Matrix.h

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/********************************************************************
 *
 *  Project     Artec 3D Scanning SDK
 *
 *  Purpose:    Definition of template matrix classes for use in
 *              geometric transformations
 *
 *  Copyright:  Artec Group
 *
 ********************************************************************/

#ifndef _MATRIX_H_
#define _MATRIX_H_

#include <artec/sdk/base/GenericMatrix.h>

namespace artec { namespace sdk { namespace base
{

template< typename Type = double >
class Matrix4x4
{
public:
    typedef Type value_type;

    Matrix4x4(){ flagBits = General; }

    Matrix4x4(Type _00, Type _01, Type _02, Type _03,
        Type _10, Type _11, Type _12, Type _13,
        Type _20, Type _21, Type _22, Type _23,
        Type _30, Type _31, Type _32, Type _33)
    {
        m[0][0] = _00; m[0][1] = _01; m[0][2] = _02; m[0][3] = _03;
        m[1][0] = _10; m[1][1] = _11; m[1][2] = _12; m[1][3] = _13;
        m[2][0] = _20; m[2][1] = _21; m[2][2] = _22; m[2][3] = _23;
        m[3][0] = _30; m[3][1] = _31; m[3][2] = _32; m[3][3] = _33;

        flagBits = General;
    }

    template< typename Type2, std::size_t sizeOfArray >
    explicit Matrix4x4(const Type2 (&values)[sizeOfArray])
    {
        int c_assert[size_ == sizeOfArray ? 1 : -1];
        (c_assert);
        for(int i = 0; i < size_; i++) 
            data[i] = values[i];
        flagBits = General;
    }

    template< typename Type2 >
    Matrix4x4(const Type2 * values, int rows2, int cols2)
    {
        for (int matrixRow = 0; matrixRow < rows_; ++matrixRow) {
            for (int matrixCol = 0; matrixCol < cols_; ++matrixCol) {
                if (matrixCol < cols2 && matrixRow < rows2)
                    m[matrixRow][matrixCol] = values[matrixRow * cols2 + matrixCol];
                else if (matrixCol == matrixRow)
                    m[matrixRow][matrixCol] = Type(1);
                else
                    m[matrixRow][matrixCol] = Type(0);
            }
        }
        flagBits = General;
    }

    /// Copying constructor
    Matrix4x4(const Matrix4x4 & second) { *this = second; }

    /// Copying constructor with size_ conversion
    template< int rows2, int cols2, typename Type2 >
    explicit Matrix4x4(const GenericMatrix< rows2, cols2, Type2 > & second) { *this = second; }

    /// Copying constructor with type conversion
    template< typename Type2 >
    explicit Matrix4x4(const Matrix4x4< Type2 > & second)
    {
        for(int i = 0; i < size_; i++) data[i] = (Type)second.data[i];
        flagBits = second.flagBits;
    }

    ///@{
    /// Assignment operators
    template< int rows2, int cols2, typename Type2 >
    Matrix4x4 operator=(const GenericMatrix< rows2, cols2, Type2 > & second)
    {
        for (int matrixRow = 0; matrixRow < rows_; ++matrixRow) {
            for (int matrixCol = 0; matrixCol < cols_; ++matrixCol) {
                if (matrixCol < cols2 && matrixRow < rows2)
                    m[matrixRow][matrixCol] = second.m[matrixRow][matrixCol];
                else if (matrixCol == matrixRow)
                    m[matrixRow][matrixCol] = Type(1);
                else
                    m[matrixRow][matrixCol] = Type(0);
            }
        }
        flagBits = General;
        return *this;
    }

    Matrix4x4 & operator=(const Matrix4x4 & second)
    {
        memcpy(data, second.data, size_*sizeof(Type));
        flagBits = second.flagBits;
        return *this;
    }
    ///@}

