Abstract
This paper investigates the possible role of the new field of computational topology for incorporating abstraction mechanisms in shape modelling. The effectiveness of computational topology techniques is exemplified with an application of discrete differential topology. In particular, a method is proposed for the extraction of a critical point configuration graph from a triangulated surface. Starting from the definition of the Reeb graph in the smooth domain, the concept of critical point is extended to critical areas, which may represent isolated as well as degenerated critical points in the discrete domain. The resulting graph effectively represents the surface shape and has been successfully used as a basis for model compression and restoring purposes.
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Biasotti, S., Falcidieno, B., Spagnuolo, M. (2002). Shape Abstraction Using Computational Topology Techniques. In: Cugini, U., Wozny, M. (eds) From Geometric Modeling to Shape Modeling. GEO 2000. IFIP — The International Federation for Information Processing, vol 80. Springer, Boston, MA. https://doi.org/10.1007/978-0-387-35495-8_16
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DOI: https://doi.org/10.1007/978-0-387-35495-8_16
Publisher Name: Springer, Boston, MA
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