In R, one can construct polyhedral surfaces such that, for some point p not on the surface, none of the vertices of the surface is visible from p. For a given compact surface K and a point we study the relation between the set of partial-linear embeddings of K with hidden vertices into R and the set of embeddings of K whose image is a smooth manifold with at least one principal curvature pointi...

This work has been carried out within the framework of the industrial project, so-called TOON, supported by the French government. TOON aims at developing tools for automating the traditional 2D cartoon content production. This paper presents preliminary results of the TOON platform. The proposed methodology concerns the issues of 2D/3D reconstruction from a limited number of drawn projections,...

In this paper we present a NURBS version of the rational interpolating spline with tension introduced in [2], and we extend our proposal to the rectangular topology case. In particular we present some rational interpolating techniques that enable us to reconstruct shape-preserving bivariate NURBS and allow us to interactively modify the resulting surface by a set of tension parameters.

The tensors of curvature play an important role in differential geometry. In surface theory (1990), it is determined by the derivative of unit normal vectors of tangent spaces of the underlying surface. However every geometric object in computation is a discrete model. We can only approximate them. In estimating the curvature on polyhedral surfaces, how to approximate normal vectors is a crucia...

This paper presents a method for interactive design by means of extending the PDE based approach for surface generation. The governing partial differential equation is generalized to arbitrary order allowing complex shapes to be designed as single patch PDE surfaces. Using this technique a designer has the flexibility of creating and manipulating the geometry of shape that satisfying an arbitra...

Compact hyperbolic 3-manifolds are used in cosmological models. Their topology is characterized by their homotopy group π1(M) whose elements multiply by path concatenation. The universal covering of the compact manifold M is the hyperbolic space H or the hyperbolic ball B. They share with M a Riemannian metric of constant negative curvature and allow for the isometric action of the group Sl(2, ...

We study the mean dimension of the moduli space of Brody curves. We introduce the notion of “mean energy” and show that this can be used to estimate the mean dimension. 1. Main results 1.1. Moduli space of Brody curves. M. Gromov introduced a remarkable notion of mean dimension in [6] (see also Lindenstrauss-Weiss [8] and Lindenstrauss [7]). In this paper we study the mean dimension of the modu...

We address the problem of extending the lifetime of wireless sensor networks using multi-path routing based on a family of flexible routes with soft quality of service guarantees in terms of the packets’ delivery latency. We introduce a methodology based on Bezier curves as guiding trajectories in the routing process and we address the balancing of the workload among neighboring nodes. An added...

The Real-Time Calculus (RTC) [16] is a framework to analyze heterogeneous real-time systems that process event streams of data. The streams are characterized by pairs of curves, called arrival curves, that express upper and lower bounds on the number of events that may arrive over any specified time interval. System properties may then be computed using algebraic techniques in a compositional w...

Real-Time Calculus (RTC) [37] is a framework to analyze heterogeneous, real-time systems that process event streams of data. The streams are characterized by pairs of curves, called arrival curves, that express upper and lower bounds on the number of events that may arrive over any specified time interval. A well-known limitation of RTC is that it cannot model systems with states and several wo...