Fachbereich Informatik an der RPTU in Kaiserslautern

Prof. Dr. Kestutis Karciauskas

(Vilnius University, Lithuania)

"Rational Multisided Patches"

Probably best known rational multisided patch is Sabin (1983) pentagonal patch. The title of the corresponding paper "Non-Rectangular Surface Patches suitable for inclusion in a B-spline Surface" justifies clearly that these patches are worth to be considered seriously.

Next two types of rational multisided patches that motivated creation of M-patches are: S-patches of Loop&DeRose (1989) and Warren hexagonal patch (1992) constructed blowing-up the base points at the corners of domain triangle.

It appeared that five-sided M-patch plays very important role in this stuff. The reason -- geometrically the same patch has two different interpretations:

  1. blown-up patch -- connection to Warren patches;
  2. rational patch over regular pentagon -- connection to S-patches and Sabin patches; moreover, regular interpretation points out the way how M-patches can be defined over any regular m-gon.

Next it is shown how M-patches are used to construct so called tensor-border patches -- tensor-border structure simplifies an inclusion of M-patch in a B-spline surface.

Some important remarks will be mentioned briefly at the end:

  1. problem of setting the coefficients of inner basis functions;
  2. problem of defining inner control points in constructions of fair surfaces;
  3. efficient representation of five- and six-sided M-patches;
  4. efficient representation of m-sided M-patches for m>6 -- guided subdivision;
  5. though six-sided Sabin, Hosaka&Kimura patches are defined over non-rational domain they are special case of rational six-sided M-patches;
  6. what is true and what is not if we want to extend to multisided M-patches such standard in CAGD procedures like degree elevation and linear precision.

Zeit: Mittwoch, 09.03.2005, 15.00 Uhr
Ort: Gebäude 36, Raum 232