Common tangents to spheres in R 3 (2009)
Ciprian Borcea, Xavier Goaoc, Sylvain Lazard, Sylvain Petitjean, Loria Inria Lorraine
Abstract. We prove that four spheres in R 3 have infinitely many real common tangents if and only if they have aligned centers and at least one real common tangent. 1
To Disjoint Balls, Ciprian Borcea
We prove that the set of directions of lines intersecting three disjoint balls in R 3 in a given order is a strictly convex subset of S 2. We then generalize this result to n disjoint balls in R d....
Ciprian Borcea, Ileana Streinu
Abstract. Rigid frameworks in some Euclidean space are embedded graphs having a unique local realization (up to Euclidean motions) for the given edge lengths, although globally they may have several....
Line transversals to disjoint balls (2008)
Borcea, Ciprian, Goaoc, Xavier, Petitjean, Sylvain
We prove that the set of directions of lines intersecting three disjoint balls in $\mathbb{R}^3$ in a given order is a strictly convex subset of $\mathbb{S}^2$. We then generalize this result to $n$...
Line transversals to disjoint balls (2008)
Borcea, Ciprian, Goaoc, Xavier, Petitjean, Sylvain
We prove that the set of directions of lines intersecting three disjoint balls in $\mathbb{R}^3$ in a given order is a strictly convex subset of $\mathbb{S}^2$. We then generalize this result to $n$...
Line transversals to disjoint balls (2007)
Borcea, Ciprian, Goaoc, Xavier, Petitjean, Sylvain
We prove that the set of directions of lines intersecting three disjoint balls in $\mathbb{R}^3$ in a given order is a strictly convex subset of $\mathbb{S}^2$. We then generalize this result to $n$...
Line transversals to disjoint balls (2007)
Borcea, Ciprian, Goaoc, Xavier, Petitjean, Sylvain
We prove that the set of directions of lines intersecting three disjoint balls in $\mathbb{R}^3$ in a given order is a strictly convex subset of $\mathbb{S}^2$. We then generalize this result to $n$...
Line transversals to disjoint balls (2006)
Borcea, Ciprian, Goaoc, Xavier, Petitjean, Sylvain
We prove that the set of directions of lines intersecting three disjoint balls in $R^3$ in a given order is a strictly convex subset of $S^2$. We then generalize this result to $n$ disjoint balls in...
Common Tangents to Spheres in $R3$ (2006)
Borcea, Ciprian, Goaoc, Xavier, Lazard, Sylvain, Petitjean, Sylvain
We prove that four spheres in $R3$ have infinitely many real common tangents if and only if they have aligned centers and at least one real common tangent.
Common Tangents to Spheres in $R3$ (2006)
Borcea, Ciprian, Goaoc, Xavier, Lazard, Sylvain, Petitjean, Sylvain
We prove that four spheres in $R3$ have infinitely many real common tangents if and only if they have aligned centers and at least one real common tangent.
Common Tangents to Spheres in R^3 (2004)
Borcea, Ciprian, Goaoc, Xavier, Lazard, Sylvain, Petitjean, Sylvain
We prove that four spheres in $\R^3$ have infinitely many real common tangents if and only if they have aligned centers and at least one real common tangent.
On tangents to quadric surfaces (2004)
Borcea, Ciprian, Goaoc, Xavier, Lazard, Sylvain, Petitjean, Sylvain
We study the variety of common tangents for up to four quadric surfaces in projective three-space, with particular regard to configurations of four quadrics admitting a continuum of common tangents....
Common Tangents to Spheres in R^3 (2004)
Borcea, Ciprian, Goaoc, Xavier, Lazard, Sylvain, Petitjean, Sylvain
We prove that four spheres in $\R^3$ have infinitely many real common tangents if and only if they have aligned centers and at least one real common tangent.
Common Tangents to Spheres in R^3 (2004)
Borcea, Ciprian, Goaoc, Xavier, Lazard, Sylvain, Petitjean, Sylvain
We prove that four spheres in $\R^3$ have infinitely many real common tangents if and only if they have aligned centers and at least one real common tangent.
On Tangents to Quadric Surfaces (2004)
Borcea, Ciprian, Goaoc, Xavier, Lazard, Sylvain, Petitjean, Sylvain
We study the variety of common tangents for up to four quadric surfaces in projective three-space, with particular regard to congurations of four quadrics admitting a continuum of common tangents. We...
On Tangents to Quadric Surfaces (2004)
Borcea, Ciprian, Goaoc, Xavier, Lazard, Sylvain, Petitjean, Sylvain
We study the variety of common tangents for up to four quadric surfaces in projective three-space, with particular regard to congurations of four quadrics admitting a continuum of common tangents. We...
On the Number of Embeddings of Minimally Rigid Graphs (2002)
Borcea, Ciprian, Streinu, Ileana
Rigid frameworks in some Euclidian space are embedded graphs having a unique local realization (up to Euclidian motions) for the given edge lengths, although globally they may have several. We study...
On the Number of Embeddings of Minimally Rigid Graphs (2002)
Ciprian Borcea, Ileana Streinu
Rigid frameworks in some Euclidian space are embedded graphs having a unique local realization (up to Euclidian motions) for the given edge lengths, although globally they may have several. We study...