MRMatrix3Decompose.h

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#pragma once
 
#include "MRMatrix3.h"
 
namespace MR
{
 
template <typename T>
void decomposeMatrix3( const Matrix3<T>& m, Matrix3<T>& rotation, Matrix3<T>& scaling )
{
    const auto [q, r] = m.qr();
 
    scaling = {};
    Matrix3<T> sign;
    for ( int i = 0; i < 3; ++i )
    {
        scaling[i][i] = std::abs( r[i][i] );
        if ( r[i][i] < 0 )
            sign[i][i] = -1;
    }
    rotation = q * sign;
}
 
template <typename T>
bool isRigid( const Matrix3<T>& m )
{
    Matrix3<T> rot, scale;
    decomposeMatrix3( m, rot, scale );
    auto eps = T( 10 ) * std::numeric_limits<T>::epsilon();
    if ( std::abs( scale.x.x - T( 1 ) ) > eps )
        return false;
    if ( std::abs( scale.y.y - T( 1 ) ) > eps )
        return false;
    if ( std::abs( scale.z.z - T( 1 ) ) > eps )
        return false;
    return true;
}
 
} // namespace MR