There are two parts in this master's project report. Part 1 describes the features implemented in Lineogrammer paper submitted in April 2008. Part 2 introduces the features implemented since then. Initially, the underlying geometrical structure of the lineogrammer only has lines. In order to manipulate polygons more conveniently, the need to recognize polygons becomes essential. Once a polygon ...

We introduce the concept of weighted skeleton of a polygon and present various decomposition and optimality results for this skeletal structure when the underlying polygon is convex.

This paper considers transformations of a planar polygon P according to two types of operations. A vertex pop (or a pop) reflects a vertex vi, i ∈ {1, . . . , n}, across the line through the two adjacent vertices vi−1 and vi+1 (where index arithmetic is modulo n). A popturn rotates vi in the plane by 180◦ about the midpoint of the line segment vi−1vi+1. Pops and popturns are polygon reconfigura...

Point vortex, first introduced by Helmholtz in 1958, is a classic model in two-dimensional incompressible fluid dynamics. The solutions to the equations of various configurations of point vortices have provided many insightful findings in various physical fields involved with vortex dynamics, such as atomic structure, large scale weather patterns and superconductors, etc (Aref 1988). One kind o...

We present the rst polynomial-time algorithm that nds the shortest route in a simple polygon such that all points of the polygon are visible from the route. This route is called the shortest watchman route, and we do not assume any restrictions on the route or on the simple polygon. Our algorithm runs in worst case O(n 6) time, but it is adaptive making it run faster on polygons with simple str...

VQ = {(q, a) ∈ Z : gcd(q, a) = 1, max{|a|, |q|} ≤ Q}. Then the Jarńık polygon PQ is the unique (up to translation) convex polygon whose sides are precisely the vectors in VQ. In other words, PQ is the polygon whose vertices can be obtained by starting from an arbitrary point in R and adding the vectors in VQ one by one, traversing those vectors in a counterclockwise direction. For example, the ...

We present optimal parallel algorithms that run in O(p n) time on a p n p n mesh-connected computer for a number of fundamental problems concerning visibility and distance properties inside a simple polygon. These include computing shortest paths, shortest path trees, shortest path partitions, all-farthest neighbors (both internal and external), the visibility polygon of a point, the weak visib...

Abstract—Conjugate natural convection in a differentially heated square enclosure containing a polygon shaped object is studied numerically in this article. The effect of various polygon types on the fluid flow and thermal performance of the enclosure is addressed for different thermal conductivities. The governing equations are modeled and solved numerically using the built-in finite element m...

We present optimal parallel algorithms that run in O p n time on a p n pn mesh connected computer for a number of fundamental problems concerning proximity and vis ibility in a simple polygon These include computing shortest paths shortest path trees shortest path partitions all farthest neighbors the visibility polygon of a point the weak visibility polygon of an edge and the ray shooting problem

Based on the planar polygon shape classification, we propose a method—Standardized Binary String Descriptor of Convex Polygon—for classification of convex polygons, making it more precise. Thus, the model database space is pruned and the number of shape models compared with, when doing match query and similarity query, is reduced. Furthermore, the number of equivalence class of convex polygon f...