    ///@{
    /// Convert matrix4x4 to generic matrix
    template <int rows, int cols>
    GenericMatrix<rows, cols, Type> toGenericMatrix() const
    {
        return toGenericMatrix<rows, cols, Type>();
    }
    
    template <int rows, int cols, typename Type2>
    GenericMatrix<rows, cols, Type2> toGenericMatrix() const
    {
        GenericMatrix<rows, cols, Type2> result;
        for (int matrixRow = 0; matrixRow < rows; ++matrixRow) {
            for (int matrixCol = 0; matrixCol < cols; ++matrixCol) {
                if (matrixRow < 4 && matrixCol < 4)
                    result.m[matrixRow][matrixCol] = m[matrixRow][matrixCol];
                else if (matrixCol == matrixRow)
                    result.m[matrixRow][matrixCol] = Type2(1);
                else
                    result.m[matrixRow][matrixCol] = Type2(0);
            }
        }
        return result;
    }
    ///@}

    /// Fill matrix with value
    void fill(const Type value)
    {
        for(int i = 0; i < size_; i++)
            data[i] = value;
        flagBits = General;
    }

    ///@{
    /// Arithmetical operations
    /// Matrix - Matrix (element-wise)
    Matrix4x4 & operator+=(const Matrix4x4 & mat)
    {
        for(int i = 0; i < size_; i++) data[i] += mat.data[i];
        flagBits = General;
        return *this;
    }
    Matrix4x4 & operator-=(const Matrix4x4 & mat)
    {
        for(int i = 0; i < size_; i++) data[i] -= mat.data[i];
        flagBits = General;
        return *this;
    }
    Matrix4x4 & operator*=(const Matrix4x4 & other)
    {
        if (other.flagBits == Identity) {
            return *this;
        }
        else if (flagBits == Identity) {
            *this = other;
            return *this;
        }
        *this = *this * other;
        return *this;
    }

    Matrix4x4 operator+(const Matrix4x4 & mat) const
    {
        Matrix4x4 m = *this;
        for(int i = 0; i < size_; i++) m.data[i] = m.data[i] + mat.data[i];
        m.flagBits = General;
        return m;
    }

    Matrix4x4 operator-(const Matrix4x4 & mat) const
    {
        Matrix4x4 m = *this;
        for(int i = 0; i < size_; i++) m.data[i] = m.data[i] - mat.data[i];
        m.flagBits = General;
        return m;
    }
    ///@}

    ///@{
    /// Matrix - matrix multiplication
    Matrix4x4 operator*(const Matrix4x4 & mat) const
    {
        if (flagBits == Identity)
            return mat;
        else if (mat.flagBits == Identity)
            return *this;

        Matrix4x4 res;
        for(int i = 0; i < rows_; i++)
            for(int j = 0; j < cols_; j++)
            {
                Type sum = 0;
                for(int k = 0; k < cols_; k++)
                    sum += m[i][k]*mat.m[k][j];

                res.m[i][j] = sum;
            }
        return res;
    }

    template< int cols2 >
    GenericMatrix< 4, cols2, Type > operator*(const GenericMatrix< 4, cols2, Type > & mat) const
    {
        GenericMatrix< 4, cols2, Type > res;
        for(int i = 0; i < rows_; i++)
            for(int j = 0; j < cols2; j++)
            {
                Type sum = 0;
                for(int k = 0; k < cols_; k++)
                    sum += m[i][k]*mat.m[k][j];

                res.m[i][j] = sum;
            }
        return res;
    }
    ///@}

    /// Matrix - point multiplication
    template <typename Type2>
    Point4< Type2 > operator*(const Point4< Type2 > & point) const
    {
        if (flagBits == Matrix4x4<Type>::Identity)
            return point;

        Point4<Type2> res;
        for(int i = 0; i < 4; i++)
        {
            double sum = 0.0;
            for(int j = 0; j < 4; j++)
                sum += m[i][j]*point.data[j];

            res.data[i] = (Type2)sum;
        }

        return res;
    }

    /// Special case of matrix-point multiplication: geometric transformation
    template <typename Type2>
    Point3< Type2 > operator*(const Point3< Type2 > & point) const
    {
        if (flagBits == Matrix4x4<Type>::Identity)
            return point;

        Point3< Type2 > res;
        for(int i = 0; i < 3; i++)
        {
            double sum = 0.0;
            for(int j = 0; j < 3; j++)
                sum += m[i][j]*point.data[j];

            sum += m[i][3];
            res.data[i] = (Type2)sum;
        }

        return res;
    }

    ///@{
    /// Matrix - Scalar
    Matrix4x4 & operator*=(const Type & val)
    {
        for(int i = 0; i < size_; i++) data[i] *= val;
        flagBits = General;
        return *this;
    }
    Matrix4x4 & operator/=(const Type & val)
    {
        for(int i = 0; i < size_; i++) data[i] /= val;
        flagBits = General;
        return *this;
    }

