133 citations · 554 across the 117 of their papers we have counts for
5 papers · 1 filter
Convex Hulls of Orbits and Orientations of a Moving Protein Domain
Marco Longinetti, Luca Sgheri, Frank Sottile
We study the facial structure and Carathéodory number of the convex hull of an orbit of the group of rotations in R^3 acting on the space of pairs of anisotropic symmetric 3\times…
Line problems in nonlinear computational geometry
Frank Sottile, Thorsten Theobald
We first review some topics in the classical computational geometry of lines, in particular the O(n^{3+ε}) bounds for the combinatorial complexity of the set of lines in R^3 intera…
Line tangents to four triangles in three-dimensional space
Hervé Brönnimann, Olivier Devillers, Sylvain Lazard +1
We investigate the lines tangent to four triangles in R^3. By a construction, there can be as many as 62 tangents. We show that there are at most 162 connected components of tangen…
Cremona Convexity, Frame Convexity, and a Theorem of Santaló
Jacob E. Goodman, Andreas Holmsen, Ricky Pollack +2
In 1940, Luis Santaló proved a Helly-type theorem for line transversals to boxes in R^d. An analysis of his proof reveals a convexity structure for ascending lines in R^d that is i…
The number of transversals to line segments in R^3
Hervé Brönnimann, Hazel Everett, Sylvain Lazard +2
We completely describe the structure of the connected components of transversals to a collection of n line segments in R^3. We show that n>2 arbitrary line segments in R^3 admit 0,…