We explore non-orientable surfaces and their associated curve complexes. Studying the combinatorics modeled by the curve complex of a surface helps elucidate the algebraic properties of the mapping class group of the surface. We begin by studying geometric properties of the curve complexes of non-orientable surfaces and the geometric properties of natural sub-complexes of the curve complex. Fin...

We present efficient and robust algorithms for intersecting a rational parametric freeform surface with a general swept surface. A swept surface is given as a one-parameter family of cross-sectional curves. By computing the intersection between a freeform surface and each cross-sectional curve in the family, we can solve the intersection problem. We propose two approaches, which are closely rel...

This paper presents an algorithm to compute the bisector curve of two planar paramet-ric curves. We reduce the problem of computing a bisector curve to that of intersecting two developable surfaces. Given an input curve C (t) = (x(t); y(t)), the corresponding developable surface D C(t) is constructed symbolically as the envelope surface of a one-parameter family of tangent planes of the parabol...

Following our previous work on metamaterial high-impedance surfaces made of Hilbert curve inclusions, here we theoretically explore the performance of the high-impedance surfaces made of another form of spacefilling curve known as the Peano curve. This metamaterial surface, formed by a 2-D periodic arrangement of Peano curve inclusions, is located above a conducting ground plane and is shown to...

Based on Freed-forward Neural Networks, we develop a new method to approximate curves contained on the given surface; the main contribution is to convert the problems of space curve approximation on surfaces into the plane curve approximation by point projection. The final approximation curve restricted on the surface is achieved via the intersection of surface and cylinder whose directrix is p...

In many high-speed automated equipment, such as placement machines in surface mount technology lines, the most important thing is to move certain device to specific positions quickly. The trajectory is not critical. These machines utilize slew motions. The process of such machines can be divided into a set of sequential tasks moving between programmed points. In order to operate the machines ef...