    Matrix4x4 operator*(const Type & val) const
    {
        Matrix4x4 m = *this;
        for(int i = 0; i < size_; i++) m.data[i] = m.data[i] * val;
        m.flagBits = General;
        return m;
    }
    Matrix4x4 operator/(const Type & val) const
    {
        Matrix4x4 m = *this;
        for(int i = 0; i < size_; i++) m.data[i] = m.data[i] / val;
        m.flagBits = General;
        return m;
    }
    ///@}

    /// Unary minus
    Matrix4x4 operator-() const
    {
        Matrix4x4 m = *this;
        for(int i = 0; i < size_; i++) m.data[i] = -m.data[i];
        flagBits = General;
        return m;
    }

    /// check matrices are equal
    bool operator==(const Matrix4x4& m)const
    {
        for(int i = 0; i < size_; i++)
            if (data[i] != m.data[i])
                return false;
        return true;
    }

    /// check matrices are not equal
    bool operator!=(const Matrix4x4& m)const
    {
        return !(*this == m);
    }

    Type& operator()(int row, int col)
    {
        flagBits = General;
        return m[row][col];
    }

    const Type& operator()(int row, int col) const
    {
        return m[row][col];
    }

    /// Identity matrix
    static Matrix4x4 identity()
    {
        Matrix4x4 m;
        m.setToIdentity();
        return m;
    }
    /// Make current matrix to identity
    void setToIdentity()
    {
        for(int x = 0; x < rows_; x++)
            for(int y = 0; y < cols_; y++)
            {
                m[x][y] = x != y ? Type() : Type(1.0);
            }
        flagBits = Identity;
    }

    /// Check if matrix is an identity matrix
    bool isIdentity() const
    {
        if (flagBits == Identity)
            return true;
    
        if (m[0][0] != Type(1.0) || m[0][1] != Type()    || m[0][2] != Type()    || m[0][3] != Type()    )
            return false;

        if (m[1][0] != Type()    || m[1][1] != Type(1.0) || m[1][2] != Type()    || m[1][3] != Type()    )
            return false;

        if (m[2][0] != Type()    || m[2][1] != Type()    || m[2][2] != Type(1.0) || m[2][3] != Type()    )
            return false;

        if (m[3][0] != Type()    || m[3][1] != Type()    || m[3][2] != Type()    || m[3][3] != Type(1.0) )
            return false;

        flagBits = Identity;
        return true;
    }

    /// Return transposed matrix copy
    Matrix4x4 transposed() const
    {
        Matrix4x4 res;
        for(size_t i = 0; i < rows_; i++)
            for(size_t j = 0; j < cols_; j++)
                res.m[i][j] = m[j][i];

        return res;
    }

    /// Inversion
    /// @return false if matrix is singular and can't be inverted, otherwise true
    Matrix4x4< Type > inverted(bool *invertible = 0) const;
    
    Point3<Type> project(const Point3<Type> & point) const
    {
        Point3<Type> pr = *this * point; 

        Type m4sum = 0;
        for(size_t j = 0; j < 3; j++)
            m4sum += m.m[3][j] * point.data[j];
        m4sum += m.m[3][3];

        for(size_t j = 0; j < 3; j++)
            pr.data[j] = Type(pr.data[j]/m4sum);

        return pr;
    }

    ///@{
    /// Rotations (* - all angles in radians)
    static Matrix4x4 rotationX(Type angle)
    {
        Matrix4x4 r;
        r.fill(0);

        Type c = std::cos(angle);
        Type s = std::sin(angle);

        r.m[1][1] = r.m[2][2] = c;
        r.m[1][2] = -s; r.m[2][1] = s;
        r.m[0][0] = r.m[3][3] = 1;

        return r;
    }
    static Matrix4x4 rotationY(Type angle)
    {
        Matrix4x4 r;
        r.fill(0);

