From scattered data to B-spline surfaces at increasing level of detail
From scattered data to B-spline surfaces at increasing level of detail
This documentation contains a brief reference manual for the SINTEF Multilevel B-spline Library developed at SINTEF Applied Mathematics. The main interface is through the class MBA which also contains a small example in its documentation. Note that only the non-adaptive/non-parametric version of the algorithms are documented here. Parametric and adaptive versions, as used to generate the head-model in the figure above, are implemented in the classes MBApar (parametric), MBAadaptive (adaptive) and MBAadaptivePar (adaptive and parametric).
For a thorough description of the basic schemes, the papers by the originators of Multilevel B-splines, S. Lee, G. Wolberg and S. Y. Shin, should be consulted.
A detailed description of the mathematical content of the algorithms, with extensions made in the SINTEF library and with numerical examples, can be found in the report:
Ø. Hjelle. Approximation of Scattered Data with Multilevel B-splines. SINTEF report, 2001.
Full report (780 K, pdf)
It's very easy - just look at the small example in class MBA and read the documentation for the functions that are called there. Then, copy the complete main program to a file - compile it and run it! The program samples the resulting spline surface and writes the result to a VRML-file. You can download a free VRML-viewer from Kongsberg SIM.
If you have got the Visual C++ workspace with all the source code, then you can just build the application and run it with the current main program.
I will make numerical examples and discuss pros and cons thoroughly later. Consult the SINTEF report for mathematical details.
Note that the basic algorithms in this library does not solve "the scattered data approximation problem" in general. The algorithms will produce anomalies near the data if the underlying grid of B-spline coefficients is dense and the data points are unevenly distributed in the domain. The remedy, as far as I have concluded through numerical experiments, is to combine the basic schemes with smoothing operators. This is now being implemented and will be available in the next version.
A GPL-version of the library (for Linux/Unix) can be downloaded from http://www.sintef.no/math_software.
Please report any problems or comments to jan.b.thomassen@sintef.no.
Øyvind Hjelle, June 2001
Last modified 28.11.2007 by Jan Thomassen
1.5.1