0) * qx * qy - T(2.0) * qz * qw;
|
|
m31 = T(2.0) * qx * qz + T(2.0) * qy * qw;
|
|
|
|
m12 = T(2.0) * qx * qy + T(2.0) * qz * qw;
|
|
m22 = T(1.0) - T(2.0) * qx2 - T(2.0) * qz2;
|
|
m32 = T(2.0) * qy * qz - T(2.0) * qx * qw;
|
|
|
|
m13 = T(2.0) * qx * qz - T(2.0) * qy * qw;
|
|
m23 = T(2.0) * qy * qz + T(2.0) * qx * qw;
|
|
m33 = T(1.0) - T(2.0) * qx2 - T(2.0) * qy2;
|
|
|
|
return *this;
|
|
}
|
|
|
|
/*!
|
|
* \brief Sets the components of the matrix from a scale
|
|
* \return A reference to this matrix which is the scale of the Vector3
|
|
*
|
|
* \param scale Vector3 representing the homothety
|
|
*
|
|
* \remark Components are unchanged, except the three first on the diagonal
|
|
*/
|
|
template<typename T>
|
|
constexpr Matrix4<T>& Matrix4<T>::SetScale(const Vector3<T>& scale)
|
|
{
|
|
m11 = scale.x;
|
|
m22 = scale.y;
|
|
m33 = scale.z;
|
|
|
|
return *this;
|
|
}
|
|
|
|
/*!
|
|
* \brief Sets the components of the matrix from a translation
|
|
* \return A reference to this matrix which is the translation of the Vector3
|
|
*
|
|
* \param translation Vector3 representing the translation
|
|
*
|
|
* \remark Components are unchanged, except the three first on the third row
|
|
*/
|
|
template<typename T>
|
|
constexpr Matrix4<T>& Matrix4<T>::SetTranslation(const Vector3<T>& translation)
|
|
{
|
|
m41 = translation.x;
|
|
m42 = translation.y;
|
|
m43 = translation.z;
|
|
|
|
return *this;
|
|
}
|
|
|
|
/*!
|
|
* \brief Gives a string representation
|
|
* \return A string representation of the object: "Matrix4(m11, m12, m13, m14,\n ...)"
|
|
*/
|
|
|
|
template<typename T>
|
|
std::string Matrix4<T>::ToString() const
|
|
{
|
|
std::ostringstream ss;
|
|
ss << *this;
|
|
|
|
return ss.str();
|
|
}
|
|
|
|
/*!
|
|
* \brief Transforms the Vector2 and two components by the matrix
|
|
* \return Vector2 transformed by the matrix
|
|
*
|
|
* \param vector To transform
|
|
* \param z Z Component of the imaginary Vector4
|
|
* \param w W Component of the imaginary Vector4
|
|
*/
|
|
template<typename T>
|
|
constexpr Vector2<T> Matrix4<T>::Transform(const Vector2<T>& vector, T z, T w) const
|
|
{
|
|
return Vector2<T>(m11 * vector.x + m21 * vector.y + m31 * z + m41 * w,
|
|
m12 * vector.x + m22 * vector.y + m32 * z + m42 * w);
|
|
}
|
|
|
|
/*!
|
|
* \brief Transforms the Vector3 and one component by the matrix
|
|
* \return Vector3 transformed by the matrix
|
|
*
|
|
* \param vector To transform
|
|
* \param w W Component of the imaginary Vector4
|
|
*/
|
|
template<typename T>
|
|
constexpr Vector3<T> Matrix4<T>::Transform(const Vector3<T>& vector, T w) const
|
|
{
|
|
return Vector3<T>(m11 * vector.x + m21 * vector.y + m31 * vector.z + m41 * w,
|
|
m12 * vector.x + m22 * vector.y + m32 * vector.z + m42 * w,
|
|
m13 * vector.x + m23 * vector.y + m33 * vector.z + m43 * w);
|
|
}
|
|
|
|
/*!
|
|
* \brief Transforms the Vector4 by the matrix
|
|
* \return Vector4 transformed by the matrix
|
|
*
|
|
* \param vector To transform
|
|
*/
|
|
template<typename T>
|
|
constexpr Vector4<T> Matrix4<T>::Transform(const Vector4<T>& vector) const
|
|
{
|
|
return Vector4<T>(m11 * vector.x + m21 * vector.y + m31 * vector.z + m41 * vector.w,
|
|
m12 * vector.x + m22 * vector.y + m32 * vector.z + m42 * vector.w,
|
|
m13 * vector.x + m23 * vector.y + m33 * vector.z + m43 * vector.w,
|
|
m14 * vector.x + m24 * vector.y + m34 * vector.z + m44 * vector.w);
|
|
}
|
|
|
|
/*!
