7b3475f1da
scale() -> scaling() translate() -> translation() rotate() -> rotation() These static functions create a matrix, they don't modify it. Fixes #826
669 lines
21 KiB
C++
669 lines
21 KiB
C++
/*
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* Copyright 2013 The Android Open Source Project
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*
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* Licensed under the Apache License, Version 2.0 (the "License");
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* you may not use this file except in compliance with the License.
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* You may obtain a copy of the License at
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*
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* http://www.apache.org/licenses/LICENSE-2.0
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*
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* Unless required by applicable law or agreed to in writing, software
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* distributed under the License is distributed on an "AS IS" BASIS,
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* WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
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* See the License for the specific language governing permissions and
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* limitations under the License.
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*/
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#ifndef MATH_MAT4_H_
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#define MATH_MAT4_H_
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#include <math/mat3.h>
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#include <math/quat.h>
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#include <math/TMatHelpers.h>
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#include <math/vec3.h>
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#include <math/vec4.h>
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#include <math/compiler.h>
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#include <stdint.h>
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#include <sys/types.h>
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#include <limits>
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namespace filament {
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namespace math {
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// -------------------------------------------------------------------------------------
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namespace details {
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template<typename T>
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class TQuaternion;
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/**
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* A 4x4 column-major matrix class.
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*
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* Conceptually a 4x4 matrix is a an array of 4 column double4:
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*
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* mat4 m =
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* \f$
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* \left(
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* \begin{array}{cccc}
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* m[0] & m[1] & m[2] & m[3] \\
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* \end{array}
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* \right)
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* \f$
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* =
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* \f$
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* \left(
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* \begin{array}{cccc}
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* m[0][0] & m[1][0] & m[2][0] & m[3][0] \\
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* m[0][1] & m[1][1] & m[2][1] & m[3][1] \\
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* m[0][2] & m[1][2] & m[2][2] & m[3][2] \\
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* m[0][3] & m[1][3] & m[2][3] & m[3][3] \\
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* \end{array}
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* \right)
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* \f$
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* =
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* \f$
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* \left(
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* \begin{array}{cccc}
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* m(0,0) & m(0,1) & m(0,2) & m(0,3) \\
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* m(1,0) & m(1,1) & m(1,2) & m(1,3) \\
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* m(2,0) & m(2,1) & m(2,2) & m(2,3) \\
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* m(3,0) & m(3,1) & m(3,2) & m(3,3) \\
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* \end{array}
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* \right)
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* \f$
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*
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* m[n] is the \f$ n^{th} \f$ column of the matrix and is a double4.
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*
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*/
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template <typename T>
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class MATH_EMPTY_BASES TMat44 :
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public TVecUnaryOperators<TMat44, T>,
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public TVecComparisonOperators<TMat44, T>,
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public TVecAddOperators<TMat44, T>,
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public TMatProductOperators<TMat44, T>,
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public TMatSquareFunctions<TMat44, T>,
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public TMatTransform<TMat44, T>,
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public TMatHelpers<TMat44, T>,
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public TMatDebug<TMat44, T> {
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public:
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enum no_init { NO_INIT };
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typedef T value_type;
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typedef T& reference;
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typedef T const& const_reference;
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typedef size_t size_type;
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typedef TVec4<T> col_type;
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typedef TVec4<T> row_type;
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static constexpr size_t COL_SIZE = col_type::SIZE; // size of a column (i.e.: number of rows)
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static constexpr size_t ROW_SIZE = row_type::SIZE; // size of a row (i.e.: number of columns)
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static constexpr size_t NUM_ROWS = COL_SIZE;
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static constexpr size_t NUM_COLS = ROW_SIZE;
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private:
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/*
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* <-- N columns -->
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*
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* a[0][0] a[1][0] a[2][0] ... a[N][0] ^
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* a[0][1] a[1][1] a[2][1] ... a[N][1] |
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* a[0][2] a[1][2] a[2][2] ... a[N][2] M rows
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* ... |
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* a[0][M] a[1][M] a[2][M] ... a[N][M] v
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*
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* COL_SIZE = M
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* ROW_SIZE = N
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* m[0] = [ a[0][0] a[0][1] a[0][2] ... a[0][M] ]
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*/
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col_type m_value[NUM_COLS];
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public:
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// array access
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inline constexpr col_type const& operator[](size_t column) const {
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// only possible in C++0x14 with constexpr
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assert(column < NUM_COLS);
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return m_value[column];
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}
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inline constexpr col_type& operator[](size_t column) {
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assert(column < NUM_COLS);
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return m_value[column];
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}
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/*
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* constructors
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*/
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// leaves object uninitialized. use with caution.
