nvMatrix.h

/*
 * Copyright 1993-2013 NVIDIA Corporation.  All rights reserved.
 *
 * Please refer to the NVIDIA end user license agreement (EULA) associated
 * with this source code for terms and conditions that govern your use of
 * this software. Any use, reproduction, disclosure, or distribution of
 * this software and related documentation outside the terms of the EULA
 * is strictly prohibited.
 *
 */

//
// Template math library for common 3D functionality
//
// nvMatrix.h - template matrix code
//
// This code is in part deriver from glh, a cross platform glut helper library.
// The copyright for glh follows this notice.
//
// Copyright (c) NVIDIA Corporation. All rights reserved.
////////////////////////////////////////////////////////////////////////////////

/*
    Copyright (c) 2000 Cass Everitt
    Copyright (c) 2000 NVIDIA Corporation
    All rights reserved.

    Redistribution and use in source and binary forms, with or
    without modification, are permitted provided that the following
    conditions are met:

     * Redistributions of source code must retain the above
       copyright notice, this list of conditions and the following
       disclaimer.

     * Redistributions in binary form must reproduce the above
       copyright notice, this list of conditions and the following
       disclaimer in the documentation and/or other materials
       provided with the distribution.

     * The names of contributors to this software may not be used
       to endorse or promote products derived from this software
       without specific prior written permission.

       THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS
       ``AS IS'' AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT
       LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS
       FOR A PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE
       REGENTS OR CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT,
       INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING,
       BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES;
       LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER
       CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT
       LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN
       ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE
       POSSIBILITY OF SUCH DAMAGE.


    Cass Everitt - cass@r3.nu
*/

#ifndef NV_MATRIX_H
#define NV_MATRIX_H

namespace nv
{

    template <class T> class vec2;
    template <class T> class vec3;
    template <class T> class vec4;

    ////////////////////////////////////////////////////////////////////////////////
    //
    //  Matrix
    //
    ////////////////////////////////////////////////////////////////////////////////
    template<class T>
    class matrix4
    {

        public:

            matrix4()
            {
                make_identity();
            }

            matrix4(T t)
            {
                set_value(t);
            }

            matrix4(const T *m)
            {
                set_value(m);
            }

            matrix4(T a00, T a01, T a02, T a03,
                    T a10, T a11, T a12, T a13,
                    T a20, T a21, T a22, T a23,
                    T a30, T a31, T a32, T a33) :
                _11(a00), _12(a01), _13(a02), _14(a03),
                _21(a10), _22(a11), _23(a12), _24(a13),
                _31(a20), _32(a21), _33(a22), _34(a23),
                _41(a30), _42(a31), _43(a32), _44(a33)
            {}


            void get_value(T *mp) const
            {
                int c = 0;

                for (int j=0; j < 4; j++)
                    for (int i=0; i < 4; i++)
                    {
                        mp[c++] = element(i,j);
                    }
            }

            const T *get_value() const
            {
                return _array;
            }

            void set_value(T *mp)
            {
                int c = 0;

                for (int j=0; j < 4; j++)
                    for (int i=0; i < 4; i++)
                    {
                        element(i,j) = mp[c++];
                    }
            }

            void set_value(T r)
            {
                for (int i=0; i < 4; i++)
                    for (int j=0; j < 4; j++)
                    {
                        element(i,j) = r;
                    }
            }

            void make_identity()
            {
                element(0,0) = 1.0;
                element(0,1) = 0.0;
                element(0,2) = 0.0;
                element(0,3) = 0.0;

                element(1,0) = 0.0;
                element(1,1) = 1.0;
                element(1,2) = 0.0;
                element(1,3) = 0.0;

                element(2,0) = 0.0;
                element(2,1) = 0.0;
                element(2,2) = 1.0;
                element(2,3) = 0.0;

                element(3,0) = 0.0;
                element(3,1) = 0.0;
                element(3,2) = 0.0;
                element(3,3) = 1.0;
            }

