@InProceedings{OliveiraNascMeer:1995:UsFiDi,
author = "Oliveira, Antonio and Nascimento, Sara do and Meerbaum, Sonja A.
L.",
affiliation = "{Programa de Engenharia de Sistemas (COPPE) da Universidade
Federal do Rio de Janeiro (UFRJ)} and {Programa de Engenharia de
Sistemas (COPPE) da Universidade Federal do Rio de Janeiro (UFRJ)}
and {Programa de Engenharia de Sistemas (COPPE) da Universidade
Federal do Rio de Janeiro (UFRJ)}",
title = "Using fields of directions defined on a triangulation to obtain a
topology preserving continuous transformation of a polygon into
another",
booktitle = "Anais...",
year = "1995",
editor = "Lotufo, Roberto de Alencar and Mascarenhas, Nelson Delfino
d'{\'A}vila",
pages = "95--102",
organization = "Simp{\'o}sio Brasileiro de Computa{\c{c}}{\~a}o Gr{\'a}fica e
Processamento de Imagens, 8. (SIBGRAPI)",
publisher = "Sociedade Brasileira de Computa{\c{c}}{\~a}o",
address = "Porto Alegre",
keywords = "direction fields, triangulation, polygon.",
abstract = "In 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
(ITIČ).",
conference-location = "S{\~a}o Carlos, SP, Brazil",
conference-year = "25-27 Oct. 1995",
isbn = "978-85-7669-273-7",
language = "en",
ibi = "8JMKD3MGPBW34M/3DJ97J2",
url = "http://urlib.net/ibi/8JMKD3MGPBW34M/3DJ97J2",
targetfile = "12 Using fields od directions.pdf",
type = "Modelagem Geom{\'e}trica",
urlaccessdate = "2024, Apr. 28"
}