matrix.h

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/***************************************************************************
 *   Copyright (C) 2005-2019 by the FIFE team                              *
 *   http://www.fifengine.net                                              *
 *   This file is part of FIFE.                                            *
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 *   FIFE is free software; you can redistribute it and/or                 *
 *   modify it under the terms of the GNU Lesser General Public            *
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/***************************************************************************
 * Includes some heavy copying from mathgl-pp project                      *
 * (http://sourceforge.net/projects/mathgl-pp/)                            *
 ***************************************************************************/

#ifndef FIFE_UTIL_MATRIX_H
#define FIFE_UTIL_MATRIX_H

// Standard C++ library includes
#include <cassert>
#include <iostream>

// Platform specific includes

// 3rd party library includes

// FIFE includes
// These includes are split up in two parts, separated by one empty line
// First block: files included from the FIFE root src directory
// Second block: files included from the same folder
#include "util/base/fife_stdint.h"
#include "util/structures/point.h"

#include "fife_math.h"

namespace FIFE {


    template <typename T>
    class Matrix {
        public:
            Matrix<T>() {}
            template <typename U> friend class Matrix;
            template <typename U> Matrix<T>(const Matrix<U>& mat) {
                memmove(m, mat.m, 16*sizeof(T));
            }
            ~Matrix() {}

            Matrix inverse() const {
                Matrix ret(adjoint());

                T determinant = m0*ret[0] + m1*ret[4] + m2*ret[8] + m3*ret[12];
                assert(determinant!=0 && "Singular matrix has no inverse");

                ret/=determinant;
                return ret;
            }

            inline Matrix& operator/= (T val) {
                for (unsigned i = 0; i < 16; ++i)
                    m[i] /= val;
                return *this;
            }

            Matrix adjoint() const {
                Matrix ret;

                ret[0] = cofactorm0();
                ret[1] = -cofactorm4();
                ret[2] = cofactorm8();
                ret[3] = -cofactorm12();

                ret[4] = -cofactorm1();
                ret[5] = cofactorm5();
                ret[6] = -cofactorm9();
                ret[7] = cofactorm13();

                ret[8] = cofactorm2();
                ret[9] = -cofactorm6();
                ret[10] = cofactorm10();
                ret[11] = -cofactorm14();

                ret[12] = -cofactorm3();
                ret[13] = cofactorm7();
                ret[14] = -cofactorm11();
                ret[15] = cofactorm15();

                return ret;
            }


            inline Matrix& loadRotate(T angle, T x, T y, T z) {
                T magSqr = x*x + y*y + z*z;
                if (magSqr != 1.0) {
                    T mag = Math<T>::Sqrt(magSqr);
                    x/=mag;
                    y/=mag;
                    z/=mag;
                }
                T c = Math<T>::Cos(angle*Math<T>::pi()/180);
                T s = Math<T>::Sin(angle*Math<T>::pi()/180);
                m0 = x*x*(1-c)+c;
                m1 = y*x*(1-c)+z*s;
                m2 = z*x*(1-c)-y*s;
                m3 = 0;

                m4 = x*y*(1-c)-z*s;
                m5 = y*y*(1-c)+c;
                m6 = z*y*(1-c)+x*s;
                m7 = 0;

                m8 = x*z*(1-c)+y*s;
                m9 = y*z*(1-c)-x*s;
                m10 = z*z*(1-c)+c;
                m11 = 0;

                m12 = 0;
                m13 = 0;
                m14 = 0;
                m15 = 1;

                return *this;
            }

            inline Matrix& applyScale(T x, T y, T z) {
                static Matrix<T> temp;
                temp.loadScale(x,y,z);
                *this = temp.mult4by4(*this);
                return  *this;
            }

            inline Matrix& loadScale(T x, T y, T z = 1) {
                m0 = x;
                m4 = 0;
                m8  = 0;
                m12 = 0;
                m1 = 0;
                m5 = y;
                m9  = 0;
                m13 = 0;
                m2 = 0;
                m6 = 0;
                m10 = z;
                m14 = 0;
                m3 = 0;
                m7 = 0;
                m11 = 0;
                m15 = 1;

                return *this;
            }

            inline Matrix& applyTranslate(T x, T y, T z) {
                static Matrix<T> temp;
                temp.loadTranslate(x,y,z);
                *this = temp.mult4by4(*this);
                return  *this;
            }

            inline Matrix& loadTranslate( const T x, const T y, const T z) {
                m0 = 1;
                m4 = 0;
                m8  = 0;
                m12 = x;
                m1 = 0;
                m5 = 1;
                m9  = 0;
                m13 = y;
                m2 = 0;
                m6 = 0;
                m10 = 1;
                m14 = z;
                m3 = 0;
                m7 = 0;
                m11 = 0;
                m15 = 1;

                return *this;
            }

            inline PointType3D<T> operator* (const PointType3D<T>& vec) {
                return PointType3D<T> (
                    vec.x * m0 + vec.y * m4 + vec.z * m8 + m12,
                    vec.x * m1 + vec.y * m5 + vec.z * m9 + m13,
                    vec.x * m2 + vec.y * m6 + vec.z * m10 + m14
                );
            }

