Project 3: Multiresolution Rendering of Voronoi Diagrams

Sibson's interpolation surface

The following images are of a sampling of the function f(x,y) = x evaluated on [0,1]. There are 12 sites in the dataset. The resolution increased by adding one additional site to an area of high error. The transfer function used is shown below.

2
0 0 1 0
1 0 0 1

Error surface

The following images are a sampling of the function f(x,y) = x^2 + y^2 evaulated on [0,1]. There are 12 sites in the dataset. The analytical function was used to generate the value to compare with Sibson's interpolant at each vertex on the surface. The resolution again is increased by adding one additional site to an area of high error. Note: there appears to be a bug in the sibson's interpolation scheme as the top right corner indicates a high error. The transfer function used is shown below.

4
0 0 0 0
0 0 .5 .4
0 0 1 .8
0 1 1 1.2