In this paper, we present a new and more general version of polygonal approximation problem (GPA). Given an N−vertex polygonal curve P in the n-dimensional space <n, we approximate P by finding another M−vertex polygonal curve Ṗ , such that the vertices of Ṗ are an ordered subsequence of the curve points along P . The definition of the classical polygonal approximation problem (PA) demands the ...

Classical dissections convert any planar polygonal region onto any other polygonal region having the same area. If two convex polygonal regions are isoparametric, that is, have equal areas and equal perimeters, our main result states that there is always a dissection, called a complete dissection, that converts not only the regions but also their boundaries onto one another. The proof is constr...

This paper is an overview of recent developments in the construction of finite element interpolants, which are C-conforming on polygonal domains. In 1975, Wachspress proposed a general method for constructing finite element shape functions on convex polygons. Only recently has renewed interest in such interpolants surfaced in various disciplines including: geometric modeling, computer graphics,...

We propose a new polygonal approximation method for soft objects. While the conventional polygonization methods decompose space into small-sized cells and compute many pieces of polygons for the cells, this new method polygonizes a soft object by smoothing an initial polygonal approximation using subdivision surface schemes. The initial polygonal approximation is generated by the union of the p...

Conspicuous and visually unpleasant polygonal silhouettes are often produced when rendering a polyhedral approximation (i.e. a polygonal mesh) of a smooth surface model, regardless whatever shading method is used to improve the appearance of the interior region. We present in this paper a technique for displaying a coarse polygonal mesh with smooth silhouette. Unlike other existing methods that...

2014 Polygonal defect arrays in lipid liquid crystals prepared from dipalmitoyl-, dimyristoyl-, and dilaurylphosphatidylcholine with various concentrations of water have been observed and characterized using optical microscopy. These arrays appear similar to the polygonal arrays previously observed in thermotropic smectic and cholesteric liquid crystals. The parabolic focal conic model proposed...

A spanning tree of an unweighted graph is a minimum average stretch spanning tree if it minimizes the ratio of sum of the distances in the tree between the end vertices of the graph edges and the number of graph edges. We consider the problem of computing a minimum average stretch spanning tree in polygonal 2-trees, a super class of 2-connected outerplanar graphs. For a polygonal 2-tree on n ve...

ß We develop an application to identify and characterize polygonal features in SAR images, based on a watershed algorithm, modified for a good robustness to radar noise. ß Our system performs a multi-scale analysis of the image. Oversegmentation is prevented by a selection of outstanding contours; regions with less prominent contours are merged ß This analysis is applied to Venus images from th...

In 2000 A. Bezdek asked which plane convex bodies have the property that whenever an annulus, consisting of the body less a sufficiently small scaled copy of itself, is covered by strips, the sum of the widths of the strips must still be at least the minimal width of the body. We characterise the polygons for which this is so. In this note we will give a complete answer for convex polygons to t...