Two dimensional IFS interpolant
Same interpolant with higher scaling factors
2D Surface Bilinear (non-affine) IFS interpolant
One dimensional IFS interpolation, showing contraction mappings of
entire domain.
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. In this paper I investigate the use of iterated function systems (IFS's) for interpolation. I show 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.
This project is supported by ONR grant N00014-92-J-1807 and NSF grant IRI-9423881.
Craig M. Wittenbrink, in IEEE Visualization '95 October 29-November 3, 1995, pages 77-84, Atlanta, GA. A postscript version of the paper in IEEE Visualization'95 is available through anonymous ftp to ftp.cse.ucsc.edu then get pub/reinas/papers/ifs_fractal_int.ps.Z, or click here . Or by can be obtained by clicking here (PDF), or by anonymous ftp to ftp.cse.ucsc.edu then get pub/reinas/papers/ifs_fractal_int.pdf.
Two dimensional IFS interpolant
Same interpolant with higher scaling factors
2D Surface Bilinear (non-affine) IFS interpolant
One dimensional IFS interpolation, showing contraction mappings of
entire domain.
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