        Type c = std::cos(angle);
        Type s = std::sin(angle);

        r.m[0][0] = r.m[2][2] = c;
        r.m[0][2] = s; r.m[2][0] = -s;
        r.m[1][1] = r.m[3][3] = 1;

        return r;
    }
    static Matrix4x4 rotationZ(Type angle)
    {
        Matrix4x4 r;
        r.fill(0);

        Type c = std::cos(angle);
        Type s = std::sin(angle);

        r.m[0][0] = r.m[1][1] = c;
        r.m[0][1] = -s; r.m[1][0] = s;
        r.m[2][2] = r.m[3][3] = 1;

        return r;
    }
    
    static Matrix4x4 rotationX(Type angle, const Point3<Type> & center)
    {
        Matrix4x4 r = rotationX(angle);

        Point3<Type> t = -r*center+center;
        r.m[0][3] = t.x; r.m[1][3] = t.y; r.m[2][3] = t.z;

        return r;
    }
    static Matrix4x4 rotationY(Type angle, const Point3<Type> & center)
    {
        Matrix4x4 r = rotationY(angle);

        Point3<Type> t = -r*center+center;
        r.m[0][3] = t.x; r.m[1][3] = t.y; r.m[2][3] = t.z;

        return r;
    }
    static Matrix4x4 rotationZ(Type angle, const Point3<Type> & center)
    {
        Matrix4x4 r = rotationZ(angle);

        Point3<Type> t = -r*center+center;
        r.m[0][3] = t.x; r.m[1][3] = t.y; r.m[2][3] = t.z;

        return r;
    }
    ///@}
    
    /// ! Important ! Direction is a unit vector, don't forget to normalize it !!!
    static Matrix4x4 rotation(Type angle, const Point3<Type> & direction)
    {
        Matrix4x4 r;

        Type c = std::cos(angle);
        Type s = std::sin(angle);

        r.m[0][0] = c+(1-c)*direction.x*direction.x;       
        r.m[0][1] = (1-c)*direction.y*direction.x-s*direction.z; 
        r.m[0][2] = (1-c)*direction.z*direction.x+s*direction.y;

        r.m[1][0] = (1-c)*direction.x*direction.y+s*direction.z;
        r.m[1][1] = c+(1-c)*direction.y*direction.y;
        r.m[1][2] = (1-c)*direction.z*direction.y-s*direction.x;

        r.m[2][0] = (1-c)*direction.x*direction.z-s*direction.y;
        r.m[2][1] = (1-c)*direction.y*direction.z+s*direction.x;
        r.m[2][2] = c+(1-c)*direction.z*direction.z;

        r.m[0][3] = r.m[1][3] = r.m[2][3] = 0;
        r.m[3][0] = r.m[3][1] = r.m[3][2] = 0; r.m[3][3] = 1;

        return r;
    }

    /// ! Important ! Direction is a unit vector, don't forget to normalize it !!!
    static Matrix4x4 rotation(Type angle, const Point3<Type> & direction, const Point3<Type> & center)
    {
        Matrix4x4 r = rotation(angle, direction);

        Point3<Type> t = -r*center+center;
        r.m[0][3] = t.x; r.m[1][3] = t.y; r.m[2][3] = t.z;

        return r;
    }

    /// Translations 
    static Matrix4x4 translation(const Point3<Type> & direction)
    {
        Matrix4x4 t;
        t.setToIdentity();

        t.m[0][3] = direction.x; t.m[1][3] = direction.y; t.m[2][3] = direction.z;
        t.flagBits = General;

        return t;
    }

    ///@{
    /// Scale 
    static Matrix4x4 scale(Type factor)
    {
        Matrix4x4 s;
        s.fill(Type(0.0));

        s.m[0][0] = s.m[1][1] = s.m[2][2] = factor;
        s.m[3][3] = 1;

        return s;
    }
    static Matrix4x4 scale(Type factor, const Point3<Type> & center)
    {
        Matrix4x4 s = scale(factor);

        Point3<Type> t = -center*factor + center;
        s.m[0][3] = t.x; s.m[1][3] = t.y; s.m[2][3] = t.z;

        return s;
    }
    ///@}

    /// Inverse transformation matrix
    static Matrix4x4 inverseMotion(const Matrix4x4 &matrix)
    {
        /// get rotation and translation components of motion
        GenericMatrix<3,3,Type> r(matrix);
        Point3<Type> t( matrix.m[0][3], matrix.m[1][3], matrix.m[2][3] );

