Non-Grid Interpolation Package

This package provides interpolation functions of 3D data which is non-grid in domain.

Preparation

Set this notebook directory to current:

Load the package:

Function of the package:

Data

Objective data (3D):

Visualization by ListDensityPlot:

Visualization by TriangularSurfacePlot (the package loads Computational Geometry Package):

Visualization by ListPlot3D:

NearestNeighbor

Basic

Get usage information:

Get interpolation function by Nearest Neighbor:

Visualization by DensityPlot:

Visualization by Plot3D:

Boundary

Data 2:

Get interpolation function by Nearest Neighbor:

Visualization by DensityPlot:

Visualization by Plot3D:

By default, use boundary process function Mean:

Boundary process function is arbitrary.
If boundary process function evaluates NearestFunction, use Hold and ReleaseHold.

Use boundary process function Max:

Use boundary process function Min:

DelaunayTriangulationPiecewiseLinear

Basic

Get usage information:

Get interpolation function by Delaunay Triangulation Piecewise Linear:

Visualization by DensityPlot:

Visualization by Plot3D:

Extrapolation

By default, use extrapolation value Indeterminate:

Extrapolation value or function is arbitrary.

Get interpolation function by Delaunay Triangulation Piecewise Linear using extrapolation value 0:

Visualization by Plot3D:

Get interpolation function by Delaunay Triangulation Piecewise Linear using extrapolation function #1^2 + #2^2 (except &):

Visualization by Plot3D:

Compile

Be quickly by compile.

Get interpolation function by Delaunay Triangulation Piecewise Linear using extrapolation value 0:

Timing to visualization:

Get compiled function:

Timing to visualization:

RadialBasisFunctionNetwork

Basic

Get usage information:

Get interpolation function by Radial Basis Function Network:

Visualization by DensityPlot:

Visualization by Plot3D:

Radial Basis Function

By default, use radial basis function Thin Plate Spline (If[#==0,0,#^2Log[#]]&):

Radial basis function is arbitrary.

Get interpolation function by Radial Basis Function Network using radial basis function #&:

Visualization by Plot3D:

Get interpolation function by Radial Basis Function Network using radial basis function Exp[-(#/(1/10))^2]&:

Visualization by Plot3D:

Compile

Be quickly by compile.

Get interpolation function by Radial Basis Function Network:

Timing to visualization:

Get compiled function:

Timing to visualization:

ProcessDuplication

Basic

Get usage information:

Data 3:

Get data processed duplication:

Process Function

By default, use process function Mean:

Process function is arbitrary.

Use process function Max:

Use process function Min:

Data 4:

Visualization by ListDensityPlot:

Visualization by ListPlot3D:

Be failed if get interpolation function of data existing duplication point:

Get data processed duplication:

Get interpolation function of data processed duplication:

Visualization by Plot3D:

Get data processed duplication using process function Max:

Get interpolation function of data processed duplication:

Visualization by Plot3D:

Get data processed duplication using process function Min:

Get interpolation function of data processed duplication:

Visualization by Plot3D:

ConvexHullQ

Basic

Get usage information:

Projection to domain (2D) of objective data (3D):

Get region function of convex hull:

Visualization by RegionPlot:

ConvexHullArea

Basic

Get usage information:

Get convex hull area:

凸包面積とそのデータ発生領域面積に対する割合：

Convex hull area and its ratio to data generation region area:

Created with Wolfram Mathematica 8.0