Sonderforschungsbereich 393
	Preprint 20 / 2003

Randrianarivony, Maharavo ; Brunnett, Guido ; Schneider, Reinhold : Constructing a diffeomorphism between a trimmed domain and the unit square

Author(s):

Randrianarivony, Maharavo
Brunnett, Guido
Schneider, Reinhold

Title:

Constructing a diffeomorphism between a trimmed domain and the unit square

Electronic source:

application/pdf

Preprint series:

Technische Universität Chemnitz, SFB 393 (Germany), SFB393-Preprint 20, 2003

Mathematics Subject Classification:

57R50			[ Diffeomorphisms ]
57R35			[ Differentiable mappings ]
68U05			[ Computer graphics; computational geometry ]
68U07			[ Computer-aided design ]
65D07			[ Splines ]

Abstract:

This document has two objectives: decomposition of a given trimmed surface into several four-sided subregions and creation of a diffeomorphism from the unit square onto each subregion. We aim at having a diffeomorphism which is easy and fast to evaluate. Throughout this paper one of our objectives is to keep the shape of the curves delineating the boundaries of the trimmed surfaces unchanged. The approach that is used invokes the use of transfinite interpolations. We will describe an automatic manner to specify internal cubic Bezier-spline curves that are to be subsequently interpolated by a Gordon patch. Some theoretical criterion pertaining to the control points of the internal curves is proposed and proved so as to ensure that the resulting Gordon patch is a diffeomorphism. Numerical results are reported to illustrate the approaches. Our benchmarks include CAD objects which come directly from IGES files.

Keywords:

Trimmed surface, diffeomorphism, surface decomposition, CAD objects, Coons patch, Gordon patch, IGES format

Language:

English

Publication time:

2 / 2004