author = "Oliveira, Antonio and Nascimento, Sara do and Meerbaum, Sonja A. 
          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 
            booktitle = "Anais...",
                 year = "1995",
               editor = "Lotufo, Roberto de Alencar and Mascarenhas, Nelson Delfino 
                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 
  conference-location = "S{\~a}o Carlos",
      conference-year = "25 - 27 out. 1995",
                 isbn = "978-85-7669-273-7",
             language = "en",
                  ibi = "8JMKD3MGPBW34M/3DJ97J2",
                  url = "",
           targetfile = "12 Using fields od directions.pdf",
                 type = "Modelagem Geom{\'e}trica",
        urlaccessdate = "2020, Nov. 23"