Continuous Maps from Spheres Converging to Boundaries of Convex Hulls

Convex hulls of spheres and convex hulls of disjoint convex polytopes

Given a set Σ of spheres in E, with d ≥ 3 and d odd, having a constant number of m distinct radii ρ1, ρ2, . . . , ρm, we show that the worst-case combinatorial complexity of the convex hull of Σ is Θ( ∑ 1≤i6=j≤m nin ⌊ d 2 ⌋ j ), where ni is the number of spheres in Σ with radius ρi. To prove the lower bound, we construct a set of Θ(n1+n2) spheres in E , with d ≥ 3 odd, where ni spheres have rad...

From Binary to Grey Scale Convex Hulls

Relative Convex Hull Determination from Convex Hulls in the Plane

A new algorithm for the determination of the relative convex hull in the plane of a simple polygon A with respect to another simple polygon B which contains A, is proposed. The relative convex hull is also known as geodesic convex hull, and the problem of its determination in the plane is equivalent to find the shortest curve among all Jordan curves lying in the difference set of B and A and en...

Using convex hulls to extract interaction interfaces from known structures

MOTIVATION Protein interactions provide an important context for the understanding of function. Experimental approaches have been complemented with computational ones, such as PSIMAP, which computes domain-domain interactions for all multi-domain and multi-chain proteins in the Protein Data Bank (PDB). PSIMAP has been used to determine that superfamilies occurring in many species have many inte...

Converging Technologies, Shifting Boundaries

At the beginning of the 21 century, most people are no longer surprised by technological revolutions. The twentieth century brought us information technology and biotechnology: key technologies for pioneering innovations such as the computer, the Internet and genetically modified plants. In the transition to the twenty-first century, two other important developments: nanotechnology (the researc...