MRQuadraticForm.h

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#pragma once
 
#include "MRSymMatrix2.h"
#include "MRSymMatrix3.h"
 
namespace MR
{
 

template <typename V>
struct QuadraticForm
{
    using T = typename V::ValueType;
    using SM = typename V::SymMatrixType;
 
    SM A;
    T c = 0;
    
    [[nodiscard]] T eval( const V & x ) const { return dot( x, A * x ) + c; }

    void addDistToOrigin( T weight ) { A += SM::diagonal( weight ); }

    void addDistToPlane( const V & planeUnitNormal )           { A +=          outerSquare( planeUnitNormal ); }
    void addDistToPlane( const V & planeUnitNormal, T weight ) { A += weight * outerSquare( planeUnitNormal ); }

    void addDistToLine( const V & lineUnitDir )           { A +=            SM::identity() - outerSquare( lineUnitDir ); }
    void addDistToLine( const V & lineUnitDir, T weight ) { A += weight * ( SM::identity() - outerSquare( lineUnitDir ) ); }
};

template <typename V>
[[nodiscard]] MRMESH_API std::pair< QuadraticForm<V>, V > sum(
    const QuadraticForm<V> & q0, const V & x0,
    const QuadraticForm<V> & q1, const V & x1, 
    bool minAmong01 = false ); 

template <typename V>
[[nodiscard]] MRMESH_API QuadraticForm<V> sumAt(
    const QuadraticForm<V> & q0, const V & x0,
    const QuadraticForm<V> & q1, const V & x1,
    const V & pos );
 
}