Separating Axes David Eberly, Geometric Tools, Redmond WA 98052 https://www.geometrictools.com/ This work is licensed under the Creative Commons Attribution 4.0 International License. To view a copy of this license, visit http://creativecommons.org/licenses/by/4.0/ or send a letter to Creative Commons, PO Box 1866, Mountain View, CA 94042, USA. Created: January 28, 2001 Last Modified: March 2, ...

Abstract: In this work, we consider the value of the momentum map of the symplectic mechanics as an affine tensor called momentum tensor. From this point of view, we analyze the underlying geometric structure of the theories of Lie group statistical mechanics and relativistic thermodynamics of continua, formulated by Souriau independently of each other. We bridge the gap between them in the cla...

Digital watermarking provides a feasible way for copyright protection of multimedia. The major disadvantage of the existing methods is their poor resistance to both extensive geometric distortions and watermark-estimation attack (WEA). In view of this fact, our goal of this paper is to propose a robust image watermarking scheme that can withstand geometric distortions and WEA. Our scheme is mai...

The literature is rich with descriptions of the possible multi-view relations and their use in computer vision. Some of them arise from a purely geometric approach, some others are derived in more of an algebraic fashion. In this paper we show that, with a re-definition of the involved objects and some additional geometric tools, we can come to a more intuitive understanding of some of the most...

Abstract. In this paper, we study geometric properties of surfaces of the generalized Fischer-Burmeister function and its induced merit function. Then, a visualization is proposed to explain how the convergent behaviors are influenced by two descent directions in merit function approach. Based on the geometric properties and visualization, we have more intuitive ideas about how the convergent b...

A view-dependent multiresolution triangulation algorithm is presented for a real-time flythrough. The triangulation of the terrain is generated incrementally onthe-fly during the rendering time. We show that since the view changes smoothly only a few incremental modifications are required to update the triangulation to a new view. The resulting triangles form a multiresolution Delaunay triangul...

Recently, vision research has centred on the extraction and organization of geometric features, and on geometric relations. It is largely assumed that topological structure, that is linked edgel chains and junctions, cannot be extracted reliably from image intensity data. In this paper we demonstrate that this view is overly pessimistic and that visual tasks, such as perceptual grouping, can be...

Advances in additive manufacturing technologies facilitate the fabrication of cellular materials that have tailored functional characteristics. The application of solid freeform fabrication techniques is especially exploited in designing scaffolds for tissue engineering. In this review, firstly, a classification of cellular materials from a geometric point of view is proposed; then, the main ap...

In the paper, the Fenchel problem of level sets in the smooth case is solved by deducing a new and “nice” geometric necessary and sufficient condition for the existence of a smooth convex function with the level sets of a given smooth pseudoconvex function. The main theorem is based on a general differential geometric tool, the space of paths defined on smooth manifolds. This approach provides ...