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.
| Identifer | oai:union.ndltd.org:DRESDEN/oai:qucosa:de:qucosa:18579 |
| Date | 31 August 2006 |
| Creators | Randrianarivony, Maharavo, Brunnett, Guido, Schneider, Reinhold |
| Publisher | Technische Universität Chemnitz |
| Source Sets | Hochschulschriftenserver (HSSS) der SLUB Dresden |
| Language | English |
| Detected Language | English |
| Type | doc-type:preprint, info:eu-repo/semantics/preprint, doc-type:Text |
| Source | Preprintreihe des Chemnitzer SFB 393, 03-20 |
| Rights | info:eu-repo/semantics/openAccess |
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