—We study the topology of the Megaparsec Cosmic Web on the basis of the Alpha Shapes of the galaxy distribution. The simplicial complexes of the alpha shapes are used to determin...
Rien van de Weygaert, Erwin Platen, Gert Vegter, B...
Let S Rk+m be a compact semi-algebraic set defined by P1 0, . . . , P 0, where Pi R[X1, . . . , Xk, Y1, . . . , Ym], and deg(Pi) 2, 1 i . Let denote the standard projection f...
We present a randomized algorithm for computing portions of an arrangement of n arcs in the plane, each pair of which intersect in at most t points. We use this algorithm to perfo...
The number of triangles in arrangements of lines and pseudolines has been object of some research. Most results, however, concern arrangements in the projective plane. In this arti...
Modeling data by multiple low-dimensional planes is an important problem in many applications such as computer vision and pattern recognition. In the most general setting where on...