Conference Agenda

Geometric modeling in the early design phase typically consists of pure shape design with little or no consideration of material properties, functionality and fabrication. The separation of geometry from engineering and manufacturing results in a costly product development process with multiple feedback loops. This minisymposium presents recent research on computational design tools which respect material properties and constraints imposed by function and fabrication. To achieve high performance, the additional constraints are closely tied to an adapted geometric representation or even formulated in terms of geometry.

Geometric modeling is very closely related to manufacturing in situations when objects modeled in the digital realm are subsequently manufactured. The leading manufacturing technology is Computer Numerically Controlled (CNC) machining and this talk will focus on the finishing stage called flank milling. At this stage of machining, high accuracy of few micrometers for objects of size of tens of centimeters is needed and therefore the path-planning algorithms have to be carefully designed to respect synergy between the geometry of the milling tool and the input object. I will discuss two recent projects that look for the best initialization of a conical milling tool and the sequential path-planning algorithm. Finally, I will discuss future research directions towards machining with custom-shaped milling tools.

We present a discrete theory for modeling developable surfaces through quadrilateral meshes satisfying simple angle constraints, termed discrete orthogonal geodesic nets (DOGs). Our model is simple, local, and, unlike previous works, it does not directly encode the surface rulings. We prove and experimentally demonstrate strong ties to smooth developable surfaces including a set of convergence theorems. We show that the constrained shape space of DOGs is locally a manifold of a fixed dimension, apart from a set of singularities, implying that generally DOGs are continuously deformable. Smooth flows can then be constructed by a smooth choice of vectors on the manifold’s tangent spaces, selected to minimize a desired objective function under a given metric. We show how to compute such vectors, and we use our findings to devise a geometrically meaningful way to handle singular points. We base our shape space metric on a novel DOG Laplacian operator, which is proved to converge under sampling of an analytical orthogonal geodesic net. We apply the developed tools in an editing system for developable surfaces that supports arbitrary bending, stretching, cutting, (curved) folds, as well as smoothing and subdivision operations

Developable surfaces can be fabricated by smoothly bending flat pieces of material without stretching or shearing. This enables a variety of fabrication methods, such as fabrication from flat material or 5-axis CNC milling. We introduce a discrete definition of developability for triangle meshes which exactly captures two key properties of smooth developable surfaces, namely flattenability and presence of straight ruling lines, and show the importance of both of these properties. This definition provides a starting point for algorithms in developable surface modeling - we consider a variational approach that drives a given mesh toward developable pieces separated by regular seam curves. Computation amounts to gradient-based optimization of an energy with support in the vertex star, without the need to explicitly cluster patches or identify seams. We also explore applications of this energy to developable design and manufacturing.

The design of 3D structures for architecture is not only geometric but involves financial, legal and statics considerations. It would be very valuable if design tools could incorporate some of these aspects already in an early state of design, in an interactive manner. In this presentation we show examples of how statics - both as a constraint and as an optimization target - can feature in the design of wide-span lightweight structures. We discuss a discretization of the Airy stress potential and its connection to selfsupporting surfaces and weight optimization.