            // set a uniform scale
            void set_scale(T s)
            {
                element(0,0) = s;
                element(1,1) = s;
                element(2,2) = s;
            }

            void set_scale(const vec3<T> &s)
            {
                for (int i = 0; i < 3; i++)
                {
                    element(i,i) = s[i];
                }
            }


            void set_translate(const vec3<T> &t)
            {
                for (int i = 0; i < 3; i++)
                {
                    element(i,3) = t[i];
                }
            }

            void set_row(int r, const vec4<T> &t)
            {
                for (int i = 0; i < 4; i++)
                {
                    element(r,i) = t[i];
                }
            }

            void set_column(int c, const vec4<T> &t)
            {
                for (int i = 0; i < 4; i++)
                {
                    element(i,c) = t[i];
                }
            }

            vec4<T> get_row(int r) const
            {
                vec4<T> v;

                for (int i = 0; i < 4; i++)
                {
                    v[i] = element(r,i);
                }

                return v;
            }

            vec4<T> get_column(int c) const
            {
                vec4<T> v;

                for (int i = 0; i < 4; i++)
                {
                    v[i] = element(i,c);
                }

                return v;
            }

            friend matrix4 inverse(const matrix4 &m)
            {
                matrix4 minv;

                T r1[8], r2[8], r3[8], r4[8];
                T *s[4], *tmprow;

                s[0] = &r1[0];
                s[1] = &r2[0];
                s[2] = &r3[0];
                s[3] = &r4[0];

                register int i,j,p,jj;

                for (i=0; i<4; i++)
                {
                    for (j=0; j<4; j++)
                    {
                        s[i][j] = m.element(i,j);

                        if (i==j)
                        {
                            s[i][j+4] = 1.0;
                        }
                        else
                        {
                            s[i][j+4] = 0.0;
                        }
                    }
                }

                T scp[4];

                for (i=0; i<4; i++)
                {
                    scp[i] = T(fabs(s[i][0]));

                    for (j=1; j<4; j++)
                        if (T(fabs(s[i][j])) > scp[i])
                        {
                            scp[i] = T(fabs(s[i][j]));
                        }

                    if (scp[i] == 0.0)
                    {
                        return minv;    // singular matrix!
                    }
                }

                int pivot_to;
                T scp_max;

                for (i=0; i<4; i++)
                {
                    // select pivot row
                    pivot_to = i;
                    scp_max = T(fabs(s[i][i]/scp[i]));

                    // find out which row should be on top
                    for (p=i+1; p<4; p++)
                        if (T(fabs(s[p][i]/scp[p])) > scp_max)
                        {
                            scp_max = T(fabs(s[p][i]/scp[p]));
                            pivot_to = p;
                        }

                    // Pivot if necessary
                    if (pivot_to != i)
                    {
                        tmprow = s[i];
                        s[i] = s[pivot_to];
                        s[pivot_to] = tmprow;
                        T tmpscp;
                        tmpscp = scp[i];
                        scp[i] = scp[pivot_to];
                        scp[pivot_to] = tmpscp;
                    }

                    T mji;

                    // perform gaussian elimination
                    for (j=i+1; j<4; j++)
                    {
                        mji = s[j][i]/s[i][i];
                        s[j][i] = 0.0;

                        for (jj=i+1; jj<8; jj++)
                        {
                            s[j][jj] -= mji*s[i][jj];
                        }
                    }
                }

                if (s[3][3] == 0.0)
                {
                    return minv;    // singular matrix!
                }

                //
                // Now we have an upper triangular matrix.
                //
                //  x x x x | y y y y
                //  0 x x x | y y y y
                //  0 0 x x | y y y y
                //  0 0 0 x | y y y y
                //
                //  we'll back substitute to get the inverse
                //
                //  1 0 0 0 | z z z z
                //  0 1 0 0 | z z z z
                //  0 0 1 0 | z z z z
                //  0 0 0 1 | z z z z
                //