        /// inverse rotation
        r = transpose(r);

        /// assemble inverse motion matrix
        Matrix4x4 i(r);
        Point3<Type> it = -r*t;

        i.m[0][3] = it.x; i.m[1][3] = it.y; i.m[2][3] = it.z;
        i.m[3][0] = i.m[3][1] = i.m[3][2] = 0; i.m[3][3] = 1;

        return i;
    }

    /// Get perspective projection matrix
    static Matrix4x4 perspective(Type left, Type right, Type bottom, Type top, Type nearVal, Type farVal)
    {
        Matrix4x4 res;
        res.m[0][0] =  2.0f * nearVal / (right - left);
        res.m[0][1] =  0.0;
        res.m[0][2] =  (right + left) / (right - left);
        res.m[0][3] =  0.0;
        res.m[1][0] =  0.0;
        res.m[1][1] =  2.0f * nearVal / (top - bottom);
        res.m[1][2] =  (top + bottom) / (top - bottom);
        res.m[1][3] =  0.0;
        res.m[2][0] =  0.0;
        res.m[2][1] =  0.0;
        res.m[2][2] = -(farVal + nearVal) / (farVal - nearVal);
        res.m[2][3] = -2.0f * farVal * nearVal / (farVal - nearVal);
        res.m[3][0] =  0.0;
        res.m[3][1] =  0.0;
        res.m[3][2] = -1.0f;
        res.m[3][3] =  0.0;
        return res;
    }

    /// Get perspective projection matrix
    static Matrix4x4 perspectiveFov(float fovy, float aspect, float zNear, float zFar)
    {
        float f    = 1.0f / tan(fovy * 0.5f);
        float dneg = zNear - zFar;
        return Matrix4x4( f / aspect, 0.0f,    0.0f,                0.0f,
            0.0f,       f,       0.0f,                0.0f,
            0.0f,       0.0f,    (zFar + zNear)/dneg, 2.0f*zNear*zFar/dneg,
            0.0f,       0.0f,    -1.0f,               0.0f );
    }

    /// Get orthogonal matrix
    static Matrix4x4 ortho(Type left, Type right, Type bottom, Type top, Type nearVal, Type farVal)
    {
        Matrix4x4 res;
        res.m[0][0] =  2.0f / (right - left);
        res.m[0][1] =  0.0;
        res.m[0][2] =  0.0;
        res.m[0][3] = -(right + left) / (right - left);
        res.m[1][0] =  0.0;
        res.m[1][1] =  2.0f / (top - bottom);
        res.m[1][2] =  0.0;
        res.m[1][3] = -(top + bottom) / (top - bottom);
        res.m[2][0] =  0.0;
        res.m[2][1] =  0.0;
        res.m[2][2] = -2.0f / (farVal - nearVal);
        res.m[2][3] = -(farVal + nearVal) / (farVal - nearVal);
        res.m[3][0] =  0.0;
        res.m[3][1] =  0.0;
        res.m[3][2] =  0.0;
        res.m[3][3] =  1.0f;
        return res;
    }

    ///@{
    /// Conversion to plain data pointer operator
    operator Type * () { flagBits = General; return data; }
    operator const Type * () const { return data; }
    ///@}
    /// Returns the number of elements in the matrix
    int size() const { return size_; }

    /// matrix data
    union
    {
        struct
        {
            Type m[4][4];
        };

        Type data[4*4];
    };

    mutable int flagBits;           // Flag bits from the enum below.

    enum {
        Identity        = 0x0001,   // Identity matrix
        General         = 0x0002,   // General matrix, unknown contents
    };

protected:

    static int const rows_;
    static int const cols_;
    static int const size_;
};

template< typename Type > int const Matrix4x4<Type>::rows_ = 4;
template< typename Type > int const Matrix4x4<Type>::cols_ = 4;
template< typename Type > int const Matrix4x4<Type>::size_ = 4 * 4;

template< int rows, typename Type >
GenericMatrix< rows, 4, Type > operator*(const GenericMatrix< rows, 4, Type > & m1, const Matrix4x4< Type > & m2)
{
    GenericMatrix< rows, 4, Type > res;
    for(int i = 0; i < rows; i++)
        for(int j = 0; j < 4; j++)
        {
            Type sum = 0;
            for(int k = 0; k < 4; k++)
                sum += m1.m[i][k]*m2.m[k][j];

            res.m[i][j] = sum;
        }
    return res;
}

/// Inversion
template< typename Type >
Matrix4x4< Type > artec::sdk::base::Matrix4x4<Type>::inverted( bool *invertible /*= 0*/ ) const
{
    //Copy source matrix
    Matrix4x4< Type > work = *this;

