HAL will be down for maintenance from Friday, June 10 at 4pm through Monday, June 13 at 9am. More information
Skip to Main content Skip to Navigation
Conference papers

Numeric and Certified Isolation of the Singularities of the Projection of a Smooth Space Curve

Rémi Imbach 1 Guillaume Moroz 1 Marc Pouget 1
1 VEGAS - Effective Geometric Algorithms for Surfaces and Visibility
LORIA - ALGO - Department of Algorithms, Computation, Image and Geometry, Inria Nancy - Grand Est
Abstract : Let CP ∩Q be a smooth real analytic curve embedded in R 3 , defined as the solutions of real analytic equations of the form P (x, y, z) = Q(x, y, z) = 0 or P (x, y, z) = ∂P ∂z = 0. Our main objective is to describe its projection C onto the (x, y)-plane. In general, the curve C is not a regular submanifold of R 2 and describing it requires to isolate the points of its singularity locus Σ. After describing the types of singularities that can arise under some assumptions on P and Q, we present a new method to isolate the points of Σ. We experimented our method on pairs of independent random polynomials (P, Q) and on pairs of random polynomials of the form (P, ∂P ∂z) and got promising results.
Complete list of metadata

Cited literature [30 references]  Display  Hide  Download

Contributor : Marc Pouget Connect in order to contact the contributor
Submitted on : Monday, December 7, 2015 - 5:50:49 PM
Last modification on : Saturday, October 16, 2021 - 11:26:08 AM
Long-term archiving on: : Saturday, April 29, 2017 - 8:28:29 AM


Files produced by the author(s)


  • HAL Id : hal-01239447, version 1



Rémi Imbach, Guillaume Moroz, Marc Pouget. Numeric and Certified Isolation of the Singularities of the Projection of a Smooth Space Curve. Proceedings of the 6th International Conferences on Mathematical Aspects of Computer and Information Sciences, Oct 2015, Berlin, Germany. ⟨hal-01239447⟩



Record views


Files downloads