            inline T& operator[] (int32_t ind) {
                assert(ind > -1 && ind < 16);
                return m[ind];
            }
            inline const T& operator[] (int32_t ind) const {
                assert(ind > -1 && ind < 16);
                return m[ind];
            }

            inline Matrix& mult3by3(const Matrix& mat) {
                Matrix temp(*this);
                m0 = temp.m0*mat.m0+temp.m4*mat.m1+temp.m8*mat.m2;
                m4 = temp.m0*mat.m4+temp.m4*mat.m5+temp.m8*mat.m6;
                m8 = temp.m0*mat.m8+temp.m4*mat.m9+temp.m8*mat.m10;

                m1 = temp.m1*mat.m0+temp.m5*mat.m1+temp.m9*mat.m2;
                m5 = temp.m1*mat.m4+temp.m5*mat.m5+temp.m9*mat.m6;
                m9 = temp.m1*mat.m8+temp.m5*mat.m9+temp.m9*mat.m10;

                m2 = temp.m2*mat.m0+temp.m6*mat.m1+temp.m10*mat.m2;
                m6 = temp.m2*mat.m4+temp.m6*mat.m5+temp.m10*mat.m6;
                m10 = temp.m2*mat.m8+temp.m6*mat.m9+temp.m10*mat.m10;

                m3 = temp.m3*mat.m0+temp.m7*mat.m1+temp.m11*mat.m2;
                m7 = temp.m3*mat.m4+temp.m7*mat.m5+temp.m11*mat.m6;
                m11 = temp.m3*mat.m8+temp.m7*mat.m9+temp.m11*mat.m10;
                return *this;
            }

            inline Matrix<T>& Rmult4by4(const Matrix<T>& mat) {
                Matrix temp(*this);

                m0 = mat.m0*temp.m0+mat.m4*temp.m1+mat.m8*temp.m2+mat.m12*temp.m3;
                m4 = mat.m0*temp.m4+mat.m4*temp.m5+mat.m8*temp.m6+mat.m12*temp.m7;
                m8 = mat.m0*temp.m8+mat.m4*temp.m9+mat.m8*temp.m10+mat.m12*temp.m11;
                m12 = mat.m0*temp.m12+mat.m4*temp.m13+mat.m8*temp.m14+mat.m12*temp.m15;

                m1 =  mat.m1*temp.m0 + mat.m5*temp.m1  + mat.m9*temp.m2+mat.m13*temp.m3;
                m5 =  mat.m1*temp.m4 + mat.m5*temp.m5  + mat.m9*temp.m6+mat.m13*temp.m7;
                m9 =  mat.m1*temp.m8 + mat.m5*temp.m9  + mat.m9*temp.m10+mat.m13*temp.m11;
                m13 = mat.m1*temp.m12+ mat.m5*temp.m13 + mat.m9*temp.m14+mat.m13*temp.m15;

                m2 = mat.m2*temp.m0+mat.m6*temp.m1+mat.m10*temp.m2+mat.m14*temp.m3;
                m6 = mat.m2*temp.m4+mat.m6*temp.m5+mat.m10*temp.m6+mat.m14*temp.m7;
                m10 = mat.m2*temp.m8+mat.m6*temp.m9+mat.m10*temp.m10+mat.m14*temp.m11;
                m14 = mat.m2*temp.m12+mat.m6*temp.m13+mat.m10*temp.m14+mat.m14*temp.m15;

                m3 = mat.m3*temp.m0+mat.m7*temp.m1+mat.m11*temp.m2+mat.m15*temp.m3;
                m7 = mat.m3*temp.m4+mat.m7*temp.m5+mat.m11*temp.m6+mat.m15*temp.m7;
                m11 = mat.m3*temp.m8+mat.m7*temp.m9+mat.m11*temp.m10+mat.m15*temp.m11;
                m15 = mat.m3*temp.m12+mat.m7*temp.m13+mat.m11*temp.m14+mat.m15*temp.m15;
                return *this;
            }


            inline Matrix<T>& mult4by4(const Matrix<T>& mat) {
                Matrix temp(*this);

                m0 = temp.m0*mat.m0+temp.m4*mat.m1+temp.m8*mat.m2+temp.m12*mat.m3;
                m4 = temp.m0*mat.m4+temp.m4*mat.m5+temp.m8*mat.m6+temp.m12*mat.m7;
                m8 = temp.m0*mat.m8+temp.m4*mat.m9+temp.m8*mat.m10+temp.m12*mat.m11;
                m12 = temp.m0*mat.m12+temp.m4*mat.m13+temp.m8*mat.m14+temp.m12*mat.m15;

