Reference TypeConference Proceedings
Citation KeyOliveiraNascMeer:1995:UsFiDi
Author1 Oliveira, Antonio
2 Nascimento, Sara do
3 Meerbaum, Sonja A. L.
Affiliation1 Programa de Engenharia de Sistemas (COPPE) da Universidade Federal do Rio de Janeiro (UFRJ)
2 Programa de Engenharia de Sistemas (COPPE) da Universidade Federal do Rio de Janeiro (UFRJ)
3 Programa de Engenharia de Sistemas (COPPE) da Universidade Federal do Rio de Janeiro (UFRJ)
TitleUsing fields of directions defined on a triangulation to obtain a topology preserving continuous transformation of a polygon into another
Conference NameSimpósio Brasileiro de Computação Gráfica e Processamento de Imagens, 8 (SIBGRAPI)
EditorLotufo, Roberto de Alencar
Mascarenhas, Nelson Delfino d'Ávila
Book TitleAnais
Date25 - 27 out. 1995
Publisher CityPorto Alegre
PublisherSociedade Brasileira de Computação
Conference LocationSão Carlos
Keywordsdirection fields, triangulation, polygon.
AbstractIn this article we present an algorithm for the following problem: Obtain a continuous transformation of any simple polygon (L (o)) into another (L (1)) with the same number of vertices, generating only simple polygons in between, that is: without introducing contour loops or whiskers during the transformation. The transformation should also take every vertex of one polygon into a corresponding one on the other. None of the best know strategies for Contour Shape Interpolation can solve the general version of this problem, although simple multi-stage transformations methods can do it. Multi-stages transformations however, generate intermediate polygons whose shape is not correlated to those of the extreme ones. The approach which will be presented here although elaborate, offers much better possibilities of getting a real blend of the extreme polygons shape at any intermediate instance. A Continuous Transformation obtained by that method is derived from another one between two Fields of Directions (D (i), i=0, 1) defined on the same Triangulation T of an Annular Region (U) containing the given polygons. Every trajectory of D (i) cross L (i) exactly once what allows us to define an homeomorphism between L (i) and the graph of a continuous function defined on the external border of U. Besides finding the D (i) s and transforming one into the other the method makes use of three more interpolation steps. The overall complexity of the non-optimized version of the algorithm that will be described here, is O (ITI²).
TypeModelagem Geométrica
Tertiary TypeArtigo
FormatImpresso, On-line.
Size6688 KiB
Number of Files1
Target File12 Using fields od directions.pdf
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Metadata Last Update2013: {D 1995}
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