IFS fractal interpolation for 2D and 3D visualization

Reconstruction is used frequently in visualization of one, two, and three dimensional data. Data uncertainty is typically ignored, and a deficiency of many interpolation schemes is smoothing which may indicate features or characteristics of the data that are not there. The author investigates the use of iterated function systems (IFS's) for interpolation. He shows new derivations for fractal interpolation in two and three dimensional scalar data, and new point and polytope rendering algorithms with tremendous speed advantages over ray tracing. The interpolations may be used to give an indication of the uncertainty of the data, statistically represent the data at a variety of scales, allow tunability from the data, and may allow more accurate data analysis.