Minimum convex partition of a constrained point set

Minimum convex partition of a constrained point set

A convex partition with respect to a point set S is a planar subdivision whose vertices are the points of S, where the boundary of the unbounded outer face is the boundary of the convex hull of S, and every bounded interior face is a convex polygon. A minimum convex partition with respect to S is a convex partition of S such that the number of convex polygons is minimised. In this paper, we wil...

Minimum Weight Convex Quadrangulation of a Constrained Point Set

A convex quadrangulation with respect to a point set S is a planar subdivision whose vertices are the points of S, where the boundary of the unbounded outer face is the boundary of the convex hull of S, and every bounded interior face is convex and has four points from S on its boundary. A minimum weight convex quadrangulation with respect to S is a convex quadrangulation of S such that the sum...

Global Minimum Point of a Convex Function

In this paper we prove the existence of an unique global minimum point of a convex function under some smoothness conditions. Our proof permits us to calculate numerically such a minimum point utilizing a constructive homotopy method.

On a partition of point sets into convex polygons

Constrained Minimum - WidthAnnuli of Point Sets ?

We study the problem of determining whether a manufactured disc of certain radius r is within tolerance. More precisely, we present algorithms that, given a set of n probe points on the surface of the manufactured object, compute the thinnest annulus whose outer (or inner, or median) radius is r and that contains all the probe points. Our algorithms run in O(n log n) time.