We construct CW spheres from the lattices that arise as the closed sets of a convex closure, the meet-distributive lattices. These spheres are nearly polytopal, in the sense that their barycentric subdivisions are simplicial polytopes. The complete information on the numbers of faces and chains of faces in these spheres can be obtained from the defining lattices in a manner analogous to the rel...

This paper introduces a framework for defining a shape-aware distance measure between any two points in the interior of a surface mesh. Our framework is based on embedding the surface mesh into a high-dimensional space in a way that best preserves boundary distances between vertices of the mesh, performing a mapping of the mesh volume into this high-dimensional space using barycentric coordinat...

In this paper, we propose a novel mesh deformation approach via manipulating differential properties non-uniformly. Guided by user-specified material properties, our method can deform the surface mesh in a non-uniform way while previous deformation techniques are mainly designed for uniform materials. The non-uniform deformation is achieved by material-dependent gradient field manipulation and ...

In this paper, we study the error in the approximation of a convex function obtained via a one-parameter family of approximation schemes, which we refer to as barycentric approximation schemes. For a given finite set of pairwise distinct points Xn := {xi}ni=0 in R, the barycentric approximation of a convex function f is of the form:

-An original procedure for the estimation of the barycentric parameters of a robot is presented. This procedure requires only the processing of measurements provided by an external experimental set-up. The procedure is based on the property that the relations between the robot motion and its reactions on the bedplate are completely independent of the internal joints forces. A convincing validat...

A quasi-regular cell complex is defined and shown to have a reasonable barycentric subdivision. In this setting, Whitney's theorem that the ^-skeleton of the barycentric subdivision of a triangulated n-manifold is dual to the (n /c)th Stiefel-Whitney cohomology class is proven, and applied to projective spaces, lens spaces and surfaces. 1. QR complexes. A (finite) cell structure on a space X is...

Pointwise products and quotients, defined in terms of barycentric and trilinear coordinates, are extended to products P ·Γ and quotients Γ/P, where P is a point and Γ is a curve. In trilinears, for example, if Γ0 denotes the circumcircle, then P ·Γ0 is a parabola if and only if P lies on the Steiner inscribed ellipse. Barycentric division by the triangle center X110 carries Γ0 onto the Kiepert ...

Given groupoids G and H as well as an isomorphism Ψ : Sd G∼= Sd Hbetween subdivisions, we construct an isomorphism P : G∼= H . If Ψ equals SdF forsome functor F , then the constructed isomorphism P is equal to F . It follows thatthe restriction of Sd to the category of groupoids is conservative. These results donot hold for arbitrary categories.

In this paper, we give a complete description of the farthest point map, as defined on regular octahedron with its intrinsic flat cone metric. As consequence show that every well-defined orbit map converges to 1-skeleton barycentric subdivision triangulation.