Some recent methods of Computer Aided Geometric Design are related to the apolar bilinear form, an inner product on the space of homogeneous multivariate polynomials of a fixed degree, already known in 19th century invariant theory. Using a generalized version of this inner product, we derive in a straightforward way some of the recent results in CAGD, like Marsden’s identity, the expression fo...

Discrete and continuous reenement equations have been widely studied in the literature for the last few years, due to their applications to the areas of wavelet analysis and geometric modeling. However, there is nòuniversal' theorem that deals with the problem about the existence of compactly supported distributional solutions for both discrete and continuous reenement equations simultaneously....

We consider the problem of integration of d-variate analytic functions defined on the unit cube with directional derivatives of all orders bounded by 1. We prove that the Clenshaw Curtis Smolyak algorithm leads to weak tractability of the problem. This seems to be the first positive tractability result for the Smolyak algorithm for a normalized and unweighted problem. The space of integrands is...

In this primarily expository paper we study the analysis of the Diederich-Fornæss worm domain in complex Euclidean space. We review its importance as a domain with nontrivial Nebenhülle, and as a counterexample to a number of basic questions in complex geometric analysis. Then we discuss its more recent significance in the theory of partial differential equations: the worm is the first smoothly...

In model-based computer vision it is necessary to have a geometric model of the object the pose of which is being estimated. In this paper a very compact model of the shoulder complex and arm is presented. First an investigation of the anatomy of the arm and the shoulder is conducted to identify the primary joints and degrees of freedom. To model the primary joints we apply image features and c...

This work presents a methodology for 3D modeling of lip motion in speech production and its application to lip tracking and visual speech animation. Firstly, a geometric modeling allows to create a 3D lip model from 30 control points for any lip shape. Secondly, a statistical analysis, performed on a set of 10 key shapes, generates a lip gesture coding with three articulatory-oriented parameter...

“Particle”-trajectories are defined as integrable dxμdp μ = 0 paths in projective space. Quantum states evoluting on such trajectories, open or closed, do not delocalise in (x, p) projection, the phase associated to the trajectories being related to the previously known geometric (Berry) phase and to the Classical Mechanics action. High Energy Physics properties of states evoluting on “particle...

This paper presents automatic methods to extract and reconstruct industrial site pipe-runs from large-scale point clouds. We observe three key characteristics in this modeling problem, namely, primitives, similarities, and joints. While primitives capture the dominant cylindric shapes, similarities reveal the inter-primitive relations intrinsic to industrial structures because of human design a...