Dupin cyclides are canal surfaces defined as envelopes of a family of oriented spheres which touch three given oriented spheres. With respect to their attractive geometric properties they are often used in Computer Aided Geometric Design and in many engineering applications. In this paper, we study these surfaces from the point of view of Lie sphere geometry. This representation enables to solv...

The acquisition of geometric information from realworld objects has become a major way of modeling complex scenes and environments. Unfortunately, most optical methods for geometric model acquisition require the combination of partial information from different view points in order to obtain a single, coherent model. This, in turn, requires the registration of partial models into a common coord...

In this paper we analyze the dynamics of N point vortices moving on a sphere from the point of view of geometric mechanics. The formalism is developed for the general case of N vortices, and the details are worked out for the ~integrable! case of three vortices. The system under consideration is SO~3! invariant; the associated momentum map generated by this SO~3! symmetry is equivariant and cor...

Marengo and the second author have developed in the last years a geometric model of social choice when this takes place among bundles of interdependent elements, showing that by bundling and unbundling the same set of constituent elements an authority has the power of determining the social outcome. In this paper we will tie the model above to tournament theory, solving some of the mathematical...

Previous research has shown that there is a clear relationship between the urban morphology on one hand and local solar irradiance air temperature other hand. In order to describe climatology its spatial variations sky view factor (SVF) plays key role. This fraction of visible provides an indication street geometry building density. Adding SVF as evaluation element in planning be used coordinat...

IVRT is an ITS for visual reasoning, using the missing view problem. It combines an ITS framework with a solid modeling kernel that supports hintgenerating rules using geometric reasoning. We develop an ontology for IVRT’s hint generation rules, and a separate ontology for IVRT’s teaching strategy. Teaching strategy rules are stored in a custom text format, with compilation to Jess. The ability...