We address unsolved problems of unfolding polyhedra in a new context, focusing on special convex patches—disklike polyhedral subsets of the surface of a convex polyhedron. One long-unsolved problem is edge-unfolding prismatoids. We show that several natural strategies for unfolding a prismatoid can fail, but obtain a positive result for “petal unfolding” topless prismatoids, which can be viewed...

Various geometric operators have been playing an important role in surface processing. For example, many shape analysis algorithms have been developed based on eigenfunctions of the Laplace–Beltrami operator (LBO), which is defined based on the first fundamental form of the surface. In this paper, we introduce two new geometric operators based on the second fundamental form of the surface, name...

It was shown in [21] that the maximal surface area of a convex set in R with respect to a rotation invariant logconcave probability measure γ is of order √ n 4 √ V ar|X| √ E|X| , where X is a random vector in R distributed with respect to γ. In the present paper we discuss surface area of convex polytopes PK with K facets. We find tight bounds on the maximal surface area of PK in terms of K. We...

in this note we first redefine the notion of a fuzzy hypervectorspace (see [1]) and then introduce some further concepts of fuzzy hypervectorspaces, such as fuzzy convex and balance fuzzy subsets in fuzzy hypervectorspaces over valued fields. finally, we briefly discuss on the convex (balanced)hull of a given fuzzy set of a hypervector space.