Elastic gridshells are efficient structures covering large spans with little material. They fabricated using a network of straight members deformed into doubly curved shapes. Researchers and builders have used two families remarkable curves to generate planks: geodesic gridshells, where the planks follow lay along tangent plane surface, asymptotic lines orthogonal surface normal. This article p...

We present a new texture discrimination method for textured color images in the wavelet domain. In each wavelet subband, the correlation between the color bands is modeled by a multivariate generalized Gaussian distribution with fixed shape parameter (Gaussian, Laplacian). On the corresponding Riemannian manifold, the shape of texture clusters is characterized by means of principal geodesic ana...

We define a geodesic distance associated with the polarization space of non-singular coherency matrices. Its introduction on HPD(2) (the manifold of Hermitian positive definite matrices of dimension 2) can be directly related to the Jones calculus. The expression of distance and related notion of mean value in this particular metric space are also presented. We investigate the properties of thi...

Given a connected graph and a vertex x ∈ V (G), the geodesic graph Px(G) has the same vertex set as G with edges uv iff either v is on an x − u geodesic path or u is on an x − v geodesic path. A characterization is given of those graphs all of whose geodesic graphs are complete bipartite. It is also shown that the geodetic number of the Cartesian product of Km,n with itself, where m,n ≥ 4, is e...

Main results. Let Tg,n andMg,n denote the Teichmüller and moduli space respectively of genus g Riemann surfaces with n marked points. The Teichmüller metric on these spaces is a natural Finsler metric that quantifies the failure of two different Riemann surfaces to be conformally equivalent. It is equal to the Kobayashi metric [Roy74], and hence reflects the intrinsic complex geometry of these ...

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, ...

Geodesics have a wide range of applications in CAD, shape design and machine learning. Current research on geodesic computation focuses primarily on parametric surfaces and mesh representations. There is little work on implicit surfaces. In this paper, we present a novel algorithm able to compute the exact geodesics on implicit surfaces. Although the existing Fast Marching Method can generate a...