    //build identity matrix
    Matrix4x4< Type > result;
    result.setToIdentity();

    const int size = 4;
    for(int i = 0; i < size; i++)
    {
        int j;

        for(j = i; (j < size) && (isZero(work[j*size+i])); j++) {};

        // matrix is singular
        if (j == size)
        {
            if (invertible)
                *invertible = false;
            return result;
        }

        if (i != j)
            for(int k = 0; k < size; k++)
            {
                Type tmp = result[i*size+k]; result[i*size+k] = result[j*size+k]; result[j*size+k] = tmp;
                tmp = work[i*size+k]; work[i*size+k] = work[j*size+k]; work[j*size+k] = tmp;
            }

            Type d = 1/work[i*size+i];
            for(j = 0; j < size; j++)
            {
                result[i*size+j] *= d;
                work[i*size+j] *= d;
            }

            for(j = i+1; j < size; j++)
            {
                d = work[j*size+i];
                for(int k = 0; k < size; k++)
                {
                    result[j*size+k] -= result[i*size+k] * d;
                    work[j*size+k] -= work[i*size+k] * d;
                }
            }
    }

    for(int i = size-1; i > 0; i--)
        for(int j = 0; j < i; j++)
        {
            Type d = work[j*size+i];
            for(int k = 0; k < size; k++)
            {
                result[j*size+k] -= result[i*size+k] * d;
                work[j*size+k] -= work[i*size+k] * d;
            }
        }
    result.flagBits = Matrix4x4<Type>::General;

    if (invertible)
        *invertible = true;
    return result;
}

/// Return false if matrix is singular and can't be inverted, otherwise true
template < typename Type > inline
    bool invert(const Matrix4x4< Type >& matrix, Matrix4x4< Type >& result)
{
    bool invertable = false;
    result = matrix.inverted(&invertable);
    return invertable;
}

/// Inversion (another one form) Given matrix shouldn't be singular.
/// Throws std::runtime_error() if matrix is singular, otherwise return inverse matrix
template < typename Type > inline
    Matrix4x4< Type > invert(const Matrix4x4< Type > & matrix)
{
    Matrix4x4< Type > res;
    if (invert(matrix,res))
        return res;
    else
        throw std::runtime_error("artec::sdk::base::invert: Try to invert singular matrix");
}

template < typename Type > inline
    Point2< Type > project(const Point3< Type > & point, const GenericMatrix< 3, 4, Type > & m)
{
    Point3< Type > pr = (Matrix4x4< Type >)m * point;
    return Point2< Type >(pr.x / pr.z, pr.y / pr.z);
}

template < typename Type > inline
    Point3< Type > project(const Point3< Type > & point, const Matrix4x4< Type > & m)
{
    return m.project(point);
}

// Selected matrices
typedef GenericMatrix< 2, 2, float >    Matrix2x2F;
typedef GenericMatrix< 2, 3, float >    Matrix2x3F;
typedef GenericMatrix< 2, 4, float >    Matrix2x4F;
typedef GenericMatrix< 3, 3, float >    Matrix3x3F;
typedef GenericMatrix< 3, 4, float >    Matrix3x4F;
typedef Matrix4x4< float >              Matrix4x4F;

typedef GenericMatrix< 2, 2, double >   Matrix2x2D;
typedef GenericMatrix< 2, 3, double >   Matrix2x3D;
typedef GenericMatrix< 2, 4, double >   Matrix2x4D;
typedef GenericMatrix< 3, 3, double >   Matrix3x3D;
typedef GenericMatrix< 3, 4, double >   Matrix3x4D;
typedef Matrix4x4< double >             Matrix4x4D;

} } } // namespace artec::sdk::base

#endif //_MATRIX_H_