heightField.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"
 
#include <Eigen/Dense>
 
#define HEIGHT_FIELD_REQUIREMENTS Is3D<DataPoint>
#define QUADRATIC_HEIGHT_FIELD_REQUIREMENTS ProvidesHeightFieldBase<T>
 
namespace Ponca
{
    template <class DataPoint, class _NFilter, typename T>
        requires HEIGHT_FIELD_REQUIREMENTS
    class HeightField : public T
    {
        PONCA_FITTING_DECLARE_DEFAULT_TYPES
 
        PONCA_EXPLICIT_CAST_OPERATORS(HeightField, heightFieldBase)
 
        
        PONCA_MULTIARCH [[nodiscard]] inline const Scalar& getHFromLocalCoordinates(const VectorType& _lq) const
        {
            return *(_lq.data());
        }
 
        PONCA_MULTIARCH [[nodiscard]] inline Scalar& getHFromLocalCoordinates(VectorType& _lq) const
        {
            return *(_lq.data());
        }
 
        PONCA_MULTIARCH [[nodiscard]] inline const Scalar& getUFromLocalCoordinates(const VectorType& _lq) const
        {
            return *(_lq.data() + 1);
        }
 
        PONCA_MULTIARCH [[nodiscard]] inline Scalar& getUFromLocalCoordinates(VectorType& _lq) const
        {
            return *(_lq.data() + 1);
        }
 
        PONCA_MULTIARCH [[nodiscard]] inline const Scalar& getVFromLocalCoordinates(const VectorType& _lq) const
        {
            return *(_lq.data() + 2);
        }
 
        PONCA_MULTIARCH [[nodiscard]] inline Scalar& getVFromLocalCoordinates(VectorType& _lq)
        {
            return *(_lq.data() + 2);
        }
    };
 
    template <class DataPoint, class _NFilter, typename T>
        requires QUADRATIC_HEIGHT_FIELD_REQUIREMENTS
    class QuadraticHeightField : public T
    {
        PONCA_FITTING_DECLARE_DEFAULT_TYPES
        using HeightFieldCoefficients = Eigen::Matrix<Scalar, 6, 1>;
        static_assert(DataPoint::Dim == 3, "QuadraticHeightField is only valid in 3D");
 
    protected:
        HeightFieldCoefficients m_coeffs{HeightFieldCoefficients::Zero()};
 
    public:
        PONCA_MULTIARCH inline QuadraticHeightField() : Base() { init(); }
 
        PONCA_EXPLICIT_CAST_OPERATORS(QuadraticHeightField, heightField)
        PONCA_EXPLICIT_CAST_OPERATORS(QuadraticHeightField, quadraticHeightField)
 
        PONCA_MULTIARCH inline void setQuadric(const HeightFieldCoefficients& coeffs) { m_coeffs = coeffs; }
 
        PONCA_MULTIARCH [[nodiscard]] inline const HeightFieldCoefficients& coeffs() const { return m_coeffs; }
 
        PONCA_MULTIARCH inline void init()
        {
            Base::init();
            m_coeffs.setZero();
        }
 
        PONCA_MULTIARCH [[nodiscard]] inline bool isValid() const
        {
            return !m_coeffs.isApprox(HeightFieldCoefficients::Zero());
        }
 
        PONCA_MULTIARCH [[nodiscard]] inline bool operator==(
            const QuadraticHeightField<DataPoint, _NFilter, T>& other) const
        {
            return m_coeffs.isApprox(other.m_params);
        }
 
        PONCA_MULTIARCH [[nodiscard]] inline bool operator!=(
            const QuadraticHeightField<DataPoint, _NFilter, T>& other) const
        {
            return !((*this) == other);
        }
 
        PONCA_MULTIARCH [[nodiscard]] inline Scalar height(Scalar u, Scalar v) const
        {
            return h_uu() * u * u + h_vv() * v * v + h_uv() * u * v + h_u() * u + h_v() * v + h_c();
        }
 