|
|
* \brief Transposes the matrix
|
|
* \return A reference to this matrix transposed
|
|
*
|
|
* \see GetTransposed
|
|
*/
|
|
template<typename T>
|
|
constexpr Matrix4<T>& Matrix4<T>::Transpose()
|
|
{
|
|
std::swap(m12, m21);
|
|
std::swap(m13, m31);
|
|
std::swap(m14, m41);
|
|
std::swap(m23, m32);
|
|
std::swap(m24, m42);
|
|
std::swap(m34, m43);
|
|
|
|
return *this;
|
|
}
|
|
|
|
/*!
|
|
* \brief Gets the component (x, y) of the matrix
|
|
* \return A reference to the component (x, y)
|
|
*
|
|
* \remark x and y must both be comprised in range [0,4[
|
|
*/
|
|
template<typename T>
|
|
constexpr T& Matrix4<T>::operator()(std::size_t x, std::size_t y)
|
|
{
|
|
NazaraAssert(x <= 3, "index out of range");
|
|
NazaraAssert(y <= 3, "index out of range");
|
|
|
|
return (&m11)[y*4 + x];
|
|
}
|
|
|
|
/*!
|
|
* \brief Gets the component (x, y) of the matrix
|
|
* \return The value of the component (x, y)
|
|
*
|
|
* \remark x and y must both be comprised in range [0,4[
|
|
*/
|
|
template<typename T>
|
|
constexpr const T& Matrix4<T>::operator()(std::size_t x, std::size_t y) const
|
|
{
|
|
NazaraAssert(x <= 3, "index out of range");
|
|
NazaraAssert(y <= 3, "index out of range");
|
|
|
|
return (&m11)[y*4+x];
|
|
}
|
|
|
|
/*!
|
|
* \brief Gets the i-th component of the matrix
|
|
* \return The value of the component (i)
|
|
*
|
|
* \remark i must be comprised in range [0,16[
|
|
*/
|
|
template<typename T>
|
|
constexpr T& Matrix4<T>::operator[](std::size_t i)
|
|
{
|
|
NazaraAssert(i <= 16, "index out of range");
|
|
|
|
return (&m11)[i];
|
|
}
|
|
|
|
/*!
|
|
* \brief Gets the i-th component of the matrix
|
|
* \return The value of the component (i)
|
|
*
|
|
* \remark i must be comprised in range [0,16[
|
|
*/
|
|
template<typename T>
|
|
constexpr const T& Matrix4<T>::operator[](std::size_t i) const
|
|
{
|
|
NazaraAssert(i <= 16, "index out of range");
|
|
|
|
return (&m11)[i];
|
|
}
|
|
|
|
/*!
|
|
* \brief Multiplies the components of the matrix with other matrix
|
|
* \return A matrix where components are the product of this matrix and the other one according to matrix product
|
|
*
|
|
* \param matrix The other matrix to multiply components with
|
|
*/
|
|
template<typename T>
|
|
constexpr Matrix4<T> Matrix4<T>::operator*(const Matrix4& matrix) const
|
|
{
|
|
Matrix4 result(*this);
|
|
return result.Concatenate(matrix);
|
|
}
|
|
|
|
/*!
|
|
* \brief Multiplies the components of the matrix with a vector
|
|
* \return A vector transposed by this matrix
|
|
*
|
|
* \param vector The vector to multiply the matrix with
|
|
*/
|
|
template<typename T>
|
|
constexpr Vector2<T> Matrix4<T>::operator*(const Vector2<T>& vector) const
|
|
{
|
|
return Transform(vector);
|
|
}
|
|
|
|
/*!
|
|
* \brief Multiplies the components of the matrix with a vector
|
|
* \return A vector transposed by this matrix
|
|
*
|
|
* \param vector The vector to multiply the matrix with
|
|
*/
|
|
template<typename T>
|
|
constexpr Vector3<T> Matrix4<T>::operator*(const Vector3<T>& vector) const
|
|
{
|
|
return Transform(vector);
|
|
}
|
|
|
|
/*!
