On the refinements of a polyhedral subdivision

Vertex-Rounding a Three-Dimensional Polyhedral Subdivision

Generating Combinatorial Complexes of Polyhedral Type

The paper describes a method for generating combinatorial complexes of polyhedral type. Building blocks B are implanted into the maximal simplices of a simplicial complex C, on which a group operates as a combinatorial reflection group. Of particular interest is the case where B is a polyhedral block and C the barycentric subdivision of a regular incidence-polytope K together with the action of...

Polyhedral representation of discrete Morse functions

It is proved that every discrete Morse function in the sense of Forman on a finite regular CW complex can be represented by a polyhedral Morse function in the sense of Banchoff on an appropriate embedding in Euclidean space of the barycentric subdivision of the CW complex; such a representation preserves critical points. The proof is stated in terms of discrete Morse functions on posets.

A Projective Framework for Polyhedral Mesh Modelling

I present a novel framework for polyhedral mesh editing with face-based projective maps, that preserves planarity by definition. Such meshes are essential in the fields of construction and architectural design. By using homogeneous coordinates to describe vertices, we gain a rich and linear shape space of meshes with planar faces. The generality of this space allows for polyhedral geometric pro...

Discrete curvatures and Gauss maps for polyhedral surfaces

The paper concerns the problem of correct curvatures estimates directly from polygonal meshes. We present a new algorithm that allows the construction of unambiguous Gauss maps for a large class of polyhedral surfaces, including surfaces of non-convex objects and even non-manifold surfaces. The resulting Gauss map provides shape recognition and curvature characterisation of the polyhedral surfa...