## Project 2: Scattered Data Interpolation

### Comparing numbers of data

The following images are of a sampling of the function x^2 + y^2 + z^2 evaluated on [0,1]. I compared the effect that different amounts of data sites
had on creating a 256x256x256 grid using Shepards Global method. I noticed that the increase in data points increased the accuracy of the reconstruction.
I used the following transfer function.

```
```6
0 1 0 0 1
0.2 1 0 0 .5
0.4 1 1 0 .2
0.6 0 1 0 .1
0.8 0 1 1 .05
1 0 0 1 .01

### Comparison of Methods

The following images are of a 128x128x128 spherical dataset. The images are in the following order: Global Shepards 2, Local Shepards 2,
Global Hardy Multiquadric, Local Hardy Multiquadric, Global Hardy Reciprocal Multiquadric, Local Hardy Recipocal Multiquadric. In all local
cases, I used the 5 nearest neighbors for the computation. For all Hardy methods, I used an R value of 1. The transfer function that I
used is listed below.

```
```6
0 1 0 0 1
0.1 1 0 0 .5
0.2 1 1 0 .2
0.3 0 1 0 .1
0.4 0 1 1 .05
1 0 0 1 .01

### Hardy's R Value

The following images are of a 128x128x128 x^2+y^2+z^2 dataset. The images compare the effects of the R value chosen for use in the Global Hardy Multiquadric method. It appears that
as R increases the quality of the reconstruction decreases. The values of R used are the following: 1, 10, 100, 1000. The transfer function used in these images is the same as the
first one listed.