Measuring and controlling fairness of triangulations

Abstract

The fairness of meshes that represent geometric shapes is a topic that has been studied extensively and thoroughly. However, the focus in such considerations often is not on the mesh itself, but rather on the smooth surface approximated by it, and fairness essentially expresses a mesh´s suitability for purposes such as visualisation or simulation. This paper focusses on meshes in the architectural context, where vertices, edges, and faces of meshes are often highly visible,and any notion of fairness must take new aspects into account. 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.