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constexpr explicit TMat44(no_init) {}
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/** initialize to identity.
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*
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* \f$
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* \left(
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* \begin{array}{cccc}
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* 1 & 0 & 0 & 0 \\
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* 0 & 1 & 0 & 0 \\
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* 0 & 0 & 1 & 0 \\
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* 0 & 0 & 0 & 1 \\
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* \end{array}
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* \right)
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* \f$
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*/
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constexpr TMat44();
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/** initialize to Identity*scalar.
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*
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* \f$
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* \left(
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* \begin{array}{cccc}
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* v & 0 & 0 & 0 \\
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* 0 & v & 0 & 0 \\
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* 0 & 0 & v & 0 \\
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* 0 & 0 & 0 & v \\
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* \end{array}
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* \right)
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* \f$
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*/
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template<typename U>
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constexpr explicit TMat44(U v);
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/** sets the diagonal to a vector.
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*
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* \f$
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* \left(
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* \begin{array}{cccc}
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* v[0] & 0 & 0 & 0 \\
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* 0 & v[1] & 0 & 0 \\
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* 0 & 0 & v[2] & 0 \\
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* 0 & 0 & 0 & v[3] \\
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* \end{array}
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* \right)
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* \f$
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*/
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template <typename U>
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constexpr explicit TMat44(const TVec4<U>& v);
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// construct from another matrix of the same size
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template <typename U>
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constexpr explicit TMat44(const TMat44<U>& rhs);
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/** construct from 4 column vectors.
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*
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* \f$
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* \left(
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* \begin{array}{cccc}
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* v0 & v1 & v2 & v3 \\
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* \end{array}
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* \right)
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* \f$
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*/
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template <typename A, typename B, typename C, typename D>
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constexpr TMat44(const TVec4<A>& v0, const TVec4<B>& v1, const TVec4<C>& v2, const TVec4<D>& v3);
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/** construct from 16 elements in column-major form.
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*
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* \f$
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* \left(
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* \begin{array}{cccc}
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* m[0][0] & m[1][0] & m[2][0] & m[3][0] \\
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* m[0][1] & m[1][1] & m[2][1] & m[3][1] \\
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* m[0][2] & m[1][2] & m[2][2] & m[3][2] \\
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* m[0][3] & m[1][3] & m[2][3] & m[3][3] \\
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* \end{array}
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* \right)
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* \f$
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*/
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template <
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typename A, typename B, typename C, typename D,
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typename E, typename F, typename G, typename H,
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typename I, typename J, typename K, typename L,
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typename M, typename N, typename O, typename P>
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constexpr explicit TMat44(A m00, B m01, C m02, D m03,
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E m10, F m11, G m12, H m13,
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I m20, J m21, K m22, L m23,
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M m30, N m31, O m32, P m33);
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struct row_major_init {
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template<
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typename A, typename B, typename C, typename D,
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typename E, typename F, typename G, typename H,
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typename I, typename J, typename K, typename L,
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typename M, typename N, typename O, typename P>
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constexpr explicit row_major_init(A m00, B m01, C m02, D m03,
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E m10, F m11, G m12, H m13,
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I m20, J m21, K m22, L m23,
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M m30, N m31, O m32, P m33) noexcept
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: m(m00, m10, m20, m30,
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m01, m11, m21, m31,
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m02, m12, m22, m32,
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m03, m13, m23, m33) {}
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private:
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friend TMat44;
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TMat44 m;
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};
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constexpr explicit TMat44(row_major_init c) : TMat44(std::move(c.m)) { }
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/**
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* construct from a quaternion
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*/
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template <typename U>
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constexpr explicit TMat44(const TQuaternion<U>& q);
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/**
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* construct from a 3x3 matrix
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*/
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template <typename U>
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constexpr explicit TMat44(const TMat33<U>& matrix);
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/**
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* construct from a 3x3 matrix and 3d translation
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*/
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template <typename U, typename V>
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constexpr TMat44(const TMat33<U>& matrix, const TVec3<V>& translation);
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/**
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* construct from a 3x3 matrix and 4d last column.
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*/
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template <typename U, typename V>
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constexpr TMat44(const TMat33<U>& matrix, const TVec4<V>& column3);
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/*
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* helpers
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*/
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// returns false if the two matrices are different. May return false if they're the
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// same, with some elements only differing by +0 or -0. Behaviour is undefined with NaNs.
