If X is a geodesic metric space and x1, x2, x3 ∈ X, a geodesic triangle T = {x1, x2, x3} is the union of the three geodesics [x1x2], [x2x3] and [x3x1] in X. The space X is δ-hy...
We develop a computational model of shape that extends existing Riemannian models of shape of curves to multidimensional objects of general topological type. We construct shape sp...
Xiuwen Liu, Yonggang Shi, Ivo D. Dinov, Washington...
We present a new algorithm to compute a geodesic path over a triangulated surface. Based on Sethian's Fast Marching Method and Polthier's Straightest Geodesics theory, w...
In this article we show that every group with a finite presentation satisfying one or both of the small cancellation conditions C (1/6) and C (1/4) − T (4) has the property that...
The video Geodesics and Waves introduces the concepts of straightest geodesics and geodesic flow on polyhedral surfaces. It is the third in a series of videos presenting research ...
Konrad Polthier, Markus Schmies, Martin Steffens, ...
The general problem of surface matching is taken up in this study. The process described in this work hinges on a geodesic distance equation for a family of surfaces embedded in t...
Hussein M. Yahia, Etienne G. Huot, Isabelle Herlin...
Geodesic curves in surfaces are not only minimizers of distance, but they are also the curves of zero geodesic (sideways) curvature. It turns out that this property makes patterns...
Helmut Pottmann, Qixing Huang, Bailin Deng, Alexan...
In this paper, we explore a new convention for drawing graphs, the (Manhattan-) geodesic drawing convention. It requires that edges are drawn as interior-disjoint monotone chains o...
Bastian Katz, Marcus Krug, Ignaz Rutter, Alexander...
This paper describes a shape signature that captures the intrinsic geometric structure of 3D objects. The primary motivation of the proposed approach is to encode a 3D shape into a...
Interactive segmentation is useful for selecting objects of interest in images and continues to be a topic of much study. Methods that grow regions from foreground/background seed...