There are dierent ways to code the geodesic flows on surfaces with negative curvature. Such code spaces give a useful tool to verify the dynamical properties of geodesic flows. Here we consider special subspaces of geodesic flows on Hecke surface whose arithmetic codings varies on a set with innite alphabet. Then we will compare the topological complexity of them by computing their topological ...

Surface curvature properties have been successfully employed for surface classification and 3D object recognition. A number of methods have been proposed in the computer vision literature for the estimation of curvature; some are based on the analytic computation of derivatives from a local surface fit, and others estimate derivatives or curvature directly from the range data. In this paper, we...

Each bacterial species has a characteristic shape, but the benefits of specific morphologies remain largely unknown. To understand potential functions for cell shape, we focused on the curved bacterium Caulobacter crescentus. Paradoxically, C. crescentus curvature is robustly maintained in the wild but straight mutants have no known disadvantage in standard laboratory conditions. Here we demons...

We introduce an efficient, robust means of obtaining reliable surface descriptions, suitable for object recognition, at multiple scales from range data. Mean and Gaussian curvatures are used to segment the surface into regions of four saliency classes, each based on curvature consistency. We evaluate curvature consistency in a robust multivoting scheme. Contiguous regions consistent in both mea...

Local shape is an important attribute that can be sensed by exploratory movements of the finger. Normally this involves a blend of tactile and proprioceptive cues. A curved surface will deform the pad of a single finger and so tactile cues can indicate whether a surface is convex or concave or whether it slopes one way or another. When more subtle discriminations must be made between different ...

This paper develops a method to analyze and compute the lines of curvature and their differential geometry defined on implicit surfaces. With our technique, we can explicitly obtain the analytic formulae of the associated geometric attributes of an implicit surface, e.g. torsion of a line of curvature and Gaussian curvature. Additionally, it can be used to directly derive the closed formulae of...