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static constexpr bool fuzzyEqual(TMat44 const& l, TMat44 const& r) noexcept {
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uint64_t const* const li = reinterpret_cast<uint64_t const*>(&l);
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uint64_t const* const ri = reinterpret_cast<uint64_t const*>(&r);
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uint64_t result = 0;
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// For some reason clang is not able to vectorize this loop when the number of iteration
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// is known and constant (!?!?!). Still this is better than operator==.
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for (size_t i = 0; i < sizeof(TMat44) / sizeof(uint64_t); i++) {
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result |= li[i] ^ ri[i];
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}
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return result != 0;
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}
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static constexpr TMat44 ortho(T left, T right, T bottom, T top, T near, T far);
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static constexpr TMat44 frustum(T left, T right, T bottom, T top, T near, T far);
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enum class Fov {
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HORIZONTAL,
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VERTICAL
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};
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static constexpr TMat44 perspective(T fov, T aspect, T near, T far, Fov direction = Fov::VERTICAL);
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template <typename A, typename B, typename C>
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static constexpr TMat44 lookAt(const TVec3<A>& eye, const TVec3<B>& center, const TVec3<C>& up);
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template <typename A>
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static constexpr TVec3<A> project(const TMat44& projectionMatrix, TVec3<A> vertice) {
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TVec4<A> r = projectionMatrix * TVec4<A>{ vertice, 1 };
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return r.xyz * (1 / r.w);
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}
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template <typename A>
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static constexpr TVec4<A> project(const TMat44& projectionMatrix, TVec4<A> vertice) {
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vertice = projectionMatrix * vertice;
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return { vertice.xyz * (1 / vertice.w), 1 };
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}
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/**
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* Constructs a 3x3 matrix from the upper-left corner of this 4x4 matrix
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*/
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inline constexpr TMat33<T> upperLeft() const {
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return TMat33<T>(m_value[0].xyz, m_value[1].xyz, m_value[2].xyz);
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}
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template <typename A>
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static constexpr TMat44 translation(const TVec3<A>& t) {
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TMat44 r;
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r[3] = TVec4<T>{ t, 1 };
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return r;
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}
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template <typename A>
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static constexpr TMat44 scaling(const TVec3<A>& s) {
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return TMat44{ TVec4<T>{ s, 1 } };
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}
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template <typename A>
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static constexpr TMat44 scaling(A s) {
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return TMat44{ TVec4<T>{ s, s, s, 1 } };
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}
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};
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// ----------------------------------------------------------------------------------------
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// Constructors
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// ----------------------------------------------------------------------------------------
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// Since the matrix code could become pretty big quickly, we don't inline most
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// operations.
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template <typename T>
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constexpr TMat44<T>::TMat44() {
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m_value[0] = col_type(1.0f, 0.0f, 0.0f, 0.0f);
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m_value[1] = col_type(0.0f, 1.0f, 0.0f, 0.0f);
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m_value[2] = col_type(0.0f, 0.0f, 1.0f, 0.0f);
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m_value[3] = col_type(0.0f, 0.0f, 0.0f, 1.0f);
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}
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template <typename T>
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template <typename U>
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constexpr TMat44<T>::TMat44(U v) {
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m_value[0] = col_type(v, 0, 0, 0);
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m_value[1] = col_type(0, v, 0, 0);
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m_value[2] = col_type(0, 0, v, 0);
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m_value[3] = col_type(0, 0, 0, v);
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}
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template<typename T>
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template<typename U>
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constexpr TMat44<T>::TMat44(const TVec4<U>& v) {
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m_value[0] = col_type(v.x, 0, 0, 0);
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m_value[1] = col_type(0, v.y, 0, 0);
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m_value[2] = col_type(0, 0, v.z, 0);
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m_value[3] = col_type(0, 0, 0, v.w);
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}
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// construct from 16 scalars
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template<typename T>
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template <
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typename A, typename B, typename C, typename D,
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typename E, typename F, typename G, typename H,
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typename I, typename J, typename K, typename L,
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typename M, typename N, typename O, typename P>
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constexpr TMat44<T>::TMat44(A m00, B m01, C m02, D m03,
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E m10, F m11, G m12, H m13,
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I m20, J m21, K m22, L m23,
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M m30, N m31, O m32, P m33) {
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m_value[0] = col_type(m00, m01, m02, m03);
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m_value[1] = col_type(m10, m11, m12, m13);
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m_value[2] = col_type(m20, m21, m22, m23);
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m_value[3] = col_type(m30, m31, m32, m33);
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}
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template <typename T>
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template <typename U>
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constexpr TMat44<T>::TMat44(const TMat44<U>& rhs) {
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for (size_t col = 0; col < NUM_COLS; ++col) {
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m_value[col] = col_type(rhs[col]);
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}
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}
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// Construct from 4 column vectors.
