16.6 3D Interpolation

Contents

Overview

3DInterpolation.png

3D Interpolation tool uses a smooth function Q(x,y,z), which is a modification of Shepard's method, to interpolate m scattered data points. You can specify the X/Y/Z Minimum and Maximum and number of interpolation points in each dimension for 3D interpolation.

To Use 3D Interpolation Tool
  1. Create a new worksheet with X, Y, Z (data) columns, plus a fourth column of values each of which is associated by row index number with a set of XYZ coordinates.
  2. Activate the worksheet.
  3. Select Analysis: Mathematics: 3D Interpolation. This opens the interp3 dialog box.
  4. Choose your input and output options and click OK. The X-Function interp3 is called to perform the calculation.

Dialog Options

Recalculate

Controls recalculation of analysis results

  • None
  • Auto
  • Manual

For more information, see: Recalculating Analysis Results

Input

Specify the input data range.

  • X
    Select one X column.
  • Y
    Select one Y column.
  • Z
    Select one Z column.
  • F
    Select one 3D function column.

For help with range controls, see: Specifying Your Input Data

Computation Control

Specify parameters of interpolated points.

Number of Points in Each Dimension
The number of interpolated points in each dimension.
X Minimun
Specify the X minimun value of this interpolation.
X Maximun
Specify the X maximun value of this interpolation.
Y Minimun
Specify the Y minimun value of this interpolation.
Y Maximun
Specify the Y maximun value of this interpolation.
Z Minimun
Specify the Z minimun value of this interpolation.
Z Maximun
Specify the Z maximun value of this interpolation.
Output

The output result for the interpolated data.

Algorithm

This function constructs a smooth function \(Q(x,y,z)\!\) which interpolates a set of \(m\!\) scatter data points \((x_r,y_r,z_r,f_r)\!\) for \(r= 1, 2, ... , m\!\), using a modification of Shepard's method. It then evaluates the interpolant at the set of selected points \((u_r,v_r,w_r)\!\), as well as its first partial derivatives. The surface is continuous and has continuous first partial derivatives.

\[Q(x,y,z)=\frac{ \sum \omega _r(x,y,z)q_r}{ \sum \omega _r(x,y,z)} \]

where

\[q_r=f_r,w_r(x,y,z)=\frac{1}{d_r^2},d_r^2=(x-x_r)^2+(y-y_r)^2+(z-z_r)^2\]

For more information on algorithms, please see documentation for these NAG functions:

References

For reference information, please see documentation for these NAG functions: