ug::IDWInterpolation< WDim, TPntIterator, TData > Class Template Reference

Class for inverse distance weighting based on a general data type. More...

#include <invdist_user_data.h>

Public Types
typedef TData	data_type
	type of the data to extrapolate More...
typedef TPntIterator	t_pnt_iter
	type of the interpolation point iterator More...

Static Public Member Functions
static void	compute (data_type &res, const MathVector< dim > &pos, number R, t_pnt_iter pnt_beg, t_pnt_iter pnt_end, number order, number small_dist=1e-7)
	computes the interpolation basing on the interpolation points in a given ball More...
static void	compute (data_type &res, const MathVector< dim > &pos, t_pnt_iter pnt_beg, t_pnt_iter pnt_end, number order, number small_dist=1e-7)
	computes the interpolation basing on all the interpolation points More...

Static Public Attributes
static const int	dim = WDim
	dimensionality of the space (i.e. of the coordinate vectors) More...

Detailed Description

template<int WDim, typename TPntIterator, typename TData = number>
class ug::IDWInterpolation< WDim, TPntIterator, TData >

Class for inverse distance weighting based on a general data type.

The static functions in the class compute the field given by the IDW interpolation of a given order for given interpolation points and values. Type of the values specified by the template parameter (and may be a scalar or a tensor arithmetic type).

Having a set of interpolation points \( \mathbf{x}_i \) with values \( u_i \) at them, the interpolated value \( u \) at point \( \mathbf{x} \not\in \{ \mathbf{x}_i \} \) is computed as

\begin{eqnarray*} u = \frac {\sum_i w_i \cdot u_i} {\sum_i w_i}, \end{eqnarray*}

where

\begin{eqnarray*} w_i := \frac{1}{\| \mathbf{x} - \mathbf{x}_i \|_2^p} \end{eqnarray*}

( \( p \) being the order of the interpolation). For \( \mathbf{x} = \mathbf{x}_i \) (up to some numerical precision), we set \( u = u_i \).

Remarks

For \( p \) less or equal the dimension of the geometric space, the interpolated value \( u \) may be essentially influenced by the values at \( \mathbf{x}_i \) located far away from \( \mathbf{x} \). However, this influence may be avoided by specifying the radius \( R \): Then only those \( \mathbf{x}_i \) (and therefore \( u_i \)) are considered in the sums, for which \( \| \mathbf{x} - \mathbf{x}_i \|_2 \le R \) holds.

Note that if the radius \( R \) is specified, then it can happen that the interpolated value depends only on values at points located on one side of \( \mathbf{x} \), completely ignoring a trend prescribed by points on the other sides. Thus, \( R \) should be large enough.

To loop the interpolation points, iterators of the templated type TPntIterator are used. Every element of the reference elements should have two members: pos and value: TPntIterator ptr; ptr->pos is a MathVector<WDim> object with the coordinates of the interpolation point; ptr->value is a TData object of the value at that point.

Template Parameters

WDim	dimensionality of the space
TPntIterator	interpolation point iterator type
TData	type of the values to interpolate

Member Typedef Documentation

data_type

template<int WDim, typename TPntIterator , typename TData = number>

typedef TData ug::IDWInterpolation< WDim, TPntIterator, TData >::data_type

type of the data to extrapolate

t_pnt_iter

template<int WDim, typename TPntIterator , typename TData = number>

typedef TPntIterator ug::IDWInterpolation< WDim, TPntIterator, TData >::t_pnt_iter

type of the interpolation point iterator

Member Function Documentation

compute() [1/2]

template<int WDim, typename TPntIterator , typename TData >

void ug::IDWInterpolation< WDim, TPntIterator, TData >::compute ( data_type &  res, const MathVector< dim > &  pos, number  R, t_pnt_iter  pnt_beg, t_pnt_iter  pnt_end, number  order, number  small_dist = 1e-7  )

static

computes the interpolation basing on the interpolation points in a given ball

Computes the interpolation basing on the interpolation points in a given ball.

Parameters

res	interpolated value
pos	geometric position where to interpolate
R	radius of the ball (if 0 then the whole space)
pnt_beg	the first interpolation point
pnt_end	delimiter of the iterpolation points
order	order of the interpolation
small_dist	distance at which we do not distinguish the points

References ug::IDWInterpolation< WDim, TPntIterator, TData >::compute(), UG_THROW, and ug::VecDistance().

compute() [2/2]

template<int WDim, typename TPntIterator , typename TData >

void ug::IDWInterpolation< WDim, TPntIterator, TData >::compute ( data_type &  res, const MathVector< dim > &  pos, t_pnt_iter  pnt_beg, t_pnt_iter  pnt_end, number  order, number  small_dist = 1e-7  )

static

computes the interpolation basing on all the interpolation points

Computes the interpolation basing on all the interpolation point.

Parameters

res	interpolated value
pos	geometric position where to interpolate
pnt_beg	the first interpolation point
pnt_end	delimiter of the iterpolation points
order	order of the interpolation
small_dist	distance at which we do not distinguish the points

References UG_THROW, and ug::VecDistance().

Referenced by ug::IDWInterpolation< WDim, TPntIterator, TData >::compute(), and ug::IDWUserData< WDim, TData >::evaluate().

Member Data Documentation

dim

template<int WDim, typename TPntIterator , typename TData = number>

const int ug::IDWInterpolation< WDim, TPntIterator, TData >::dim = WDim

static

dimensionality of the space (i.e. of the coordinate vectors)

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The documentation for this class was generated from the following files:

• ugbase/lib_disc/spatial_disc/user_data/common_user_data/invdist_user_data.h
• ugbase/lib_disc/spatial_disc/user_data/common_user_data/invdist_user_data_impl.h