        PONCA_MULTIARCH [[nodiscard]] inline const Scalar& h_uu() const { return *(m_coeffs.data()); }
        PONCA_MULTIARCH [[nodiscard]] inline const Scalar& h_vv() const { return *(m_coeffs.data() + 1); }
        PONCA_MULTIARCH [[nodiscard]] inline const Scalar& h_uv() const { return *(m_coeffs.data() + 2); }
        PONCA_MULTIARCH [[nodiscard]] inline const Scalar& h_u() const { return *(m_coeffs.data() + 3); }
        PONCA_MULTIARCH [[nodiscard]] inline const Scalar& h_v() const { return *(m_coeffs.data() + 4); }
        PONCA_MULTIARCH [[nodiscard]] inline const Scalar& h_c() const { return *(m_coeffs.data() + 5); }
 
        PONCA_MULTIARCH [[nodiscard]] inline Scalar dh_du(Scalar u = Scalar(0), Scalar v = Scalar(0)) const
        {
            return Scalar(2) * h_uu() * u + h_uv() * v + h_u();
        }
 
        PONCA_MULTIARCH [[nodiscard]] inline Scalar dh_dv(Scalar u = Scalar(0), Scalar v = Scalar(0)) const
        {
            return Scalar(2) * h_vv() * v + h_uv() * u + h_v();
        }
 
        PONCA_MULTIARCH [[nodiscard]] inline Scalar d2h_duu(Scalar u = Scalar(0), Scalar v = Scalar(0)) const
        {
            return Scalar(2) * h_uu();
        }
 
        PONCA_MULTIARCH [[nodiscard]] inline Scalar d2h_dvv(Scalar u = Scalar(0), Scalar v = Scalar(0)) const
        {
            return Scalar(2) * h_vv();
        }
 
        PONCA_MULTIARCH [[nodiscard]] inline Scalar d2h_duv(Scalar u = Scalar(0), Scalar v = Scalar(0)) const
        {
            return h_uv();
        }
 
        PONCA_MULTIARCH [[nodiscard]] inline VectorType heightTangentULocal(const VectorType& _localQ) const
        {
            const Scalar tu = dh_du(Base::getUFromLocalCoordinates(_localQ), Base::getVFromLocalCoordinates(_localQ));
            return VectorType(tu, Scalar(1), Scalar(0)).normalized();
        }
 
        PONCA_MULTIARCH [[nodiscard]] inline VectorType heightTangentVLocal(const VectorType& _localQ) const
        {
            const Scalar tv = dh_dv(Base::getUFromLocalCoordinates(_localQ), Base::getVFromLocalCoordinates(_localQ));
            return VectorType(tv, Scalar(0), Scalar(1)).normalized();
        }
    }; // class QuadraticHeightField
    template <class DataPoint, class _NFilter, typename T>
        requires QUADRATIC_HEIGHT_FIELD_REQUIREMENTS
    class RestrictedQuadraticHeightField : public T
    {
        PONCA_FITTING_DECLARE_DEFAULT_TYPES
        using HeightFieldCoefficients = Eigen::Matrix<Scalar, 4, 1>;
        static_assert(DataPoint::Dim == 3, "QuadraticHeightField is only valid in 3D");
 
    protected:
        HeightFieldCoefficients m_coeffs{HeightFieldCoefficients::Zero()};
 
    public:
        PONCA_MULTIARCH inline RestrictedQuadraticHeightField() : Base() { init(); }
 
        PONCA_EXPLICIT_CAST_OPERATORS(QuadraticHeightField, heightField)
        PONCA_EXPLICIT_CAST_OPERATORS(RestrictedQuadraticHeightField, quadraticHeightField)
 
        PONCA_MULTIARCH inline void setQuadric(const HeightFieldCoefficients& coeffs) { m_coeffs = coeffs; }
 
