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The complexity and enumerative geometry of aspect graphs of smooth surfaces

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Algorithms in Algebraic Geometry and Applications

Part of the book series: Progress in Mathematics ((PM,volume 143))

Abstract

Informally, the aspect graph [KvD79] (also called view graph) is a qualitative, viewer-centered representation which enumerates all possible appearances of an object. More formally, choosing a camera model (orthographic-parallel or perspective-central-projection) and a viewpoint determines the aspect of an object (i.e., the structure of the observed line-drawing). The range of possible viewpoints can be partitioned into maximal connected sets (regions) that yield identical aspects. The change in aspect at the boundary between regions is called a visual event. The maximal regions and the associated aspects form the nodes of an aspect graph, whose arcs correspond to the visual event boundaries between adjacent regions.

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Author information

Authors and Affiliations

  1. CRIN/INRIA Lorraine, BP 239, 54506, Vandoeuvre Cedex, France

    S. Petitjean

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  1. S. Petitjean
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Editors and Affiliations

  1. Departamento de Matemáticas, Facultad de Ciencias, Avenida Los Castros s/n, Santander, 39071, Spain

    Laureano González-Vega  & Tomás Recio  & 

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© 1996 Birkhäuser Verlag Basel/Switzerland

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Petitjean, S. (1996). The complexity and enumerative geometry of aspect graphs of smooth surfaces. In: González-Vega, L., Recio, T. (eds) Algorithms in Algebraic Geometry and Applications. Progress in Mathematics, vol 143. Birkhäuser Basel. https://doi.org/10.1007/978-3-0348-9104-2_16

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  • DOI: https://doi.org/10.1007/978-3-0348-9104-2_16

  • Publisher Name: Birkhäuser Basel

  • Print ISBN: 978-3-0348-9908-6

  • Online ISBN: 978-3-0348-9104-2

  • eBook Packages: Springer Book Archive

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