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Laboratoire Angevin de Recherche en Ingénierie des Systèmes

Séparés par des virgules

Projection of analytic surfaces

Sény DIATTA1 and Guillaume MOROZ2

1 Phd student at INRIA Nancy in Gamble Team (formerly Vegas Team)

2 Researcher at INRIA Nancy in Gamble Team (formerly Vegas Team)


For some robotic problems we need to represent a singular surface that is the projection of a smooth surface embedded in higher dimension.
In this work, we focus on the problem of computing a triangulation of the projection on R^3 of an analytic surface embedded in R^4. Based on Transversality and Singularity Classification theories, we first show that, under generic assumptions, the set of singularities of the projected surface are generated by only three types of multi-germs: 

  • double points, triple points and cross-caps. Then, using this
  • information we design an algorithm taking as input an analytic surface
  • and returning a triangulation isotopic to its projected surface.

(joint work with Marc Pouget )