Survey of two-dimensional acute triangulations

AbstractWe give a brief introduction to the topic of two-dimensional acute triangulations, mention results on related areas, survey existing achievements–with emphasis on recent activity–and list related open problems, both concrete and conceptual

Generalized D-Forms Have No Spurious Creases

A convex surface that is flat everywhere but on finitely many smooth curves (or seams) and points is a seam form. We show that the only creases through the flat components of a seam form are either between vertices or tangent to the seams. As corollaries we resolve open problems about certain special seam forms: the flat components of a D-form have no creases at all, and the flat component of a pita-form has at most one crease, between the seam’s endpoints

Development of Physical Connectors To Assemble Unfolded Planar Panels for the Construction of Large Shapes

In this work, I propose to identify and construct physical counterparts of the links in geometric data structures that are used in shape modeling. These physical connections will be used to construct large shapes from unfolded polygonal meshes that are represented by geometric data structures. I will implement physical connectors as an extension to a unfolding system that has been developing in our laboratory at Texas A&M University. Using these connectors, any unfolded shape can be constructed by using laser-cut developable panels based on corresponding data structures. This approach is particularly suitable to construct complicated sculptural and architectural shapes from anisotropic materials that can only be bent in one direction