# 16.6 3D Interpolation

## Overview 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 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 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. 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 $q_r=f_r,w_r(x,y,z)=\frac{1}{d_r^2},d_r^2=(x-x_r)^2+(y-y_r)^2+(z-z_r)^2$