In architectural freeform design, the relation between shape and fabrication poses new
challenges and requires more sophistication from the underlying geometry. The new …

We define a discrete Laplace–Beltrami operator for simplicial surfaces (Definition 16). It
depends only on the intrinsic geometry of the surface and its edge weights are positive. Our …

The geometric challenges in the architectural design of freeform shapes come mainly from
the physical realization of beams and nodes. We approach them via the concept of parallel …

The cotangent formula constitutes an intrinsic discretization of the Laplace-Beltrami operator
on polyhedral surfaces in a finite-element sense. This note gives an overview of …

We establish a connection between two previously unrelated topics: a particular discrete
version of conformal geometry for triangulated surfaces, and the geometry of ideal polyhedra …

In the last years triangle meshes have become increasingly popular and are nowadays
intensively used in many different areas of computer graphics and geometry processing. In …

We present a discrete theory for modeling developable surfaces as quadrilateral meshes
satisfying simple angle constraints. The basis of our model is a lesser-known …

We provide conditions for convergence of polyhedral surfaces and their discrete geometric
properties to smooth surfaces embedded in Euclidean 3-space. Under the assumption of …

The circle is arguably the most studied ob-ject in mathematics, yet I am here to tell the tale of
circle packing, a topic which is likely to be new to most readers. These packings are …

We describe a new algorithm that solves a classical geometric problem: Find a surface of
minimal area bordered by an arbitrarily prescribed boundary curve. Existing numerical …