Matrix.hpp

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/*
    Copyright (c) 2009 Christopher A. Taylor.  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.
    * Neither the name of LibCat nor the names of its contributors may 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 COPYRIGHT HOLDER 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
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    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
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*/

#ifndef CAT_MATRIX_HPP
#define CAT_MATRIX_HPP

#include <cat/gfx/Vector.hpp>

namespace cat {

#define FOR_EACH_ELEMENT(index) for (int index = 0; index < ELEMENTS; ++index)


/*
    4x4 matrix elements arranged column major (row, column):

        m[0]  m[4]  m[8]  m[12]
        m[1]  m[5]  m[9]  m[13]
        m[2]  m[6]  m[10] m[14]
        m[3]  m[7]  m[11] m[15]

    Matrix element order corresponds to OpenGL matrix ordering s.t. in a
    4x4 matrix the elements define the following new coordinate system:

        new x-axis vector: { m[0]  m[1]  m[2]  }
        new y-axis vector: { m[4]  m[5]  m[6]  }
        new z-axis vector: { m[7]  m[9]  m[10] }
        new origin:        { m[12] m[13] m[14] }
*/

template<int ROWS, int COLS, class Scalar> class Matrix
{
protected:
    static const int ELEMENTS = ROWS * COLS;
    Scalar _elements[ROWS * COLS];

public:
    // Short-hand for the current matrix type
    typedef Matrix<ROWS, COLS, Scalar> mytype;

    // Default constructor does not initialize elements
    Matrix()
    {
    }

    // Copy constructor
    Matrix(const mytype &u)
    {
        memcpy(_elements, u._elements, sizeof(_elements));
    }

    // Assignment operator
    mytype &operator=(const mytype &u)
    {
        memcpy(_elements, u._elements, sizeof(_elements));
    }

    // Load zero matrix
    void loadZero()
    {
        OBJCLR(_elements);
    }

    // Load identity matrix
    void loadIdentity()
    {
        OBJCLR(_elements);

        // Write a 1 along the diagonal
        for (int ii = 0; ii < ROWS && ii < COLS; ++ii)
        {
            _elements[ii * ROWS + ii] = static_cast<Scalar>( 1 );
        }
    }

    // Addition in-place
    mytype &operator+=(const mytype &u)
    {
        FOR_EACH_ELEMENT(ii) _elements[ii] += u._elements[ii];
    }

    // Subtraction in-place
    mytype &operator-=(const mytype &u)
    {
        FOR_EACH_ELEMENT(ii) _elements[ii] -= u._elements[ii];
    }

    // Multiplication by scalar in-place
    mytype &operator*=(Scalar u)
    {
        FOR_EACH_ELEMENT(ii) _elements[ii] *= u;
    }

    // Division by scalar in-place
    mytype &operator/=(Scalar u)
    {
        FOR_EACH_ELEMENT(ii) _elements[ii] /= u;
    }

    // Matrix multiplication
    template<int OTHER_COLS>
    Matrix<ROWS, OTHER_COLS, Scalar> operator*(const Matrix<COLS, OTHER_COLS, Scalar> &u)
    {
        Matrix<ROWS, OTHER_COLS, Scalar> result;

        // For each row of the matrix product,
        for (int r = 0; r < ROWS; ++r)
        {
            // For each column of the matrix product,
            for (int c = 0; c < OTHER_COLS; ++c)
            {
                Scalar x = static_cast<Scalar>( 0 );

                // For each row of the right operand (u),
                for (int ii = 0; ii < COLS; ++ii)
                {
                    // Accumulate sum of products
                    x += (*this)(r, ii) * u(ii, c);
                }

                // Write the sum
                result(r, c) = x;
            }
        }

        return result;
    }

    // Accessors
    inline Scalar &operator()(int ii) { return _elements[ii]; }
    inline const Scalar &operator()(int ii) const { return _elements[ii]; }

    inline Scalar &operator()(int row, int col) { return _elements[col * ROWS + row]; }
    inline const Scalar &operator()(int row, int col) const { return _elements[col * ROWS + row]; }
};


// Short-hand for common usages:

typedef Matrix<2, 2, u32> Matrix2x2u;
typedef Matrix<3, 3, u32> Matrix3x3u;
typedef Matrix<4, 4, u32> Matrix4x4u;

typedef Matrix<2, 2, s32> Matrix2x2i;
typedef Matrix<3, 3, s32> Matrix3x3i;
typedef Matrix<4, 4, s32> Matrix4x4i;

typedef Matrix<2, 2, f32> Matrix2x2f;
typedef Matrix<3, 3, f32> Matrix3x3f;
typedef Matrix<4, 4, f32> Matrix4x4f;

typedef Matrix<2, 2, f64> Matrix2x2d;
typedef Matrix<3, 3, f64> Matrix3x3d;
typedef Matrix<4, 4, f64> Matrix4x4d;


#undef FOR_EACH_ELEMENT

} // namespace cat

#endif // CAT_MATRIX_HPP