                T mij;

                for (i=3; i>0; i--)
                {
                    for (j=i-1; j > -1; j--)
                    {
                        mij = s[j][i]/s[i][i];

                        for (jj=j+1; jj<8; jj++)
                        {
                            s[j][jj] -= mij*s[i][jj];
                        }
                    }
                }

                for (i=0; i<4; i++)
                    for (j=0; j<4; j++)
                    {
                        minv(i,j) = s[i][j+4] / s[i][i];
                    }

                return minv;
            }


            friend matrix4 transpose(const matrix4 &m)
            {
                matrix4 mtrans;

                for (int i=0; i<4; i++)
                    for (int j=0; j<4; j++)
                    {
                        mtrans(i,j) = m.element(j,i);
                    }

                return mtrans;
            }

            matrix4 &operator *= (const matrix4 &rhs)
            {
                matrix4 mt(*this);
                set_value(T(0));

                for (int i=0; i < 4; i++)
                    for (int j=0; j < 4; j++)
                        for (int c=0; c < 4; c++)
                        {
                            element(i,j) += mt(i,c) * rhs(c,j);
                        }

                return *this;
            }

            friend matrix4 operator * (const matrix4 &lhs, const matrix4 &rhs)
            {
                matrix4 r(T(0));

                for (int i=0; i < 4; i++)
                    for (int j=0; j < 4; j++)
                        for (int c=0; c < 4; c++)
                        {
                            r.element(i,j) += lhs(i,c) * rhs(c,j);
                        }

                return r;
            }

            // dst = M * src
            vec4<T> operator *(const vec4<T> &src) const
            {
                vec4<T> r;

                for (int i = 0; i < 4; i++)
                    r[i]  = (src[0] * element(i,0) + src[1] * element(i,1) +
                             src[2] * element(i,2) + src[3] * element(i,3));

                return r;
            }

            // dst = src * M
            friend vec4<T> operator *(const vec4<T> &lhs, const matrix4 &rhs)
            {
                vec4<T> r;

                for (int i = 0; i < 4; i++)
                    r[i]  = (lhs[0] * rhs.element(0,i) + lhs[1] * rhs.element(1,i) +
                             lhs[2] * rhs.element(2,i) + lhs[3] * rhs.element(3,i));

                return r;
            }

            T &operator()(int row, int col)
            {
                return element(row,col);
            }

            const T &operator()(int row, int col) const
            {
                return element(row,col);
            }

            T &element(int row, int col)
            {
                return _array[row | (col<<2)];
            }

            const T &element(int row, int col) const
            {
                return _array[row | (col<<2)];
            }

            matrix4 &operator *= (const T &r)
            {
                for (int i = 0; i < 4; ++i)
                {
                    element(0,i) *= r;
                    element(1,i) *= r;
                    element(2,i) *= r;
                    element(3,i) *= r;
                }

                return *this;
            }

            matrix4 &operator += (const matrix4 &mat)
            {
                for (int i = 0; i < 4; ++i)
                {
                    element(0,i) += mat.element(0,i);
                    element(1,i) += mat.element(1,i);
                    element(2,i) += mat.element(2,i);
                    element(3,i) += mat.element(3,i);
                }

                return *this;
            }


            friend bool operator == (const matrix4 &lhs, const matrix4 &rhs)
            {
                bool r = true;

                for (int i = 0; i < 16; i++)
                {
                    r &= lhs._array[i] == rhs._array[i];
                }

                return r;
            }

            friend bool operator != (const matrix4 &lhs, const matrix4 &rhs)
            {
                bool r = true;

                for (int i = 0; i < 16; i++)
                {
                    r &= lhs._array[i] != rhs._array[i];
                }

                return r;
            }

            union
            {
                struct
                {
                    T _11, _12, _13, _14;   // standard names for components
                    T _21, _22, _23, _24;   // standard names for components
                    T _31, _32, _33, _34;   // standard names for components
                    T _41, _42, _43, _44;   // standard names for components
                };
                T _array[16];     // array access
            };
    };

};

#endif