Polygon clipping is an important operation that computers execute all the time. An algorithm that clips a polygon is rather complex. Each edge of the polygon must be tested against each edge of the clipping window, usually a rectangle. As a result, new edges may be added, and existing edges may be discarded, retained, or divided. Multiple polygons may result from clipping a single polygon. Afte...

Problem 1: Evaluating Convex Polygons This write-up presents several simple algorithms for determining whether a given set of twodimensional points defines a convex polygon (i.e., a convex hull). In Section 1.1, we introduce the notion of regular polygons and provide examples of both convex and non-convex point sets. Section 1.2 presents an algorithm for ordering a set of points such that a cou...

This document proposes a set of deliverables for which—upon completion—I hope to be given the PhD degree. In the next section I motivate why I should spend four years of my life and several ten-thousand dollars of my supervisor’s grant money into the development of various algorithms that operate on polygon meshes. In Section 2 I detail the research contributions that I aim to achieve in the or...

In this paper simulation of the alternating current loss (AC loss) in a high temperature superconducting tape and a HTS cable having 4 layers of polygon conductors using COMSOL Multiphysics software has been reported. The simulation results for the single rectangular tape are verified with the Norris equation for a HTS tape. The effect of increased number of layers on AC loss is also observed u...

‎In this work‎, ‎a regular polygon with $n$ sides is described by a periodic (circular) sequence with period $n$‎. ‎Each element of the sequence represents a vertex of the polygon‎. ‎Each symmetry of the polygon is the rotation of the polygon around the center-point and/or flipping around a symmetry axis‎. ‎Here each symmetry is considered as a system that takes an input circular sequence and g...

Abstract. In this paper, we continue to develop the systematic decomposition theory [18] for the generic Newton polygon attached to a family of zeta functions over finite fields and more generally a family of L-functions of n-dimensional exponential sums over finite fields. Our aim is to establish a new collapsing decomposition theorem (Theorem 3.7) for the generic Newton polygon. A number of a...

In this paper, we reveal a remarkable connection between the Thue-Morse sequence and the Koch snowflake. Using turtle geometry and polygon maps, we realize the Thue-Morse sequence as the limit of polygonal curves in the plane. We then prove that a sequence of such curves converges to the Koch snowflake in the Hausdorff metric. In the final section we consider generalized Thue-Morse sequences an...