Persistent homology is the mathematical core of recent work on shape, including reconstruction, recognition, and matching. Its pertinent information is encapsulated by a pairing o...
David Cohen-Steiner, Herbert Edelsbrunner, Dmitriy...
We prove that the lines tangent to four possibly intersecting convex polyhedra in 3 with n edges in total form Θ(n2 ) connected components in the worst case. In the generic ca...
We describe how to count the cases that arise in a family of visualization techniques, including Marching Cubes, Sweeping Simplices, Contour Meshing, Interval Volumes, and Separat...
The flow complex is a geometric structure, similar to the Delaunay tessellation, to organize a set of (weighted) points in Rk. Flow shapes are topological spaces corresponding to ...
Kevin Buchin, Tamal K. Dey, Joachim Giesen, Matthi...
Dupin cyclides are algebraic surfaces introduced for the first time in 1822 by the French mathematician Pierre-Charles Dupin. They have a low algebraic degree and have been propo...