Geometry for Digital Fabrication and Architecture

Surface Reconstruction

Andreas Bærentzen (DTU)

Topics in Surface Reconstruction. We will introduce the PyGel Python geometry processing library, and then introduce some advance techniques in mesh reconstruction such as volumetric reconstruction and our new Rotation System Reconstruction method.

Directional-Field Methods for Meshing in Fabrication Pipelines

Amir Vaxman (U. Edinburgh)

We will explore a classical meshing pipeline that involves defining directional fields on triangle meshes, representing candidate gradients of a parameterization that can be traced into a mesh. This flexible pipeline allows for prescribing diverse objectives and constraints within the meshing process. Building on this framework, we will explore applications such as fabric tessellation, architectural geometry, and physical simulation.

3D Elastic Curves from Multiple Perspectives

Oliver Gross (UCSD)

This mini-course will discuss 3D elastic curves through a range of different characterizations. Starting from the classical variational formulation and a brief introduction to the relevant geometric variational principles, we will compare several ways of recognizing elastic curves and discuss how these viewpoints provide useful ways to study and explore them. The goal is to show how continuous theory, geometric structure, and discrete models give different but related perspectives on the same objects. The exercises will give participants a hands-on opportunity to investigate some of the concepts and geometric objects introduced in the lectures.

Elastic Rod Assemblies: From Geometric Principles to Physics-Based Design Optimization

Quentin Becker (U. Tokyo)

Elastic rod assemblies turn slender, bendable elements into complex curved geometries: bending-active gridshells, umbrella meshes, and woven structures have been realized as pavilions, shading screens, and furniture. Their appeal is partly practical—such structures can be manufactured flat from sheet stock and then deployed or assembled into doubly curved shapes—yet predicting and controlling the resulting form demands both geometric abstraction and accurate physical models.

This mini-course presents the discrete elastic rod (DER) model and its use for both forward simulation and physics-based inverse design of such assemblies. We begin with a geometric perspective, characterizing how isolated lamellae deform and how coupled rod networks exhibit emergent behaviors that can often be interpreted through Gauss–Bonnet-type arguments. We then introduce DER as a discrete elastic energy, cast force-balance equations as variational problems solved with sparse Newton-type methods, and express the deployment through the resulting KKT systems. Building on this, we formulate design optimization as a nested two-stage problem and develop adjoint sensitivity analysis to efficiently differentiate through the forward simulation—the inner problem. Two hands-on Python sessions complement the lectures: participants will implement parts of the DER model, compute equilibria of pinned rods, and explore design through interactive examples.

Topology Optimization for Generating Geometries

Niels Aage (DTU)

(Description to follow)