                m1 =  temp.m1*mat.m0 + temp.m5*mat.m1  + temp.m9*mat.m2+temp.m13*mat.m3;
                m5 =  temp.m1*mat.m4 + temp.m5*mat.m5  + temp.m9*mat.m6+temp.m13*mat.m7;
                m9 =  temp.m1*mat.m8 + temp.m5*mat.m9  + temp.m9*mat.m10+temp.m13*mat.m11;
                m13 = temp.m1*mat.m12+ temp.m5*mat.m13 + temp.m9*mat.m14+temp.m13*mat.m15;

                m2 = temp.m2*mat.m0+temp.m6*mat.m1+temp.m10*mat.m2+temp.m14*mat.m3;
                m6 = temp.m2*mat.m4+temp.m6*mat.m5+temp.m10*mat.m6+temp.m14*mat.m7;
                m10 = temp.m2*mat.m8+temp.m6*mat.m9+temp.m10*mat.m10+temp.m14*mat.m11;
                m14 = temp.m2*mat.m12+temp.m6*mat.m13+temp.m10*mat.m14+temp.m14*mat.m15;

                m3 = temp.m3*mat.m0+temp.m7*mat.m1+temp.m11*mat.m2+temp.m15*mat.m3;
                m7 = temp.m3*mat.m4+temp.m7*mat.m5+temp.m11*mat.m6+temp.m15*mat.m7;
                m11 = temp.m3*mat.m8+temp.m7*mat.m9+temp.m11*mat.m10+temp.m15*mat.m11;
                m15 = temp.m3*mat.m12+temp.m7*mat.m13+temp.m11*mat.m14+temp.m15*mat.m15;
                return *this;
            }

            Matrix& applyRotate(T angle, T x, T y, T z) {
                static Matrix<T> temp;
                temp.loadRotate(angle,x,y,z);
                *this = temp.mult4by4(*this);
                return  *this;
            }


        private:
#define cofactor_maker(f1,mj1,mi1, f2,mj2,mi2, f3,mj3,mi3) \
        f1*(mj1*mi1-mj2*mi3) + f2*(mj2*mi2-mj3*mi1) + f3*(mj3*mi3-mj1*mi2)

            inline T cofactorm0() const {
                return cofactor_maker(m5,m10,m15, m6,m11,m13, m7,m9,m14);
            }
            inline T cofactorm1() const {
                return cofactor_maker(m6,m11,m12, m7,m8,m14, m4,m10,m15);
            }
            inline T cofactorm2() const {
                return cofactor_maker(m7,m8,m13, m4,m9,m15, m5,m11,m12);
            }
            inline T cofactorm3() const {
                return cofactor_maker(m4,m9,m14, m5,m10,m12, m6,m8,m13);
            }
            inline T cofactorm4() const {
                return cofactor_maker(m9,m14,m3, m10,m15,m1, m11,m13,m2);
            }
            inline T cofactorm5() const {
                return cofactor_maker(m10,m15,m0, m11,m12,m2, m8,m14,m3);
            }
            inline T cofactorm6() const {
                return cofactor_maker(m11,m12,m1, m8,m13,m3, m9,m15,m0);
            }
            inline T cofactorm7() const {
                return cofactor_maker(m8,m13,m2, m9,m14,m0, m10,m12,m1);
            }
            inline T cofactorm8() const {
                return cofactor_maker(m13,m2,m7, m14,m3,m5, m15,m1,m6);
            }
            inline T cofactorm9() const {
                return cofactor_maker(m14,m13,m4, m15,m0,m6, m12,m2,m7);
            }
            inline T cofactorm10() const {
                return cofactor_maker(m15,m0,m5, m12,m1,m7, m13,m3,m4);
            }
            inline T cofactorm11() const {
                return cofactor_maker(m12,m1,m6, m13,m2,m4, m14,m0,m5);
            }
            inline T cofactorm12() const {
                return cofactor_maker(m1,m6,m11, m2,m7,m9, m3,m5,m10);
            }
            inline T cofactorm13() const {
                return cofactor_maker(m2,m7,m8, m3,m4,m10, m10,m6,m11);
            }
            inline T cofactorm14() const {
                return cofactor_maker(m3,m4,m9, m0,m5,m11, m1,m7,m8);
            }
            inline T cofactorm15() const {
                return cofactor_maker(m0,m5,m10, m1,m6,m8, m2,m4,m9);
            }

        public:
            union {
                T m[16];
                struct {
                    T m0,m1,m2,m3,m4,m5,m6,m7,m8,m9,m10,m11,m12,m13,m14,m15;
                };
            };
    };

    typedef Matrix<double> DoubleMatrix;
    typedef Matrix<int32_t> IntMatrix;

    template<typename T>
    std::ostream& operator<<(std::ostream& os, const Matrix<T>& m) {

        return os << "\n|" << m[0] << "," << m[4] << "," << m[8] << ","  << m[12] << "|\n" << \
                       "|" << m[1] << "," << m[5] << "," << m[9] << ","  << m[13] << "|\n" << \
                       "|" << m[2] << "," << m[6] << "," << m[10] << "," << m[14] << "|\n" << \
                       "|" << m[3] << "," << m[7] << "," << m[11] << "," << m[15] << "|\n";
    }


}

#endif