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- Xavier Goaoc, Hyo-Sil Kim, Sylvain Lazard
- SIAM J. Comput.
- 2010

We consider the problem of computing shortest paths having curvature at most one almost everywhere and visiting a sequence of $n$ points in the plane in a given order. This problem arises naturally… (More)

- Olivier Devillers, Vida Dujmovic, +4 authors Sylvain Petitjean
- SIAM J. Comput.
- 2003

In this paper, we show that, amongst $n$ uniformly distributed unit balls in $\mathbb{R}^3$, the expected number of maximal nonoccluded line segments tangent to four balls is linear. Using our… (More)

- Hervé Brönnimann, Olivier Devillers, +6 authors Sue Whitesides
- SIAM J. Comput.
- 2007

Motivated by visibility problems in three dimensions, we investigate the complexity and construction of the set of tangent lines in a scene of three-dimensional polyhedra. We prove that the set of… (More)

- Ciprian Borcea, Xavier Goaoc, Sylvain Petitjean
- Symposium on Computational Geometry
- 2006

We prove that the set of directions of lines intersecting three disjoint balls in R3 in a given order is a strictly convex subset of S2. We then generalize this result to n disjoint balls in Rd. As a… (More)

We present an exact method to compute the boundaries between umbra, penumbra and full-light regions cast on a plane by a set of disjoint convex polyhedra, some of which are light sources. This method… (More)

- Éric Colin de Verdière, Grégory Ginot, Xavier Goaoc
- Symposium on Computational Geometry
- 2012

The nerve of a family of sets is a simplicial complex that records the intersection pattern of its subfamilies. Nerves are widely used in computational geometry and topology, because the nerve… (More)

- Hervé Brönnimann, Olivier Devillers, +6 authors Sue Whitesides
- CCCG
- 2002

We prove that, under a certain general position assumption, the number of lines tangent to four bounded disjoint convex polyhedra in $\Real^3$ with a total of $n$ edges is $O(n^2)$. Under the same… (More)

Assume that Y is a noisy version of a point set X in convex position. How many vertices does the convex hull of Y have, that is, what is the number of extreme points of Y? We consider the case where… (More)

Let K be a compact convex body in Rd, let Kn be the convex hull of n points chosen uniformly and independently in K, and let fi(Kn) denote the number of i-dimensional faces of Kn. We show that for… (More)

- Otfried Cheong, Xavier Goaoc, Hyeon-Suk Na
- Comput. Geom.
- 2005

We show that a set of n disjoint unit spheres in Rd admits at most two distinct geometric permutations if n ≥ 9, and at most three if 3 ≤ n ≤ 8. This result improves a Helly-type theorem on line… (More)