This study contributes to the discrete differential geometry of triangle meshes, in combination with discrete line congruences associated with such meshes.
We use concepts from discrete differential geometry (star-shaped Gauss images) to express fairness, and we also demonstrate how fairness can be incorporated into interactive geometric design of triangulated freeform skins.
This poster addresses two closely related geometric rationalizations of freeform surfaces with repetitive elements, freeform honeycomb structures defined as torsion-free structures where the walls of cells meet at 120 degrees, and Lobel frames formed by equilateral triangles.
This paper is an overview of architectural structures which are either composed of polyhedral cells or closely related to them. We introduce the concept of a support structure of such a polyhedral cell packing.
Not only do various kinds of meshes with additional properties (like planar faces, or with equilibrium forces in their edges) become available for interactive geometric modeling, but so do other arrangements of geometric primitives, like honeycomb structures.
Motivated by requirements of freeform architecture, and inspired by the geometry of hexagonal combs in beehives, this paper addresses torsion-free structures aligned with hexagonal meshes.
The topic of this paper is optimized shading and lighting systems which consist of planar fins arranged along the edges of a quad-dominant base mesh, that mesh itself covering a reference surface.