matrix3.h

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/*
   This program is free software: you can redistribute it and/or modify
   it under the terms of the GNU General Public License as published by
   the Free Software Foundation, either version 3 of the License, or
   (at your option) any later version.

   This program is distributed in the hope that it will be useful,
   but WITHOUT ANY WARRANTY; without even the implied warranty of
   MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
   GNU General Public License for more details.

   You should have received a copy of the GNU General Public License
   along with this program.  If not, see <http://www.gnu.org/licenses/>.
 */

// Copyright 2010 Michael Smith, all rights reserved.

// Inspired by:
/****************************************
 * 3D Vector Classes
 * By Bill Perone (billperone@yahoo.com)
 */

//
// 3x3 matrix implementation.
//
// Note that the matrix is organised in row-normal form (the same as
// applies to array indexing).
//
// In addition to the template, this header defines the following types:
//
// Matrix3i     3x3 matrix of signed integers
// Matrix3ui    3x3 matrix of unsigned integers
// Matrix3l     3x3 matrix of signed longs
// Matrix3ul    3x3 matrix of unsigned longs
// Matrix3f     3x3 matrix of signed floats
//
#pragma once

#include "vector3.h"

// 3x3 matrix with elements of type T
template <typename T>
class Matrix3 {
public:

    // Vectors comprising the rows of the matrix
    Vector3<T>        a, b, c;

    // trivial ctor
    // note that the Vector3 ctor will zero the vector elements
    constexpr Matrix3<T>() {}

    // setting ctor
    constexpr Matrix3<T>(const Vector3<T> &a0, const Vector3<T> &b0, const Vector3<T> &c0)
        : a(a0)
        , b(b0)
        , c(c0) {}

    // setting ctor
    constexpr Matrix3<T>(const T ax, const T ay, const T az,
                         const T bx, const T by, const T bz,
                         const T cx, const T cy, const T cz)
        : a(ax,ay,az)
        , b(bx,by,bz)
        , c(cx,cy,cz) {}

    // function call operator
    void operator        () (const Vector3<T> &a0, const Vector3<T> &b0, const Vector3<T> &c0)
    {
        a = a0; b = b0; c = c0;
    }

    // test for equality
    bool operator        == (const Matrix3<T> &m)
    {
        return (a==m.a && b==m.b && c==m.c);
    }

    // test for inequality
    bool operator        != (const Matrix3<T> &m)
    {
        return (a!=m.a || b!=m.b || c!=m.c);
    }

    // negation
    Matrix3<T> operator        - (void) const
    {
        return Matrix3<T>(-a,-b,-c);
    }

    // addition
    Matrix3<T> operator        + (const Matrix3<T> &m) const
    {
        return Matrix3<T>(a+m.a, b+m.b, c+m.c);
    }
    Matrix3<T> &operator        += (const Matrix3<T> &m)
    {
        return *this = *this + m;
    }

    // subtraction
    Matrix3<T> operator        - (const Matrix3<T> &m) const
    {
        return Matrix3<T>(a-m.a, b-m.b, c-m.c);
    }
    Matrix3<T> &operator        -= (const Matrix3<T> &m)
    {
        return *this = *this - m;
    }

    // uniform scaling
    Matrix3<T> operator        * (const T num) const
    {
        return Matrix3<T>(a*num, b*num, c*num);
    }
    Matrix3<T> &operator        *= (const T num)
    {
        return *this = *this * num;
    }
    Matrix3<T> operator        / (const T num) const
    {
        return Matrix3<T>(a/num, b/num, c/num);
    }
    Matrix3<T> &operator        /= (const T num)
    {
        return *this = *this / num;
    }

    // allow a Matrix3 to be used as an array of vectors, 0 indexed
    Vector3<T> & operator[](uint8_t i) {
        Vector3<T> *_v = &a;
#if MATH_CHECK_INDEXES
        assert(i >= 0 && i < 3);
#endif
        return _v[i];
    }

    const Vector3<T> & operator[](uint8_t i) const {
        const Vector3<T> *_v = &a;
#if MATH_CHECK_INDEXES
        assert(i >= 0 && i < 3);
#endif
        return _v[i];
    }

    // multiplication by a vector
    Vector3<T> operator         *(const Vector3<T> &v) const;

    // multiplication of transpose by a vector
    Vector3<T>                  mul_transpose(const Vector3<T> &v) const;

    // multiplication by a vector giving a Vector2 result (XY components)
    Vector2<T> mulXY(const Vector3<T> &v) const;

    // extract x column
    Vector3<T>                  colx(void) const
    {
        return Vector3<T>(a.x, b.x, c.x);
    }

    // extract y column
    Vector3<T>        coly(void) const
    {
        return Vector3<T>(a.y, b.y, c.y);
    }

    // extract z column
    Vector3<T>        colz(void) const
    {
        return Vector3<T>(a.z, b.z, c.z);
    }

    // multiplication by another Matrix3<T>
    Matrix3<T> operator *(const Matrix3<T> &m) const;

    Matrix3<T> &operator        *=(const Matrix3<T> &m)
    {
        return *this = *this * m;
    }

    // transpose the matrix
    Matrix3<T>          transposed(void) const;

    void transpose(void)
    {
        *this = transposed();
    }

    T det() const;

    bool inverse(Matrix3<T>& inv) const;

    bool invert();

    // zero the matrix
    void        zero(void);

    // setup the identity matrix
    void        identity(void) {
        a.x = b.y = c.z = 1;
        a.y = a.z = 0;
        b.x = b.z = 0;
        c.x = c.y = 0;
    }

    // check if any elements are NAN
    bool        is_nan(void)
    {
        return a.is_nan() || b.is_nan() || c.is_nan();
    }

    // create a rotation matrix from Euler angles
    void        from_euler(float roll, float pitch, float yaw);

    // create eulers from a rotation matrix
    void        to_euler(float *roll, float *pitch, float *yaw) const;

    // create matrix from rotation enum
    void from_rotation(enum Rotation rotation);
    
    /*
      calculate Euler angles (312 convention) for the matrix.
      See http://www.atacolorado.com/eulersequences.doc
      vector is returned in r, p, y order
    */
    Vector3<T> to_euler312() const;

    /*
      fill the matrix from Euler angles in radians in 312 convention
    */
    void from_euler312(float roll, float pitch, float yaw);

    // apply an additional rotation from a body frame gyro vector
    // to a rotation matrix.
    void        rotate(const Vector3<T> &g);

    // create rotation matrix for rotation about the vector v by angle theta
    // See: https://en.wikipedia.org/wiki/Rotation_matrix#General_rotations
    // "Rotation matrix from axis and angle"
    void        from_axis_angle(const Vector3<T> &v, float theta);
    
    // normalize a rotation matrix
    void        normalize(void);
};

typedef Matrix3<int16_t>                Matrix3i;
typedef Matrix3<uint16_t>               Matrix3ui;
typedef Matrix3<int32_t>                Matrix3l;
typedef Matrix3<uint32_t>               Matrix3ul;
typedef Matrix3<float>                  Matrix3f;
typedef Matrix3<double>                 Matrix3d;