Le 15 novembre 2017

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)

Abstract:

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 )