algebraicSphere.hpp

/*
 This Source Code Form is subject to the terms of the Mozilla Public
 License, v. 2.0. If a copy of the MPL was not distributed with this
 file, You can obtain one at http://mozilla.org/MPL/2.0/.
*/
 
template <class DataPoint, class _NFilter, typename T> // Outer template for the class
    requires ALGEBRAIC_SPHERE_REQUIREMENTS
typename AlgebraicSphere<DataPoint, _NFilter, T>::VectorType // Return type
AlgebraicSphere<DataPoint, _NFilter, T>::project(const VectorType& _q) const
{
    PONCA_MULTIARCH_STD_MATH(sqrt);
 
    // turn to centered basis
    const VectorType lq = Base::getNeighborFrame().convertToLocalBasis(_q);
 
    if (isPlane())
    {
        Scalar sqnorm = m_ul.squaredNorm();
        return Base::getNeighborFrame().convertToGlobalBasis(lq - m_ul * (lq.dot(m_ul)) / sqnorm);
    }
    else
    {
        Scalar potential = potentialLocal(lq);
        VectorType grad  = primitiveGradientLocal(lq);
        Scalar norm      = grad.norm();
        Scalar t         = -(norm - sqrt(norm * norm - Scalar(4) * m_uq * potential)) / (Scalar(2) * m_uq * norm);
        return Base::getNeighborFrame().convertToGlobalBasis(lq + t * grad);
    }
}
 
template <class DataPoint, class _NFilter, typename T>
    requires ALGEBRAIC_SPHERE_REQUIREMENTS
typename AlgebraicSphere<DataPoint, _NFilter, T>::Scalar AlgebraicSphere<DataPoint, _NFilter, T>::potentialLocal(
    const VectorType& _lq) const
{
    return m_uc + _lq.dot(m_ul) + m_uq * _lq.squaredNorm();
}
 
template <class DataPoint, class _NFilter, typename T>
    requires ALGEBRAIC_SPHERE_REQUIREMENTS
typename AlgebraicSphere<DataPoint, _NFilter, T>::VectorType AlgebraicSphere<
    DataPoint, _NFilter, T>::primitiveGradientLocal(const VectorType& _lq) const
{
    return (m_ul + Scalar(2.) * m_uq * _lq);
}