|
|
* \brief Multiplies the components of the matrix with a vector
|
|
* \return A vector transposed by this matrix
|
|
*
|
|
* \param vector The vector to multiply the matrix with
|
|
*/
|
|
template<typename T>
|
|
constexpr Vector4<T> Matrix4<T>::operator*(const Vector4<T>& vector) const
|
|
{
|
|
return Transform(vector);
|
|
}
|
|
|
|
/*!
|
|
* \brief Multiplies the components of the matrix with a scalar
|
|
* \return A Matrix4 where components are the product of matrix'components and the scalar
|
|
*
|
|
* \param scalar The scalar to multiply the matrix'components with
|
|
*/
|
|
template<typename T>
|
|
constexpr Matrix4<T> Matrix4<T>::operator*(T scalar) const
|
|
{
|
|
Matrix4 mat;
|
|
for (unsigned int i = 0; i < 16; ++i)
|
|
mat[i] = (&m11)[i] * scalar;
|
|
|
|
return mat;
|
|
}
|
|
|
|
/*!
|
|
* \brief Multiplies this matrix with another one
|
|
* \return A reference to this matrix which is the product with the other one
|
|
*
|
|
* \param matrix The matrix to multiply with
|
|
*/
|
|
template<typename T>
|
|
constexpr Matrix4<T>& Matrix4<T>::operator*=(const Matrix4& matrix)
|
|
{
|
|
Concatenate(matrix);
|
|
|
|
return *this;
|
|
}
|
|
|
|
/*!
|
|
* \brief Multiplies the components of the matrix with a scalar
|
|
* \return A reference to this matrix where components are the product with the scalar
|
|
*
|
|
* \param scalar The scalar to multiply with
|
|
*/
|
|
template<typename T>
|
|
constexpr Matrix4<T>& Matrix4<T>::operator*=(T scalar)
|
|
{
|
|
for (unsigned int i = 0; i < 16; ++i)
|
|
(&m11)[i] *= scalar;
|
|
|
|
return *this;
|
|
}
|
|
|
|
/*!
|
|
* \brief Compares the matrix to other one
|
|
* \return true if the matrices are the same
|
|
*
|
|
* \param mat Other matrix to compare with
|
|
*/
|
|
template<typename T>
|
|
constexpr bool Matrix4<T>::operator==(const Matrix4& mat) const
|
|
{
|
|
for (unsigned int i = 0; i < 16; ++i)
|
|
if ((&m11)[i] != (&mat.m11)[i])
|
|
return false;
|
|
|
|
return true;
|
|
}
|
|
|
|
/*!
|
|
* \brief Compares the matrix to other one
|
|
* \return false if the matrices are the same
|
|
*
|
|
* \param mat Other matrix to compare with
|
|
*/
|
|
template<typename T>
|
|
constexpr bool Matrix4<T>::operator!=(const Matrix4& mat) const
|
|
{
|
|
return !operator==(mat);
|
|
}
|
|
|
|
/*!
|
|
* \brief Shorthand for the concatenation of two matrices
|
|
* \return A Matrix4 which is the product of two
|
|
*
|
|
* \param left Left-hand side matrix
|
|
* \param right Right-hand side matrix
|
|
*
|
|
* \see Concatenate
|
|
*/
|
|
template<typename T>
|
|
constexpr bool Matrix4<T>::ApproxEqual(const Matrix4& lhs, const Matrix4& rhs, T maxDifference)
|
|
{
|
|
return lhs.ApproxEqual(rhs, maxDifference);
|
|
}
|
|
|
|
template<typename T>
|
|
constexpr Matrix4<T> Matrix4<T>::Concatenate(const Matrix4& left, const Matrix4& right)
|
|
{
|
|
Matrix4 matrix(left); // Copy of left-hand side matrix
|
|
matrix.Concatenate(right); // Concatenation with right-hand side
|
|
|
|
return matrix;
|
|
}
|
|
|
|
/*!