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template <typename T>
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template <typename A, typename B, typename C, typename D>
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constexpr TMat44<T>::TMat44(const TVec4<A>& v0, const TVec4<B>& v1,
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const TVec4<C>& v2, const TVec4<D>& v3) {
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m_value[0] = col_type(v0);
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m_value[1] = col_type(v1);
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m_value[2] = col_type(v2);
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m_value[3] = col_type(v3);
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}
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template <typename T>
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template <typename U>
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constexpr TMat44<T>::TMat44(const TQuaternion<U>& q) {
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const U n = q.x*q.x + q.y*q.y + q.z*q.z + q.w*q.w;
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const U s = n > 0 ? 2/n : 0;
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const U x = s*q.x;
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const U y = s*q.y;
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const U z = s*q.z;
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const U xx = x*q.x;
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const U xy = x*q.y;
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const U xz = x*q.z;
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const U xw = x*q.w;
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const U yy = y*q.y;
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const U yz = y*q.z;
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const U yw = y*q.w;
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const U zz = z*q.z;
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const U zw = z*q.w;
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m_value[0] = col_type(1-yy-zz, xy+zw, xz-yw, 0);
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m_value[1] = col_type( xy-zw, 1-xx-zz, yz+xw, 0); // NOLINT
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m_value[2] = col_type( xz+yw, yz-xw, 1-xx-yy, 0); // NOLINT
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m_value[3] = col_type( 0, 0, 0, 1); // NOLINT
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}
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template <typename T>
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template <typename U>
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constexpr TMat44<T>::TMat44(const TMat33<U>& m) {
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m_value[0] = col_type(m[0][0], m[0][1], m[0][2], 0);
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m_value[1] = col_type(m[1][0], m[1][1], m[1][2], 0);
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m_value[2] = col_type(m[2][0], m[2][1], m[2][2], 0);
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m_value[3] = col_type( 0, 0, 0, 1); // NOLINT
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}
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template <typename T>
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template <typename U, typename V>
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constexpr TMat44<T>::TMat44(const TMat33<U>& m, const TVec3<V>& v) {
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m_value[0] = col_type(m[0][0], m[0][1], m[0][2], 0);
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m_value[1] = col_type(m[1][0], m[1][1], m[1][2], 0);
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m_value[2] = col_type(m[2][0], m[2][1], m[2][2], 0);
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m_value[3] = col_type( v[0], v[1], v[2], 1); // NOLINT
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}
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template <typename T>
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template <typename U, typename V>
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constexpr TMat44<T>::TMat44(const TMat33<U>& m, const TVec4<V>& v) {
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m_value[0] = col_type(m[0][0], m[0][1], m[0][2], 0); // NOLINT
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m_value[1] = col_type(m[1][0], m[1][1], m[1][2], 0); // NOLINT
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m_value[2] = col_type(m[2][0], m[2][1], m[2][2], 0); // NOLINT
|
|
m_value[3] = col_type( v[0], v[1], v[2], v[3]); // NOLINT
|
|
}
|
|
|
|
// ----------------------------------------------------------------------------------------
|
|
// Helpers
|
|
// ----------------------------------------------------------------------------------------
|
|
|
|
template <typename T>
|
|
constexpr TMat44<T> TMat44<T>::ortho(T left, T right, T bottom, T top, T near, T far) {
|
|
TMat44<T> m;
|
|
m[0][0] = 2 / (right - left);
|
|
m[1][1] = 2 / (top - bottom);
|
|
m[2][2] = -2 / (far - near);
|
|
m[3][0] = -(right + left) / (right - left);
|
|
m[3][1] = -(top + bottom) / (top - bottom);
|
|
m[3][2] = -(far + near) / (far - near);
|
|
return m;
|
|
}
|
|
|
|
template <typename T>
|
|
constexpr TMat44<T> TMat44<T>::frustum(T left, T right, T bottom, T top, T near, T far) {
|
|
TMat44<T> m;
|
|
m[0][0] = (2 * near) / (right - left);
|
|
m[1][1] = (2 * near) / (top - bottom);
|
|
m[2][0] = (right + left) / (right - left);
|
|
m[2][1] = (top + bottom) / (top - bottom);
|
|
m[2][2] = -(far + near) / (far - near);
|
|
m[2][3] = -1;
|
|
m[3][2] = -(2 * far * near) / (far - near);
|
|
m[3][3] = 0;
|
|
return m;
|
|
}
|
|
|
|
template <typename T>
|
|
constexpr TMat44<T> TMat44<T>::perspective(T fov, T aspect, T near, T far, TMat44::Fov direction) {
|
|
T h;
|
|
T w;
|
|
|
|
if (direction == TMat44::Fov::VERTICAL) {
|
|
h = std::tan(fov * M_PI / 360.0f) * near;
|
|
w = h * aspect;
|
|
} else {
|
|
w = std::tan(fov * M_PI / 360.0f) * near;
|
|
h = w / aspect;
|
|
}
|
|
return frustum(-w, w, -h, h, near, far);
|
|
}
|
|
|
|
/*
|
|
* Returns a matrix representing the pose of a virtual camera looking towards -Z in its
|
|
* local Y-up coordinate system. "eye" is where the camera is located, "center" is the points its
|
|
* looking at and "up" defines where the Y axis of the camera's local coordinate system is.
