Area control in generating smooth and convex grids over general plane regions

Area control in generating smooth and convex grids over general plane regions

A new method (adaptive smoothness functional) to produce convex and smooth grids over general plane regions has been introduced in a recent work by the authors [10]; this method belongs to the variational grid generation approach. Theoretical results showing that a convex grid over a region is obtained when this method is applied, were presented; the basic assumption was that at least one conve...

Smooth and Convex Grid Generation over General Plane Regions

A new method to produce convex and smooth grids over general plane regions is introduced. This method belongs to the discrete variational grid generation approach. Theoretical results presented guarantee that a convex grid over a region is obtained when this method is applied; the basic assumption is that at least one convex grid exists. A procedure to control large cells, in addition to smooth...

Convex Regions in the Plane and Their Domes

Area Distances of Convex Plane Curves and Improper Affine Spheres

Abstract. The area distance to a convex plane curve is an important concept in computer vision. In this paper we describe a strong link between area distances and improper affine spheres. This link makes possible a better understanding of both theories. The concepts of the theory of affine spheres lead to a new definition of an area distance on the outer part of a convex plane arc. Also, based ...

Cutting plane oracles to minimize non-smooth non-convex functions

We discuss a bundle method for non-smooth non-convex optimization programs. In the absence of convexity, a substitute for the cutting plane mechanism has to be found. We propose such a mechanism and prove convergence of our method in the sense that every accumulation point of the sequence of serious iterates is critical.