|
|
* \brief Shorthand for the concatenation of two affine matrices
|
|
* \return A Matrix4 which is the product of two
|
|
*
|
|
* \param left Left-hand side matrix
|
|
* \param right Right-hand side matrix
|
|
*
|
|
* \see ConcatenateTransform
|
|
*/
|
|
template<typename T>
|
|
constexpr Matrix4<T> Matrix4<T>::ConcatenateTransform(const Matrix4& left, const Matrix4& right)
|
|
{
|
|
Matrix4 matrix(left); // Copy of left-hand side matrix
|
|
matrix.ConcatenateTransform(right); // Affine concatenation with right-hand side
|
|
|
|
return matrix;
|
|
}
|
|
|
|
/*!
|
|
* \brief Shorthand for the identity matrix
|
|
* \return A Matrix4 which is the identity matrix
|
|
*/
|
|
template<typename T>
|
|
constexpr Matrix4<T> Matrix4<T>::Identity()
|
|
{
|
|
return Matrix4(
|
|
T(1.0), T(0.0), T(0.0), T(0.0),
|
|
T(0.0), T(1.0), T(0.0), T(0.0),
|
|
T(0.0), T(0.0), T(1.0), T(0.0),
|
|
T(0.0), T(0.0), T(0.0), T(1.0)
|
|
);
|
|
}
|
|
|
|
/*!
|
|
* \brief Shorthand for the 'look at' matrix
|
|
* \return A Matrix4 which is the 'look at' matrix
|
|
*
|
|
* \param eye Position of the camera
|
|
* \param target Position of the target of the camera
|
|
* \param up Direction of up vector according to the orientation of camera
|
|
*/
|
|
template<typename T>
|
|
constexpr Matrix4<T> Matrix4<T>::LookAt(const Vector3<T>& eye, const Vector3<T>& target, const Vector3<T>& up)
|
|
{
|
|
Vector3<T> f = Vector3<T>::Normalize(target - eye);
|
|
Vector3<T> s = Vector3<T>::Normalize(f.CrossProduct(up));
|
|
Vector3<T> u = s.CrossProduct(f);
|
|
|
|
return Matrix4(
|
|
s.x, u.x, -f.x, T(0.0),
|
|
s.y, u.y, -f.y, T(0.0),
|
|
s.z, u.z, -f.z, T(0.0),
|
|
-s.DotProduct(eye), -u.DotProduct(eye), f.DotProduct(eye), T(1.0)
|
|
);
|
|
}
|
|
|
|
/*!
|
|
* \brief Shorthand for the 'orthographic' matrix
|
|
* \return A Matrix4 which is the 'orthographic' matrix
|
|
*
|
|
* \param left Distance between center and left
|
|
* \param right Distance between center and right
|
|
* \param top Distance between center and top
|
|
* \param bottom Distance between center and bottom
|
|
* \param zNear Distance where 'vision' begins
|
|
* \param zFar Distance where 'vision' ends
|
|
*/
|
|
template<typename T>
|
|
constexpr Matrix4<T> Matrix4<T>::Ortho(T left, T right, T top, T bottom, T zNear, T zFar)
|
|
{
|
|
// http://msdn.microsoft.com/en-us/library/windows/desktop/bb204942(v=vs.85).aspx
|
|
return Matrix4(
|
|
T(2.0) / (right - left), T(0.0), T(0.0), T(0.0),
|
|
T(0.0), T(2.0) / (top - bottom), T(0.0), T(0.0),
|
|
T(0.0), T(0.0), T(1.0) / (zNear - zFar), T(0.0),
|
|
(left + right) / (left - right), (top + bottom) / (bottom - top), zNear / (zNear - zFar), T(1.0)
|
|
);
|
|
}
|
|
|
|
/*!
|
|
* \brief Shorthand for the 'perspective' matrix
|
|
* \return A Matrix4 which is the 'perspective' matrix
|
|
*
|
|
* \param angle FOV angle
|
|
* \param ratio Rendering ratio (typically 16/9 or 4/3)
|
|
* \param zNear Distance where 'vision' begins
|
|
* \param zFar Distance where 'vision' ends
|
|
*/
|
|
template<typename T>
|
|
Matrix4<T> Matrix4<T>::Perspective(RadianAngle<T> angle, T ratio, T zNear, T zFar)
|
|
{
|
|
angle /= T(2.0);
|
|
|
|
T yScale = angle.GetTan();
|
|
|
|
return Matrix4(
|
|
T(1.0) / (ratio * yScale), T(0.0), T(0.0), T(0.0),
|
|
T(0.0), T(-1.0) / (yScale), T(0.0), T(0.0),
|
|
T(0.0), T(0.0), zFar / (zNear - zFar), T(-1.0),
|
|
T(0.0), T(0.0), -(zNear * zFar) / (zFar - zNear), T(0.0)
|
|
);
|
|
}
|
|
|
|
/*!
