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The WEB-Method

Scattered Data Approximation

WEB-splines settle a notorious problem in scattered data approximation: If the data sites are given on a non-rectangular domain, then the standard B-spline approximation typically reveals shape artifacts at grid cells with few data points. This undesired behavior is avoided when web-splines are used as approximation space.

As an example, we consider scattered data sampled from a smooth function. The grid lines are non-uniform and adapted to the structure of the domain.

data sites and grid lines
      function to be approximated

The standard B-spline approximation yields a large deviation near the boundary due to the instability of the basis. By contrast, the web-spline approximation is perfectly smooth and its maximal deviation from the given function is significantly smaller.

standard approximation

maximum error = 0.3
      web-spline approximation

maximum error = 0.0002


K. Höllig, U. Reif: Nonuniform Web-Splines. Computer Aided Geometric Design, Volume 20, Issue 5, pp. 277-294, 2003.

See Publications for a complete list of WEB-publications.

Author: Ulricht Reif ; Last modification: 2003/10/29 08:36:58 UTC.

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