Maintaining the Extent of a Moving Point Set

Maintaining the Extent of a Moving Point Set

Let S be a set of n moving points in the plane. We give new eecient and compact kinetic data structures for maintaining the diameter, width, and smallest area or perimeter bounding rectangle of the points. When the points in S move with pseudo-algebraic motions, these structures process O(n 2+) events. We also give constructions showing that (n 2) combinatorial changes are possible in these ext...

Maintaining the point correspondence in the level set framework

In this paper, we propose a completely Eulerian approach to maintain a point correspondence during a level set evolution. Our work is in the spirit of some recent methods (Adalsteinsson & Sethian, J. Comp. Phys. 2003; Xu & Zhao, J. Sci. Comp. 2003) for handling interfacial data on moving level set interfaces. Our approach maintains an explicit backward correspondence from the evolving interface...

Structure of the Fixed Point of Condensing Set-Valued Maps

In this paper, we present structure of the fixed point set results for condensing set-valued map. Also, we prove a generalization of the Krasnosel'skii-Perov connectedness principle to the case of condensing set-valued maps.

Maintaining Visibility of a Polygon with a Moving Point of View

Maintaining Visibility Polygon of a Moving Point Observer in Polygons with Holes∗

Computing the visible region from a moving point in planar environments has many applications in computer graphics and computational geometry. This problem has been considered thoroughly before and several algorithms have been proposed for it. Almost all these solutions use a preprocessing step to build data structures which reflect the visibility coherence of the scene. Then, this data is used...