|
|
* \brief Shorthand for the 'rotation' matrix
|
|
* \return A Matrix4 which is the rotation of the quaternion
|
|
*
|
|
* \param rotation Quaternion representing a rotation of space
|
|
*/
|
|
template<typename T>
|
|
constexpr Matrix4<T> Matrix4<T>::Rotate(const Quaternion<T>& rotation)
|
|
{
|
|
Matrix4 matrix = Matrix4::Identity();
|
|
matrix.SetRotation(rotation);
|
|
|
|
return matrix;
|
|
}
|
|
|
|
/*!
|
|
* \brief Shorthand for the 'scale' matrix
|
|
* \return A Matrix4 which is is the scale
|
|
*
|
|
* \param scale Vector3 representing the scale
|
|
*/
|
|
template<typename T>
|
|
constexpr Matrix4<T> Matrix4<T>::Scale(const Vector3<T>& scale)
|
|
{
|
|
return Matrix4(
|
|
scale.x, T(0.0), T(0.0), T(0.0),
|
|
T(0.0), scale.y, T(0.0), T(0.0),
|
|
T(0.0), T(0.0), scale.z, T(0.0),
|
|
T(0.0), T(0.0), T(0.0), T(1.0)
|
|
);
|
|
}
|
|
|
|
/*!
|
|
* \brief Shorthand for the 'translation' matrix
|
|
* \return A Matrix4 which is is the translation
|
|
*
|
|
* \param translation Vector3 representing the translation
|
|
*/
|
|
template<typename T>
|
|
constexpr Matrix4<T> Matrix4<T>::Translate(const Vector3<T>& translation)
|
|
{
|
|
return Matrix4(
|
|
T(1.0), T(0.0), T(0.0), T(0.0),
|
|
T(0.0), T(1.0), T(0.0), T(0.0),
|
|
T(0.0), T(0.0), T(1.0), T(0.0),
|
|
translation.x, translation.y, translation.z, T(1.0)
|
|
);
|
|
}
|
|
|
|
/*!
|
|
* \brief Shorthand for the 'transform' matrix
|
|
* \return A Matrix4 which is transformation obtained by the translation and the rotation
|
|
*
|
|
* \param translation Vector3 representing the translation
|
|
* \param rotation Quaternion representing a rotation of space
|
|
*
|
|
* \remark Rotation is applied first
|
|
*/
|
|
template<typename T>
|
|
constexpr Matrix4<T> Matrix4<T>::Transform(const Vector3<T>& translation, const Quaternion<T>& rotation)
|
|
{
|
|
Matrix4 mat = Matrix4f::Identity();
|
|
mat.SetRotation(rotation);
|
|
mat.SetTranslation(translation);
|
|
|
|
return mat;
|
|
}
|
|
|
|
/*!
|
|
* \brief Shorthand for the 'transform' matrix
|
|
* \return A Matrix4 which is transformation obtained by the translation, the rotation and the scale
|
|
*
|
|
* \param translation Vector3 representing the translation
|
|
* \param rotation Quaternion representing a rotation of space
|
|
* \param scale Vector3 representing the homothety
|
|
*
|
|
* \remark Rotation is applied first, then translation
|
|
*/
|
|
template<typename T>
|
|
constexpr Matrix4<T> Matrix4<T>::Transform(const Vector3<T>& translation, const Quaternion<T>& rotation, const Vector3<T>& scale)
|
|
{
|
|
Matrix4 mat = Transform(translation, rotation);
|
|
mat.ApplyScale(scale);
|
|
|
|
return mat;
|
|
}
|
|
|
|
/*!
|
|
* \brief Shorthand for the 'view' matrix
|
|
* \return A Matrix4 which is the 'view matrix'
|
|
*
|
|
* \param translation Vector3 representing the translation
|
|
* \param rotation Quaternion representing a rotation of space
|
|
*/
|
|
template<typename T>
|
|
constexpr Matrix4<T> Matrix4<T>::TransformInverse(const Vector3<T>& translation, const Quaternion<T>& rotation)
|
|
{
|
|
// A view matrix must apply an inverse transformation of the 'world' matrix
|
|
Quaternion<T> invRot = rotation.GetConjugate(); // Inverse of the rotation
|
|
|
|
return Transform(-(invRot * translation), invRot);
|
|
}
|
|
|
|
/*!
