Quantitative Combinatorial Geometry for Continuous Parameters

Quantitative Combinatorial Geometry for Continuous Parameters

Combinatorial Geometry

Combinatorial geometry is the study of combinatorial properties of fundamental geometric objects, whose origins go back to antiquity. It has come into maturity in the last century through the seminal works of O. Helly, K. Borsuk, P. Erdős, H. Hadwidger, L. Fejes Tóth, B. Grübaum and many other excellent mathematicians who initiated new combinatorial approaches to classical questions studied by ...

Furrow geometry nnder surge and continuous flow

Combinatorial optimization in geometry

In this paper we extend and unify the results of [20] and [19]. As a consequence, the results of [20] are generalized from the framework of ideal polyhedra in H to that of singular Euclidean structures on surfaces, possibly with an infinite number of singularities (by contrast, the results of [20] can be viewed as applying to the case of non-singular structures on the disk, with a finite number...

Combinatorial Geometry for Shape Representation and Indexing

Combinatorial geometry is the study of order and incidence properties of groups of geometric features. Ordering properties for point sets in 2-D and 3-D can be seen as a generalization of ordering properties in 1-D and incidences are conngurations of features that are non-generic such as collinearity of points. By deening qualitative shape properties using combinatorial geometry we get a common...