Figure 1: Our algorithm produces smooth frame fields in volumes. Frames (a) are represented by spherical harmonic functions (b), attached to each vertex of a tetrahedral mesh. Streamlines and singularities of the field are shown in yellow and red, respectively.

No abstract

It is shown in the paper that the problem of speed observation for mechanical systems that are partially linearisable via coordinate changes admits a very simple and robust (exponentially stable) solution with a Luenberger-like observer. This result should be contrasted with the very complicated observers based on immersion and invariance reported in the literature. A second contribution of the paper is to compare, via realistic simulations and highly detailed experiments, the performance of the proposed observer with well-known high-gain and sliding mode observers. In particular, to show that-due to their high sensitivity to noise, that is unavoidable in mechanical systems applications-the performance of the two latter designs is well below par.

Figure 1: Our algorithm traces polylines on triangulated surfaces. Unlike streamline tracing algorithms, polylines produced by our technique cannot cross each others. It works even with highly perturbed surfaces (left) and supports any type of vector field singularities (right). This property is required to segment surfaces with chart boundaries aligned with a vector field (right). AbstractWe propose an algorithm for tracing polylines on a triangle mesh such that: they are aligned with a Nsymmetry direction field, and two such polylines cannot cross or merge. This property is fundamental for mesh segmentation and is very difficult to enforce with numerical integration of vector fields. We propose an alternative solution based on "stream-mesh", a new combinatorial data structure that defines, for each point of a triangle edge, where the corresponding polyline leaves the triangle. It makes it possible to trace polylines by iteratively crossing trian- * e-mail: ray@loria.fr † e-mail: sokolovd@loria.fr gles. Vector field singularities and polyline/vertex crossing are characterized and consistently handled. The polylines inherits the cross-free property of the stream-mesh, except inside triangles where avoiding local overlaps would require higher order polycurves.