weingarten.h

/*
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/.
*/
 
#pragma once
 
#include "../../defines.h"
#include "../concepts.h"
 
#define FUNDAMENTAL_FORM_WEINGARTEN_ESTIMATOR_REQUIREMENTS \
    ProvidesFirstFondamentalFormComponents<T>&& ProvidesSecondFondamentalFormComponents<T>
#define WIENGARTEN_CURVATURE_ESTIMATOR_REQUIREMENTS ProvidesTangentPlaneBasis<T>&& ProvidesWeingartenMap<T>
 
namespace Ponca
{
    template <class DataPoint, class _NFilter, typename T>
        requires FUNDAMENTAL_FORM_WEINGARTEN_ESTIMATOR_REQUIREMENTS
    class FundamentalFormWeingartenEstimator : public T
    {
        PONCA_FITTING_DECLARE_DEFAULT_TYPES
        using Matrix2 = Eigen::Matrix<Scalar, 2, 2>;
        static_assert(DataPoint::Dim == 3, "FundamentalFormWeingartenEstimator is only valid in 3D");
 
    public:
        PONCA_EXPLICIT_CAST_OPERATORS(FundamentalFormWeingartenEstimator, fundamentalFormWeingartenEstimator)
        PONCA_EXPLICIT_CAST_OPERATORS(FundamentalFormWeingartenEstimator, firstFondamentalFormComponent)
        PONCA_EXPLICIT_CAST_OPERATORS(FundamentalFormWeingartenEstimator, secondFondamentalFormComponent)
 
        PONCA_MULTIARCH [[nodiscard]] inline Matrix2 firstFundamentalForm() const;
 
        template <typename Matrix2Derived>
        PONCA_MULTIARCH inline void firstFundamentalForm(Matrix2Derived& first) const;
 
        PONCA_MULTIARCH [[nodiscard]] inline Matrix2 secondFundamentalForm() const;
 
        template <typename Matrix2Derived>
        PONCA_MULTIARCH inline void secondFundamentalForm(Matrix2Derived& second) const;
 
        PONCA_MULTIARCH [[nodiscard]] inline Matrix2 weingartenMap() const;
 
        template <typename Matrix2Derived>
        PONCA_MULTIARCH inline void weingartenMap(Matrix2Derived& w) const;
 
        PONCA_MULTIARCH inline Scalar kMean() const;
 
        PONCA_MULTIARCH inline Scalar GaussianCurvature() const;
    };
 
    template <class DataPoint, class _NFilter, int DiffType, typename T>
    class NormalDerivativeWeingartenEstimator : public T
    {
        PONCA_FITTING_DECLARE_DEFAULT_TYPES
        PONCA_FITTING_DECLARE_MATRIX_TYPE
        PONCA_FITTING_DECLARE_DEFAULT_DER_TYPES
        using Matrix2 = Eigen::Matrix<Scalar, 2, 2>;
        static_assert(DataPoint::Dim == 3, "NormalDerivativeWeingartenEstimator is only valid in 3D");
        static_assert(Base::isSpaceDer(), "NormalDerivativeWeingartenEstimator requires spatial derivation");
 
    private:
        MatrixType m_tangentBasis{MatrixType::Zero()};
 
    public:
        PONCA_EXPLICIT_CAST_OPERATORS_DER(NormalDerivativeWeingartenEstimator, normalDerivativeWeingartenEstimator)
        PONCA_EXPLICIT_CAST_OPERATORS_DER(NormalDerivativeWeingartenEstimator, tangentPlaneBasis)
        PONCA_FITTING_DECLARE_FINALIZE
 
        PONCA_MULTIARCH [[nodiscard]] inline Matrix2 weingartenMap() const;
 
        template <typename Matrix2Derived>
        PONCA_MULTIARCH inline void weingartenMap(Matrix2Derived& w) const;
 
        PONCA_MULTIARCH inline VectorType worldToTangentPlane(const VectorType& _q,
                                                              bool _isPositionVector = true) const;
 
        PONCA_MULTIARCH inline VectorType tangentPlaneToWorld(const VectorType& _q,
                                                              bool _isPositionVector = true) const;
    };
 
    namespace internal
    {
        template <class DataPoint, class _NFilter, typename T>
            requires WIENGARTEN_CURVATURE_ESTIMATOR_REQUIREMENTS
        class WeingartenCurvatureEstimatorBase : public T
        {
            PONCA_FITTING_DECLARE_DEFAULT_TYPES
            using Matrix2 = Eigen::Matrix<Scalar, 2, 2>;
            static_assert(DataPoint::Dim == 3, "WeingartenCurvatureEstimator is only valid in 3D");
 
        private:
            Eigen::SelfAdjointEigenSolver<Matrix2> m_solver;
 
        public:
            PONCA_FITTING_DECLARE_FINALIZE
 
            PONCA_MULTIARCH [[nodiscard]] inline Scalar kmin() const { return m_solver.eigenvalues().x(); }
 
            PONCA_MULTIARCH [[nodiscard]] inline Scalar kmax() const { return m_solver.eigenvalues().y(); }
 
            PONCA_MULTIARCH [[nodiscard]] inline VectorType kminDirection() const
            {
                VectorType vmin;
                vmin(0)                       = Scalar(0); // set height
                vmin.template bottomRows<2>() = m_solver.eigenvectors().col(0);
                vmin                          = Base::tangentPlaneToWorld(vmin, false);
                return vmin;
            }
 
            PONCA_MULTIARCH [[nodiscard]] inline VectorType kmaxDirection() const
            {
                VectorType vmax;
                vmax(0)                       = Scalar(0); // set height
                vmax.template bottomRows<2>() = m_solver.eigenvectors().col(1);
                vmax                          = Base::tangentPlaneToWorld(vmax, false);
                return vmax;
            }
 
            PONCA_MULTIARCH [[nodiscard]] inline Scalar kMean() const { return (kmin() + kmax()) / Scalar(2); }
 
            PONCA_MULTIARCH [[nodiscard]] inline Scalar GaussianCurvature() const { return kmin() * kmax(); }
        };
    } // namespace internal
 
    template <class DataPoint, class _NFilter, typename T>
    struct WeingartenCurvatureEstimator : public internal::WeingartenCurvatureEstimatorBase<DataPoint, _NFilter, T>
    {
        PONCA_FITTING_DECLARE_DEFAULT_TYPES
        PONCA_EXPLICIT_CAST_OPERATORS(WeingartenCurvatureEstimator, meanCurvature)
        PONCA_EXPLICIT_CAST_OPERATORS(WeingartenCurvatureEstimator, curvatureTensor)
    };
 
    template <class DataPoint, class _NFilter, int DiffType, typename T>
    struct WeingartenCurvatureEstimatorDer : public internal::WeingartenCurvatureEstimatorBase<DataPoint, _NFilter, T>
    {
        PONCA_FITTING_DECLARE_DEFAULT_TYPES
        PONCA_FITTING_DECLARE_DEFAULT_DER_TYPES
        PONCA_EXPLICIT_CAST_OPERATORS_DER(WeingartenCurvatureEstimatorDer, meanCurvature)
        PONCA_EXPLICIT_CAST_OPERATORS_DER(WeingartenCurvatureEstimatorDer, curvatureTensor)
    };
 
} // namespace Ponca
 
#include "weingarten.hpp"