Show simple item record

dc.contributor.authorVigo Anglada, Marc
dc.contributor.authorPla García, Núria
dc.contributor.authorBrunet Crosa, Pere
dc.contributor.otherUniversitat Politècnica de Catalunya. Departament d'Òptica i Optometria
dc.identifier.citationVigo, M., Pla, N., Brunet, P. "From degenerate patches to triangular and trimmed patches". 1995.
dc.description.abstractCAD systems are usually based on a tensor product representation of free form surfaces. Trimmed patches provide a reasonable solution for the representation of general topologies, provided that the gap between equivalent trimming curves in the euclidean space is small enough. Several commercial CAD systems, however, represent certain non-rectangular surface regions through degenerate rectangular patches. Degenerate patches produce rendering artifacts and can lead to malfunctions in the subsequent geometric operations. In this paper, two algorithms for converting degenerate tensor-product patches into triangular and trimmed rectangular patches are presented. The algorithms are based on specific degree reduction algorithms for Bézier curves. In both algorithms, the final surface approximates the initial one in a quadratic sense while inheriting its boundary curves. In the second one, e-G^1 continuity is achieved. Approximation errors are analyzed and some examples are presented and discussed. Approximation errors can be arbitrarily decreased through the degree elevation of the degenerate patches.
dc.format.extent43 p.
dc.subjectÀrees temàtiques de la UPC::Informàtica
dc.subject.otherCAD systems
dc.subject.otherTrimmed patches
dc.titleFrom degenerate patches to triangular and trimmed patches
dc.typeExternal research report
dc.rights.accessOpen Access
dc.description.versionPostprint (published version)
local.citation.authorVigo, M.; Pla, N.; Brunet, P.

Files in this item


This item appears in the following Collection(s)

Show simple item record

All rights reserved. This work is protected by the corresponding intellectual and industrial property rights. Without prejudice to any existing legal exemptions, reproduction, distribution, public communication or transformation of this work are prohibited without permission of the copyright holder