weightKernel.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 PONCA_MULTIARCH_INCLUDE_CU_STD(cmath)
 
namespace Ponca
{
template <typename _Scalar>
class ConstantWeightKernel
{
public:
    typedef _Scalar Scalar;
 
    // Init
    PONCA_MULTIARCH inline ConstantWeightKernel(const Scalar& _value = Scalar(1.)) : m_y(_value){}
    PONCA_MULTIARCH inline void setValue(const Scalar& _value){ m_y = _value; }
 
    // Functor
    PONCA_MULTIARCH inline Scalar f  (const Scalar&) const { return m_y; }
    PONCA_MULTIARCH inline Scalar df (const Scalar&) const { return Scalar(0.); }
    PONCA_MULTIARCH inline Scalar ddf(const Scalar&) const { return Scalar(0.); }
 
    static constexpr bool isDValid = true;
    static constexpr bool isDDValid = true;
 
private:
    Scalar m_y; 
};// class ConstantWeightKernel
 
 
template <typename _Scalar>
class SmoothWeightKernel
{
public:
    typedef _Scalar Scalar;
 
    // Functor
    PONCA_MULTIARCH inline Scalar f  (const Scalar& _x) const { Scalar v = _x*_x - Scalar(1.); return v*v; }
    PONCA_MULTIARCH inline Scalar df (const Scalar& _x) const { return Scalar(4.)*_x*(_x*_x-Scalar(1.)); }
    PONCA_MULTIARCH inline Scalar ddf(const Scalar& _x) const { return Scalar(12.)*_x*_x - Scalar(4.); }
    static constexpr bool isDValid = true;
    static constexpr bool isDDValid = true;
};//class SmoothWeightKernel
 
template <typename _Scalar, int m, int n>
class PolynomialSmoothWeightKernel
{
public:
 
    typedef _Scalar Scalar;
    // Functor
    PONCA_MULTIARCH inline Scalar f  (const Scalar& _x) const {
        PONCA_MULTIARCH_STD_MATH(pow);
        return pow(
            pow(_x, Scalar(n)) - Scalar(1.),
            Scalar(m)
        );
    }
    PONCA_MULTIARCH inline Scalar df (const Scalar& _x) const {
        PONCA_MULTIARCH_STD_MATH(pow);
        return pow(
            Scalar(m*n)*_x,
            Scalar(n-1)) * pow(pow(_x, Scalar(n)) -1, Scalar(m-1)
        );
    }
    PONCA_MULTIARCH inline Scalar ddf(const Scalar& _x) const {
        PONCA_MULTIARCH_STD_MATH(pow);
        return Scalar((m-1)*m*n*n)
            * pow( _x, Scalar(2*n-2))
            * pow(
                pow(_x, Scalar(n))-Scalar(1),
                Scalar(m-2)
            )
            + Scalar(m*(n-1)*n)
            * pow(
                _x,
                Scalar(n-2)
            )
            * pow(
                pow(_x, Scalar(n))-Scalar(1),
                Scalar(m-1)
            );
    }
    static constexpr bool isDValid = true;
    static constexpr bool isDDValid = true;
};//class PolynomialSmoothWeightKernel
 
template <typename _Scalar>
class WendlandWeightKernel
{
public:
    typedef _Scalar Scalar;
 
    // Functor
    PONCA_MULTIARCH inline Scalar f  (const Scalar& _x) const {
        const Scalar v = Scalar(1.) - _x;
        return v * v * v * v * ((Scalar(4.) * _x) + Scalar(1.));
    }
    PONCA_MULTIARCH inline Scalar df (const Scalar& _x) const {
        const Scalar v = _x - Scalar(1.);
        return Scalar(20.) * _x * v * v * v;
    }
    PONCA_MULTIARCH inline Scalar ddf(const Scalar& _x) const {
        const Scalar v = _x - Scalar(1.);
        return v * v * (Scalar(80.) * _x - Scalar(20));
    }
    static constexpr bool isDValid = true;
    static constexpr bool isDDValid = true;
};//class WendlandWeightKernel
 
 
template <typename _Scalar>
class SingularWeightKernel
{
public:
    typedef _Scalar Scalar;
 
    // Functor
    PONCA_MULTIARCH inline Scalar f  (const Scalar& _x) const {
        return Scalar(1.) / (_x * _x);
    }
    PONCA_MULTIARCH inline Scalar df (const Scalar& _x) const {
        return Scalar(-2.) / (_x * _x * _x);
    }
    PONCA_MULTIARCH inline Scalar ddf(const Scalar& _x) const {
        return Scalar(6.) / (_x * _x * _x * _x);
    }
    static constexpr bool isDValid = true;
    static constexpr bool isDDValid = true;
};//class SingularWeightKernel
 
 
template <typename _Scalar>
class CompactExpWeightKernel
{
public:
    typedef _Scalar Scalar;
 
    // Functor
    PONCA_MULTIARCH inline Scalar f  (const Scalar& _x) const { Scalar v = _x*_x; return exp(-v/(Scalar(1)-v)); }
    PONCA_MULTIARCH inline Scalar df (const Scalar& _x) const { Scalar v = _x*_x; Scalar mv = v-Scalar(1); return -(Scalar(2) * exp(v/mv) * _x)/(mv*mv); }
    PONCA_MULTIARCH inline Scalar ddf(const Scalar& _x) const {
        Scalar v = _x*_x;            // x^2
        Scalar mv = v-Scalar(1);     // x^2-1
        Scalar mvpow = Scalar(2)/mv; // 2/(x^2-1)
        Scalar cmvpow = pow(_x,mvpow); // x^{2/(x^2-1)}
        return Scalar(2) * exp(cmvpow) * ((Scalar(4) * pow(_x,mvpow + Scalar(2)) * log(_x) - mv * (-Scalar(3) * v + Scalar(2) * cmvpow - Scalar(1))))/(mv*mv*mv*mv);
    }
 
    static constexpr bool isDValid = true;
    static constexpr bool isDDValid = false;
};//class CompactExpWeightKernel
 
 
}// namespace Ponca