|
|
*/
|
|
template <typename T>
|
|
template <typename A, typename B, typename C>
|
|
constexpr TMat44<T> TMat44<T>::lookAt(const TVec3<A>& eye, const TVec3<B>& center, const TVec3<C>& up) {
|
|
TVec3<T> z_axis(normalize(center - eye));
|
|
TVec3<T> norm_up(normalize(up));
|
|
if (std::abs(dot(z_axis, norm_up)) > T(0.999)) {
|
|
// Fix up vector if we're degenerate (looking straight up, basically)
|
|
norm_up = { norm_up.z, norm_up.x, norm_up.y };
|
|
}
|
|
TVec3<T> x_axis(normalize(cross(z_axis, norm_up)));
|
|
TVec3<T> y_axis(cross(x_axis, z_axis));
|
|
return TMat44<T>(
|
|
TVec4<T>(x_axis, 0),
|
|
TVec4<T>(y_axis, 0),
|
|
TVec4<T>(-z_axis, 0),
|
|
TVec4<T>(eye, 1));
|
|
}
|
|
|
|
// ----------------------------------------------------------------------------------------
|
|
// Arithmetic operators outside of class
|
|
// ----------------------------------------------------------------------------------------
|
|
|
|
/* We use non-friend functions here to prevent the compiler from using
|
|
* implicit conversions, for instance of a scalar to a vector. The result would
|
|
* not be what the caller expects.
|
|
*
|
|
* Also note that the order of the arguments in the inner loop is important since
|
|
* it determines the output type (only relevant when T != U).
|
|
*/
|
|
|
|
// matrix * column-vector, result is a vector of the same type than the input vector
|
|
template <typename T, typename U>
|
|
constexpr typename TMat44<T>::col_type MATH_PURE operator *(const TMat44<T>& lhs, const TVec4<U>& rhs) {
|
|
// Result is initialized to zero.
|
|
typename TMat44<T>::col_type result = {};
|
|
for (size_t col = 0; col < TMat44<T>::NUM_COLS; ++col) {
|
|
result += lhs[col] * T(rhs[col]);
|
|
}
|
|
return result;
|
|
}
|
|
|
|
// mat44 * vec3, result is vec3( mat44 * {vec3, 1} )
|
|
template <typename T, typename U>
|
|
constexpr typename TMat44<T>::col_type MATH_PURE operator *(const TMat44<T>& lhs, const TVec3<U>& rhs) {
|
|
return lhs * TVec4<U>{ rhs, 1 };
|
|
}
|
|
|
|
|
|
// row-vector * matrix, result is a vector of the same type than the input vector
|
|
template <typename T, typename U>
|
|
constexpr typename TMat44<U>::row_type MATH_PURE operator *(const TVec4<U>& lhs, const TMat44<T>& rhs) {
|
|
typename TMat44<U>::row_type result;
|
|
for (size_t col = 0; col < TMat44<T>::NUM_COLS; ++col) {
|
|
result[col] = dot(lhs, rhs[col]);
|
|
}
|
|
return result;
|
|
}
|
|
|
|
// matrix * scalar, result is a matrix of the same type than the input matrix
|
|
template <typename T, typename U>
|
|
constexpr typename std::enable_if<std::is_arithmetic<U>::value, TMat44<T>>::type MATH_PURE
|
|
operator *(TMat44<T> lhs, U rhs) {
|
|
return lhs *= rhs;
|
|
}
|
|
|
|
// scalar * matrix, result is a matrix of the same type than the input matrix
|
|
template <typename T, typename U>
|
|
constexpr typename std::enable_if<std::is_arithmetic<U>::value, TMat44<T>>::type MATH_PURE
|
|
operator *(U lhs, const TMat44<T>& rhs) {
|
|
return rhs * lhs;
|
|
}
|
|
|
|
// ----------------------------------------------------------------------------------------
|
|
|
|
/* FIXME: this should go into TMatSquareFunctions<> but for some reason
|
|
* BASE<T>::col_type is not accessible from there (???)
