Introduction Let P = p1, . . . , pn be a simple polygon (all polygons are assumed convex throughout this paper). A fundamental problem in geometric optimization is to compute a minimum-area or a minimum-perimeter convex k-gon (denoted QA or Qp, resp.) that encloses P . While efficient algorithms for finding QA are known for more than 20 years [8, 1, 2], the problem of finding Qp has remained op...

Uncontrolled variables often limit meaningful assessment of visual sensitivity. Previously, we developed a procedure and apparatus for in vivo assessment of light absorption by the human lens. In the current study, we modified a widely used automated perimeter to include our procedure for obtaining an index of lens density. Nineteen individuals were tested on both the original apparatus and the...

We consider generalizations of the honeycomb problem to the sphere S and seek the perimeter-minimizing partition into n regions of equal area. We provide a new proof of Masters’ result that three great semicircles meeting at the poles at 120 degrees minimize perimeter among partitions into three equal areas. We also treat the case of four equal areas, and we prove under various hypotheses that ...

Given a set of points P in the plane and profits (or prizes) π : P → R≥0 we want to select a maximum profit set X ⊆ P which maximizes P p∈X π(p) − μ(X) for some particular criterion μ(X). In this paper we consider four such criteria, namely the perimeter and the area of the smallest axis-parallel rectangle containing X, and the perimeter and the area of the convex hull conv(X) of X. Our key res...

BACKGROUND Currently available perimeters have limited capabilities of performing measurements of the visual field in children. In addition, they do not allow for fully automatic measurement even in adults. The patient in each case (in any type of perimeter) has at his disposal a button which he uses to indicate that he has seen a light stimulus. Such restrictions have been offset in the presen...

Coastal dunes are globally recognized as natural features that can be important adaptation approaches for climate change along urban and shores. We evaluated the recovery of coastal on an intensively groomed beach in southern California over a six-year period after grooming was discontinued. Restoration actions were minimal included installation three sides perimeter sand fencing, cessation mec...

Current evidence suggests that the size of the capillary-to-fiber (C/F) interface is a major determinant of O2 flux into muscle fibers, and methods have been developed for estimating the size of this region via the C/F perimeter ratio in perfusion-fixed material (Mathieu-Costello O, Ellis CG, Potter RF, MacDonald IC, and Groom AC. Am J Physiol Heart Circ Physiol 261: H1617-H1625, 1991) and the ...

There are many hard shortest-path search problems that cannot be solved, because best-first search runs out of memory space and depth-first search runs out of time. We propose Forward Perimeter Search (FPS), a heuristic search with controlled use of memory. It builds a perimeter around the root node and tests each perimeter node for a shortest path to the goal. The perimeter is adaptively exten...