Journal for Geometry and Graphics, Vol. 2, No. 2, pp. 109 - 121 (1998)

Edge-Orthogonal Patches through a Given Rational Bézier Curve

Johann Lang, Hans-Peter Schröcker

Institute for Geometry, Graz University of Technology
Kopernikusgasse 24, A-8010 Graz, Austria

Abstract: Applications in computational fluid dynamics (CFD) have led to the problem of finding a rational Bézier patch with a given edge parameter line $k$ the way that the parameter lines of the other type intersect $k$ orthogonally. This is what we call an orthogonal continuation of $k$. The variety of solutions to the problem is being investigated and a very geometric way for the construction of the solutions is being offered. Using some fundamental features of polynomials we can establish a link between the properties of the weight polynomial and the elevation of degree which is necessary to find non-trivial orthogonal continuations. For some cases which turn out to be unsolvable, and for cases where the solution existing has a very high degree, we can describe a Monte Carlo method providing surprisingly good approximations. This method is even capable of coping with tasks where the right angle is replaced by some arbitrary angle function.

Keywords: Bézier surfaces, orthogonal continuation, Monte Carlo method

Classification (MSC2000): 53A05; 68U05

Full text of the article:

[Next Article] [Contents of this Number]
© 2000--2001 ELibM for the EMIS Electronic Edition