7 citations · 53 across the 30 of their papers we have counts for
32 papers
Counting normals to closed curves in
Gaiane Panina, Dirk Siersma
We prove the following results: (1) For every generic closed smooth curve in , {whose torsion has a constant sign}, there is a point with at least emanating norma…
Squared Distance Function on the Configuration Space of a planar Spider with Applications to Hooke Energy and Voronoi Distance
Maciej Denkowski, Gaiane Panina, Dirk Siersma
Spider mechanisms are the simplest examples of arachnoid mechanisms, they are one step more complicated than polygonal linkages. Their configuration spaces have been studied intens…
Concurrent normals problem for convex polytopes and Euclidean distance degree
Ivan Nasonov, Gaiane Panina, Dirk Siersma
It is conjectured since long that for any convex body there exists a point in its interior which belongs to at least normals from different points on t…
Hooke and Coulomn Energy of Tripod Spiders
Giorgi Khimshiashvili, Dirk Siersma
Tripod spiders are the simplest examples of arachnoid mechanisms. Their workspaces and configuration spaces are well known. For Hooke potential, we give a complete description of t…
Concurrent normals of immersed manifolds
Gaiane Panina, Dirk Siersma
It is conjectured since long that for any convex body there exists a point in the interior of which belongs to at least normals from different poi…
Extremal Area of Polygons sliding along Curves
Dirk Siersma
In this paper we study the area function of polygons, where the vertices are sliding along curves. We give geometric criteria for the critical points and determine also the Hesse m…