|
|
*/
|
|
template<typename T>
|
|
constexpr typename TMat44<T>::col_type MATH_PURE diag(const TMat44<T>& m) {
|
|
return matrix::diag(m);
|
|
}
|
|
|
|
} // namespace details
|
|
|
|
// ----------------------------------------------------------------------------------------
|
|
|
|
typedef details::TMat44<double> mat4;
|
|
typedef details::TMat44<float> mat4f;
|
|
|
|
// ----------------------------------------------------------------------------------------
|
|
} // namespace math
|
|
} // namespace filament
|
|
|
|
namespace std {
|
|
template <typename T>
|
|
constexpr void swap( filament::math::details::TMat44<T>& lhs, filament::math::details::TMat44<T>& rhs) noexcept {
|
|
// This generates much better code than the default implementation
|
|
// It's unclear why, I believe this is due to an optimization bug in the clang.
|
|
//
|
|
// filament::math::details::TMat44<T> t(lhs);
|
|
// lhs = rhs;
|
|
// rhs = t;
|
|
//
|
|
// clang always copy lhs on the stack, even if it's never using it (it's using the
|
|
// copy it has in registers).
|
|
|
|
const T t00 = lhs[0][0];
|
|
const T t01 = lhs[0][1];
|
|
const T t02 = lhs[0][2];
|
|
const T t03 = lhs[0][3];
|
|
const T t10 = lhs[1][0];
|
|
const T t11 = lhs[1][1];
|
|
const T t12 = lhs[1][2];
|
|
const T t13 = lhs[1][3];
|
|
const T t20 = lhs[2][0];
|
|
const T t21 = lhs[2][1];
|
|
const T t22 = lhs[2][2];
|
|
const T t23 = lhs[2][3];
|
|
const T t30 = lhs[3][0];
|
|
const T t31 = lhs[3][1];
|
|
const T t32 = lhs[3][2];
|
|
const T t33 = lhs[3][3];
|
|
|
|
lhs[0][0] = rhs[0][0];
|
|
lhs[0][1] = rhs[0][1];
|
|
lhs[0][2] = rhs[0][2];
|
|
lhs[0][3] = rhs[0][3];
|
|
lhs[1][0] = rhs[1][0];
|
|
lhs[1][1] = rhs[1][1];
|
|
lhs[1][2] = rhs[1][2];
|
|
lhs[1][3] = rhs[1][3];
|
|
lhs[2][0] = rhs[2][0];
|
|
lhs[2][1] = rhs[2][1];
|
|
lhs[2][2] = rhs[2][2];
|
|
lhs[2][3] = rhs[2][3];
|
|
lhs[3][0] = rhs[3][0];
|
|
lhs[3][1] = rhs[3][1];
|
|
lhs[3][2] = rhs[3][2];
|
|
lhs[3][3] = rhs[3][3];
|
|
|
|
rhs[0][0] = t00;
|
|
rhs[0][1] = t01;
|
|
rhs[0][2] = t02;
|
|
rhs[0][3] = t03;
|
|
rhs[1][0] = t10;
|
|
rhs[1][1] = t11;
|
|
rhs[1][2] = t12;
|
|
rhs[1][3] = t13;
|
|
rhs[2][0] = t20;
|
|
rhs[2][1] = t21;
|
|
rhs[2][2] = t22;
|
|
rhs[2][3] = t23;
|
|
rhs[3][0] = t30;
|
|
rhs[3][1] = t31;
|
|
rhs[3][2] = t32;
|
|
rhs[3][3] = t33;
|
|
}
|
|
}
|
|
|
|
#endif // MATH_MAT4_H_
|