Local 1-shock curve arcs and local reverse 2-shock curve arcs were constructed, in the geometric context of the wave manifold, in a previous paper. In that geometric context, sonic and sonic’ surfaces are the boundaries of admissible shock curve arcs; in order to introduce the concept of non-local 1-shock curve arcs and non-local reverse 2shock curve arcs it is necessary to understand how a hug...

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 design signatures for curves defined on genus zero surfaces. The signature classifies curves according to the conformal geometry of the given curves and their embedded surface. Based on Teichmüller theory, our signature describes not only the curve shape but also the intrinsic relationship between the curve and its embedded surface. Furthermore, the signature metric is stable, it is close to...

Robust curve design on surface meshes with flexible controls is useful in a wide range of applications but remains challenging. Most existing methods fall into one the two strategies: to discretize polyline, which then optimized, and other directly smooth splines meshes. While former approach usually needs sufficiently dense sampling points, computational costly, latter relaxes requirement suff...

Objective: To evaluate the learning curve of cytoreductive surgery (CRS) and hyperthermic intraperitoneal chemotherapy (HIPEC) in treating peritoneal surface malignancies (PSM). Summary and Background: CRS and HIPEC to treat PSM is a complex procedure with a significant morbidity. A long-lasting training program is required to acquire expertise in this type of operation. Methods: We performed C...

Variational Methods have been frequently used for surface reconstruction and contour extraction (snakes). We present a surface reconstruction method where we assume the surface composed of two regions of di erent types of smoothness. One region of the surface models a \lake" (constant height region with uphill borders). It is surrounded by the other background region which is reconstructed usin...

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...

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...