Topological Evolution of Surfaces
نویسندگان
چکیده
This paper presents a framework for generating smooth-looking transformations between pairs of surfaces that may differ in topology. The user controls the transformation by specifying a sparse control mesh on each surface and by associating each face in one control mesh with a corresponding face in the other. The algorithm builds a transformation from this information in two steps. The first step constructs a series of shapes and meshes (according the theory of topological surgery) that describes how topological changes should occur at critical points during the transformation. This makes possible the second step, which establishes smooth transformations by combining intermediate shapes in this series. Control meshes allow the user precise but intuitive control of the morph, while the 3D surfaces that result can be used for rendering or keyframing. Résumé Cet article presente une méthode pour engendrer des transformations continues entre deux surfaces dont la topologie peut etre différente. L’utilisateur controle la transformation en spécifiant une grille de controle sur chacune des surfaces, et en associant a chaque face de l’une des deux grilles une face correspondante de l’autre. Notre algorithme construit une transformation à partir de cette information en deux étapes. La première étape construit une suite de formes et de grilles (suivant la théorie de la chirurgie topologique) qui decrivent la façon dont les changements de topologie doivent se produire en certains moments critiques. Ceci rend possible la deuxième étape, qui construit une transformation continue en combinant les étapes intermédiaires. Les grilles de controle donnent à l’utilisateur un controle precis mais intuitif de la métamorphose, et les surfaces qui en résultent peuvent être utilisées pour la visualisation ou l’animation.
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