Motivated by analogies to classical differential geometry, we propose a theory of smoothness of polyhedral surfaces including suitable notions of normal vectors, tangent planes, asymptotic directions, and parabolic curves that are invariant under projective transformations.
In this paper we study pleated structures generated by folding paper along curved creases. We discuss their properties and the special case of principal pleated structures.
In this paper we study pleated structures generated by folding paper along curved creases. We discuss their properties and the special case of principal pleated structures.
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.