Triangulation of polygon is of very importance in three-dimensional software applications. An algorithm for triangulation of polygon based on binary space-partitioning (BSP) tree idea is proposed in this paper. That is, this algorithm implements triangulation of poly-gon with recursive method according to BSP tree structure. It is suitable for not only simple polygons with arbitrary convex or c...

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.

We present new computations of approximately length-minimizing polygons with fixedthickness. These curves model the centerlines of “tight” knotted tubes with minimal length and fixedcircular cross-section. Our curves approximately minimize the ropelength (or quotient of length andthickness) for polygons in their knot types. While previous authors have minimized ropelength forpol...

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...