WeightFunc.h

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#ifndef __GfxTL_WEIGHTFUNC_HEADER__
#define __GfxTL_WEIGHTFUNC_HEADER__
#include <iterator>
#include <GfxTL/MathHelper.h>
 
namespace GfxTL
{
 
    template< class ScalarT >
    class BSplineWeightFunc
    {
    public:
        typedef ScalarT ScalarType;
 
        BSplineWeightFunc(ScalarType r)
        {
            _r = r;
            _f = ScalarType(1.5) / r;
        }
 
        ScalarType operator()(ScalarType dist) const
        {
            if (dist >= _r)
            {
                return 0;
            }
            return EvalBSpline(_f * dist);
        }
 
    private:
        ScalarType EvalBSpline(ScalarType t) const
        {
            //B-spline (degree = 2)
            if (t < ScalarType(0.5))
            {
                return -t * t + ScalarType(0.75);
            }
            else
                return ScalarType(0.5) * (ScalarType(1.5) - t)
                       * (ScalarType(1.5) - t);
            /*ScalarType x = t + (ScalarType)1.5;   // shifted value
            if(((ScalarType)-1.5 <= t) && (t < (ScalarType)-0.5))
                return  (ScalarType)0.5 * x * x;
            if(((ScalarType)-0.5 <= t) && (t < (ScalarType)0.5))
                return (ScalarType)-1.0 * x * x + (ScalarType)3.0 * x
                    - (ScalarType)(3.0 / 2.0);
            if(((ScalarType)0.5 <= t) && (t < (ScalarType)1.5))
                return (ScalarType)0.5 * x * x - (ScalarType)3.0 * x
                    + (ScalarType)(9.0 / 2.0);
            return (ScalarType)0.0; // bspline zero*/
        }
 
    private:
        ScalarType _f;
        ScalarType _r;
    };
 
    template< class Point >
    class UnitWeightFunc
    {
    public:
        typedef Point PointType;
        typedef typename Point::ScalarType ScalarType;
 
        double Weight(const Point&)
        {
            return (double)1;
        }
 
        double operator()(const Point&)
        {
            return (double)1;
        }
    };
 
    class UnitWeightIterator
    {
    public:
        typedef unsigned int value_type;
        typedef unsigned int* pointer;
        typedef unsigned int& reference;
        typedef std::forward_iterator_tag iterator_category;
        typedef size_t difference_type;
 
        const unsigned int operator*() const
        {
            return 1;
        }
 
        UnitWeightIterator operator++() const
        {
            return *this;
        }
    };
 
    template< class PointT >
    class InverseDistanceSingularWeightFunc
    {
    public:
        typedef PointT PointType;
        typedef typename PointType::ScalarType ScalarType;
 
        InverseDistanceSingularWeightFunc(const PointType& center,
                                          ScalarType radius)
            : _center(center)
            , _radius(radius)
        {}
 
        ScalarType operator()(const PointType& p) const
        {
            ScalarType d = (p - _center).Length();
            return operator()(d);
        }
 
        ScalarType operator()(ScalarType d) const
        {
            ScalarType a = Math< ScalarType >::Max(_radius - d, 0)
                           / (_radius * d);
            return a * a;
        }
 
    private:
        PointType _center;
        ScalarType _radius;
    };
 
    template< class PointT >
    class InterpolatingExponentialWeightFunc
    {
    public:
        typedef PointT PointType;
        typedef typename PointType::ScalarType ScalarType;
 
        InterpolatingExponentialWeightFunc(const PointType& center,
                                           ScalarType sqrRadius)
            : _center(center)
        {
            _scale = ScalarType(11.38335808) / sqrRadius;
        }
 
        InterpolatingExponentialWeightFunc()
        {
            _center.Zero();
            _scale = 1;
        }
 
        ScalarType operator()(const PointType& p) const
        {
            return operator()(_center.SqrDistance(p));
        }
 
        ScalarType operator()(ScalarType sqrDist) const
        {
            sqrDist *= _scale;
            return std::exp(-sqrDist) / sqrDist;
        }
 
        bool WeightAndDerivative(const PointType& x, ScalarType* weight,
                                 PointType* derivative)
        {
            ScalarType sqrDist = _scale * _center.SqrDistance(x);
            if (sqrDist < 1e-6)
            {
                return false;
            }
            *weight = std::exp(-sqrDist) / sqrDist;
            for (unsigned int i = 0; i < PointType::Dim; ++i)
            {
                (*derivative)[i] = *weight * (2 * (x[i] - _center[i]));
                (*derivative)[i] += (*derivative)[i] / sqrDist;
            }
            return true;
        }
 
    private:
        PointType _center;
        ScalarType _scale;
    };
 
    template< class PointT >
    class CubicGaussApproximationWeightFunc
    {
    public:
        typedef PointT PointType;
        typedef typename PointType::ScalarType ScalarType;
 
        CubicGaussApproximationWeightFunc(ScalarType radius)
            : _radius(radius)
            , _sqrRadius(_radius * _radius)
            , _cbcRadius(_sqrRadius * _radius)
        {}
 
        CubicGaussApproximationWeightFunc(PointType center,
                                          ScalarType radius)
            : _center(center)
            , _radius(radius)
            , _sqrRadius(_radius * _radius)
            , _cbcRadius(_sqrRadius * _radius)
        {}
 
        ScalarType operator()(const PointType& p) const
        {
            return operator()((p - _center).Length());
        }
 
        ScalarType operator()(ScalarType dist) const
        {
            ScalarType sqrDist = dist * dist;
            return 2 * sqrDist * dist / _cbcRadius -
                   3 * sqrDist / _sqrRadius + 1;
        }
 
        bool WeightAndDerivative(const PointType& x, ScalarType* weight,
                                 PointType* derivative)
        {
            return false;
        }
 
    private:
        ScalarType _radius, _sqrRadius, _cbcRadius;
        PointType _center;
    };
};
 
#endif