|
|
* \brief Shorthand for the 'view' matrix
|
|
* \return A Matrix4 which is the 'view matrix'
|
|
*
|
|
* \param translation Vector3 representing the translation
|
|
* \param rotation Quaternion representing a rotation of space
|
|
* \param scale Vector3 representing the scale
|
|
*/
|
|
template<typename T>
|
|
constexpr Matrix4<T> Matrix4<T>::TransformInverse(const Vector3<T>& translation, const Quaternion<T>& rotation, const Vector3<T>& scale)
|
|
{
|
|
return TransformInverse(translation, rotation).ApplyScale(T(1.0) / scale);
|
|
}
|
|
|
|
/*!
|
|
* \brief Shorthand for the 'zero' matrix
|
|
* \return A Matrix4 with components (0 everywhere)
|
|
*/
|
|
template<typename T>
|
|
constexpr Matrix4<T> Matrix4<T>::Zero()
|
|
{
|
|
return Matrix4(
|
|
T(0.0), T(0.0), T(0.0), T(0.0),
|
|
T(0.0), T(0.0), T(0.0), T(0.0),
|
|
T(0.0), T(0.0), T(0.0), T(0.0),
|
|
T(0.0), T(0.0), T(0.0), T(0.0)
|
|
);
|
|
}
|
|
|
|
/*!
|
|
* \brief Serializes a Matrix4
|
|
* \return true if successfully serialized
|
|
*
|
|
* \param context Serialization context
|
|
* \param matrix Input matrix
|
|
*/
|
|
template<typename T>
|
|
bool Serialize(SerializationContext& context, const Matrix4<T>& matrix, TypeTag<Matrix4<T>>)
|
|
{
|
|
for (unsigned int i = 0; i < 16; ++i)
|
|
{
|
|
if (!Serialize(context, matrix[i]))
|
|
return false;
|
|
}
|
|
|
|
return true;
|
|
}
|
|
|
|
/*!
|
|
* \brief Unserializes a Matrix4
|
|
* \return true if successfully unserialized
|
|
*
|
|
* \param context Serialization context
|
|
* \param matrix Output matrix
|
|
*/
|
|
template<typename T>
|
|
bool Unserialize(SerializationContext& context, Matrix4<T>* matrix, TypeTag<Matrix4<T>>)
|
|
{
|
|
T* head = &matrix->m11;
|
|
for (unsigned int i = 0; i < 16; ++i)
|
|
{
|
|
if (!Unserialize(context, head + i))
|
|
return false;
|
|
}
|
|
|
|
return true;
|
|
}
|
|
|
|
/*!
|
|
* \brief Output operator
|
|
* \return The stream
|
|
*
|
|
* \param out The stream
|
|
* \param matrix The matrix to output
|
|
*/
|
|
|
|
template<typename T>
|
|
std::ostream& operator<<(std::ostream& out, const Matrix4<T>& matrix)
|
|
{
|
|
return out << "Matrix4(" << matrix.m11 << ", " << matrix.m12 << ", " << matrix.m13 << ", " << matrix.m14 << ",\n"
|
|
<< " " << matrix.m21 << ", " << matrix.m22 << ", " << matrix.m23 << ", " << matrix.m24 << ",\n"
|
|
<< " " << matrix.m31 << ", " << matrix.m32 << ", " << matrix.m33 << ", " << matrix.m34 << ",\n"
|
|
<< " " << matrix.m41 << ", " << matrix.m42 << ", " << matrix.m43 << ", " << matrix.m44 << ')';
|
|
}
|
|
|
|
/*!
|
|
* \brief Multiplies the components of the matrix with a scalar
|
|
* \return A Matrix4 where components are the product of matrix'components and the scalar
|
|
*
|
|
* \param scale The scalar to multiply the matrix'components with
|
|
* \param matrix Matrix to multiply with
|
|
*/
|
|
template<typename T>
|
|
constexpr Matrix4<T> operator*(T scale, const Matrix4<T>& matrix)
|
|
{
|
|
return matrix * scale;
|
|
}
|
|
}
|
|
|
|
|
|
#include <Nazara/Core/DebugOff.hpp>
|