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.
