Polygonal designs form a special class of partially balanced incomplete block designs. We resolve the existence problem for polygonal designs with various parameter sets and present several construction methods with blocks of small sizes.

This paper describes a dataow vertex detection algorithm for polygonal modeling of 2D contours. VLSI implementation by a parallel architecture is also proposed. This work is part of a real-time shape recognition system using polygonal models, presently under development.

In the applications such as scientific and medical visualization, highly detailed polygonal meshes are needed. Rendering these polygonal meshes usually exceeds the capabilities of graphics hardware. To improve rendering efficiency and maintain proper interactivity, the polygonal mesh simplification technique is commonly used to reduce the number of polygons of the mesh and to construct the mult...

Thawing permafrost in the Canadian Arctic tundra leads to peat erosion and slumping in narrow and shallow runnel ponds that surround more commonly studied polygonal ponds. Here we compared the methane production between runnel and polygonal ponds using stable isotope ratios, ¹⁴C signatures, and investigated potential methanogenic communities through high-throughput sequencing archaeal 16S rRNA ...

The length of curves may be measured by numeric integration if the curves are given by analytic formulas. Not all curves can or should be described parametrically. In this report we use the alternative grid topology approach. The shortest polygonal Jordan curve in a simple closed one-dimensional grid continuum is used to estimate a curve's length. An O(n) algorithm for finding the shortest poly...

Subdivision rules have traditionally been designed to generate smooth surfaces from polygonal meshes. In this paper we propose to employ subdivision rules as a polygonal modeling tool, specifically to add additional level of detail to meshes. However, existing subdivision schemes have several undesirable properties making them ill suited for polygonal modeling. In this paper we propose a genera...

We consider gauge invariant quark two-point Green’s functions in which the gluonic phase factor follows a skew-polygonal line. Using a particular representation for the quark propagator in the presence of an external gluon field, functional relations between Green’s functions with different numbers of segments of the polygonal lines are established. An integral equation is obtained for the Gree...

Given a polygonal shape Q with n vertices, can it be expressed, up to a tolerance ε in Hausdorff distance, as the Minkowski sum of another polygonal shape with a disk of fixed radius? If it does, we also seek a preferably simple solution shape P; P’s offset constitutes an accurate, vertex-reduced, and smoothened approximation of Q. We give a decision algorithm for fixed radius in O(n logn) time...

Polygonal simplification is at once a very current and a very old topic in computer graphics. As early as 1976 James Clark described the benefits of representing objects within a scene at several resolutions, and flight simulators have long used hand-crafted multi-resolution models of airplanes to guarantee a constant frame rate [Clark 76, Cosman 81]. Recent years have seen a flurry of research...