        PONCA_MULTIARCH [[nodiscard]] inline const HeightFieldCoefficients& coeffs() const { return m_coeffs; }
 
        PONCA_MULTIARCH inline void init()
        {
            Base::init();
            m_coeffs.setZero();
        }
 
        PONCA_MULTIARCH [[nodiscard]] inline bool isValid() const
        {
            return !m_coeffs.isApprox(HeightFieldCoefficients::Zero());
        }
 
        PONCA_MULTIARCH [[nodiscard]] inline bool operator==(
            const RestrictedQuadraticHeightField<DataPoint, _NFilter, T>& other) const
        {
            return m_coeffs.isApprox(other.m_params);
        }
 
        PONCA_MULTIARCH [[nodiscard]] inline bool operator!=(
            const RestrictedQuadraticHeightField<DataPoint, _NFilter, T>& other) const
        {
            return !((*this) == other);
        }
 
        template <typename Other>
        PONCA_MULTIARCH [[nodiscard]] inline bool isApprox(
            const Other& other, const Scalar& epsilon = Eigen::NumTraits<Scalar>::dummy_precision()) const
        {
            return m_coeffs.isApprox(other.m_params, epsilon);
        }
 
        PONCA_MULTIARCH [[nodiscard]] inline Scalar height(Scalar u, Scalar v) const
        {
            return h_uu() * u * u + h_vv() * v * v + h_uv() * u * v + h_c();
        }
 
        PONCA_MULTIARCH [[nodiscard]] inline const Scalar& h_uu() const { return *(m_coeffs.data()); }
        PONCA_MULTIARCH [[nodiscard]] inline const Scalar& h_vv() const { return *(m_coeffs.data() + 1); }
        PONCA_MULTIARCH [[nodiscard]] inline const Scalar& h_uv() const { return *(m_coeffs.data() + 2); }
        PONCA_MULTIARCH [[nodiscard]] inline const Scalar& h_c() const { return *(m_coeffs.data() + 3); }
 
        PONCA_MULTIARCH [[nodiscard]] inline Scalar dh_du(Scalar u = Scalar(0), Scalar v = Scalar(0)) const
        {
            return Scalar(2) * h_uu() * u + h_uv() * v;
        }
 
        PONCA_MULTIARCH [[nodiscard]] inline Scalar dh_dv(Scalar u = Scalar(0), Scalar v = Scalar(0)) const
        {
            return Scalar(2) * h_vv() * v + h_uv() * u;
        }
 
        PONCA_MULTIARCH [[nodiscard]] inline Scalar d2h_duu(Scalar u = Scalar(0), Scalar v = Scalar(0)) const
        {
            return Scalar(2) * h_uu();
        }
 
        PONCA_MULTIARCH [[nodiscard]] inline Scalar d2h_dvv(Scalar u = Scalar(0), Scalar v = Scalar(0)) const
        {
            return Scalar(2) * h_vv();
        }
 
        PONCA_MULTIARCH [[nodiscard]] inline Scalar d2h_duv(Scalar u = Scalar(0), Scalar v = Scalar(0)) const
        {
            return h_uv();
        }
 
        PONCA_MULTIARCH [[nodiscard]] inline VectorType heightTangentULocal(const VectorType& _localQ) const
        {
            const Scalar tu = dh_du(Base::getUFromLocalCoordinates(_localQ), Base::getVFromLocalCoordinates(_localQ));
            return VectorType(tu, Scalar(1), Scalar(0)).normalized();
        }
 
        PONCA_MULTIARCH [[nodiscard]] inline VectorType heightTangentVLocal(const VectorType& _localQ) const
        {
            const Scalar tv = dh_dv(Base::getUFromLocalCoordinates(_localQ), Base::getVFromLocalCoordinates(_localQ));
            return VectorType(tv, Scalar(0), Scalar(1)).normalized();
        }
    }; // class RestrictedQuadraticHeightField
 
} // namespace Ponca