Smoothing techniques are essential in providing high quality renderings out of polygonal objects that are described with a minimal amount of geometrical information. In order to remove the "polygonal" aspect of rough polygonal meshes, several techniques are available, such as shading or interpolation techniques. Combining the benefits of polygonal interpolation with a very simple and straightfo...

This paper discusses techniques for embedding data into three-dimensional (3D) polygonal models of geometry. Given objects consisting of points, lines, (connected) polygons, or curved surfaces, the algorithms described in this paper produce polygonal models with data embedded into either their vertex coordinates, their vertex topology (connectivity), or both. Such data embedding can be used, fo...

This paper concerns a variant of the multi-goal path planning problem in which goals may be polygonal regions. The problem is to find a closed shortest path in a polygonal map such that all goals are visited. The proposed solution is based on a self-organizing map algorithm for the traveling salesman problem, which is extended to the polygonal goals. Neurons’ weights are considered as nodes ins...

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...