Edge offset meshes in Laguerre geometry

Edge offset meshes in Laguerre geometry

A mesh M with planar faces is called an edge offset (EO) mesh if there exists a combinatorially equivalent mesh M d such that corresponding edges of M and M d lie on parallel lines of constant distance d. The edges emanating from a vertex of M lie on a right circular cone. Viewing M as set of these vertex cones, we show that the image of M under any Laguerre transformation is again an EO mesh. ...

Generalization of Laguerre Geometry

The article deals with the relationship between Laguerre geometry and Minkowski sum. This relationship is used to create new geometry based generally on fundamental objects different to closed balls that formed Laguerre geometry. In the end of the article, there is defined also generalization of medial axis transform to the newly defined spaces and proved its uniqueness. The article continues t...

Laguerre Geometry of Hypersurfaces in Rn

Laguerre geometry of surfaces in R is given in the book of Blaschke [1], and have been studied by E.Musso and L.Nicolodi [5], [6], [7], B. Palmer [8] and other authors. In this paper we study Laguerre differential geometry of hypersurfaces in Rn. For any umbilical free hypersurface x : M → Rn with non-zero principal curvatures we define a Laguerre invariant metric g on M and a Laguerre invarian...

Edge Flips in Surface Meshes

Little theoretical work has been done on edge flips in surface meshes despite their popular usage in graphics and solid modeling to improve mesh equality. We propose the class of (ε, α)-meshes of a surface that satisfy several properties: the vertex set is an ε-sample of the surface, the triangle angles are no smaller than a constant α, some triangle has a good normal, and the mesh is homeomorp...

Divisible Designs, Laguerre Geometry, and Beyond