Mark Pauly | EPFL Graph Search

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Mark Pauly is a full professor at the School of Computer and Communication Sciences at EPFL. Prior to joining EPFL, he was assistant professor at the CS department of ETH Zurich since April 2005. From August 2003 to March 2005 he was a postdoctoral scholar at Stanford University, where he also held a position as visiting assistant professor during the summer of 2005. He received his Ph.D. degree (with distinction) in 2003 from ETH Zurich and his M.S. degree (with highest honors) in 1999 from TU Kaiserslautern. His research interests include computer graphics and animation, shape modeling and analysis, geometry processing, architectural geometry, and digital fabrication. He received the ETH medal for outstanding dissertation, was awarded the Eurographics Young Researcher Award in 2006 and the Eurographics Outstanding Technical Contributions Award in 2016.

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Computational geometry

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Algorithm

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Geometry

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Computational Exploration of Multistable Elastic Knots

Mark Pauly, Yingying Ren, Michele Vidulis

We present an algorithmic approach to discover, study, and design multistable elastic knots. Elastic knots are physical realizations of closed curves embedded in 3-space. When endowed with the material thickness and bending resistance of a physical wire, these knots settle into equilibrium states that balance the forces induced by elastic deformation and self-contacts of the wire. In general, elastic knots can have many distinct equilibrium states, i.e. they are multistable mechanical systems. We propose a computational pipeline that combines randomized spatial sampling and physics simulation to efficiently find stable equilibrium states of elastic knots. Leveraging results from knot theory, we run our pipeline on thousands of different topological knot types to create an extensive data set of multistable knots. By applying a series of filters to this data, we discover new transformable knots with interesting geometric and physical properties. A further analysis across knot types reveals geometric and topological patterns, yielding constructive principles that generalize beyond the currently tabulated knot types. We show how multistable elastic knots can be used to design novel deployable structures and engaging recreational puzzles. Several physical prototypes at different scales highlight these applications and validate our simulation.

2023

The Canopy Pavilion: A lightweight shading structure using a deployable auxetic linkage membrane

Arthur François Blanc, Etienne Bouleau, Tian Chen, Dieter Dietz, Florin Isvoranu, Mark Pauly

We present the Canopy Pavilion, a lightweight shading structure for a social gathering space. The shading surface is realized as a tensioned auxetic linkage membrane, composed of two double-curved anticlastic layers separated by a compression pole. The membrane is assembled flat on the ground from laser-cut hexagonal aluminium panels, and is subsequently mounted on a circular support frame. Tensioning then deploys the surface to its desired target shape. We apply numerical optimization to form-find the equilibrium shape of the tensioned membrane. The geometry of each individual linkage panel is further adapted to reduce material usage, while maximizing the main function of the structure, to provide shading. Our material system offers a number of distinct advantages. Individual panels can be cut from standard sheet material, all connections between panels are identical, the surfaces can be assembled on the ground and deployed easily to their double-curved shape. The pavilion is a first demonstrator for a novel lightweight construction system at architectural scale that has potential applications in facades, roofs, or support structures.

2022

Umbrella Meshes: Elastic Mechanisms for Freeform Shape Deployment

Tian Chen, Florin Isvoranu, Uday Kusupati, Mark Pauly, Davide Pellis, Yingying Ren

We present a computational inverse design framework for a new class of volumetric deployable structures that have compact rest states and deploy into bending-active 3D target surfaces. Umbrella meshes consist of elastic beams, rigid plates, and hinge joints that can be directly printed or assembled in a zero-energy fabrication state. During deployment, as the elastic beams of varying heights rotate from vertical to horizontal configurations, the entire structure transforms from a compact block into a target curved surface. Umbrella Meshes encode both intrinsic and extrinsic curvature of the target surface and in principle are free from the area expansion ratio bounds of past auxetic material systems. We build a reduced physics-based simulation framework to accurately and efficiently model the complex interaction between the elastically deforming components. To determine the mesh topology and optimal shape parameters for approximating a given target surface, we propose an inverse design optimization algorithm initialized with conformal flattening. Our algorithm minimizes the structure's strain energy in its deployed state and optimizes actuation forces so that the final deployed structure is in stable equilibrium close to the desired surface with few or no external constraints. We validate our approach by fabricating a series of physical models at various scales using different manufacturing techniques.

2022

CS-341: Introduction to computer graphics

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