We propose a novel type of planar-to-spatial deployable structures that we call elastic geodesic grids. Our approach aims at the approximation of freeform surfaces with spatial grids of bent lamellas which can be deployed from a planar configuration using a simple kinematic mechanism. Such elastic structures are easy-to-fabricate and easy-to-deploy and approximate shapes which combine physics and aesthetics. We propose a solution based on networks of geodesic curves on target surfaces and we introduce a set of conditions and assumptions which can be closely met in practice. Our formulation allows for a purely geometric approach which avoids the necessity of numerical shape optimization by building on top of theoretical insights from differential geometry. We propose a solution for the design, computation, and physical simulation of elastic geodesic grids, and present several fabricated small-scale examples with varying complexity. Moreover, we provide an empirical proof of our method by comparing the results to laser-scans of the fabricated models. Our method is intended as a form-finding tool for elastic gridshells in architecture and other creative disciplines and should give the designer an easy-to-handle way for the exploration of such structures.

Abstract In this paper we propose a novel method for the automatic computation and digital fabrication of artistic string images. String art is a technique used by artists for the creation of abstracted images which are composed of straight lines of strings tensioned between pins distributed on a frame. Together the strings fuse to a perceptible image. Traditionally, artists craft such images manually in a highly sophisticated and tedious design process. To achieve this goal fully automatically we propose a computational setup driven by a discrete optimization algorithm which takes an ordinary picture as input and converts it into a connected graph of strings that tries to reassemble the input image best possibly. Furthermore, we propose a hardware setup for automatic digital fabrication of these images using an industrial robot that spans the strings. Finally, we demonstrate the applicability of our approach by generating and fabricating a set of real string art images.

Abstract We propose a novel method for interactive design of well‐fitting body‐supporting surfaces that is driven by the pressure distribution on the body's surface. Our main contribution is an interactive modeling system that utilizes captured body poses and computes an importance field that is proportional to the pressure distribution on the body for a given pose. This distribution indicates where the body should be supported in order to easily hold a particular pose, which is one of the measures of comfortable sitting. Using our approximation, we propose the entire workflow for interactive design of C 2 smooth surfaces which serve as seats, or generally, as body supporting furniture for comfortable sitting. Finally, we also provide a design tool for R hinoceros /G rasshopper that allows for interactive creation of single designs or entire multi‐person sitting scenarios. We also test the tool with design students and present several results. Our method aims at interactive design in order to help designers to create appropriate surfaces digitally without additional empirical design passes.

We present a novel framework for visualizing routes on mobile devices. Our framework is suitable for helping users explore their environment. First, given a starting point and a maximum route length, the system retrieves nearby points of interest (POIs). Second, we automatically compute an attractive walking path through the environment trying to pass by as many highly ranked POIs as possible. Third, we automatically compute a route visualization that shows the current user position, POI locations via pins, and detail lenses for more information about the POIs. The visualization is an animation of an orthographic map view that follows the current user position. We propose an optimization based on a binary integer program (BIP) that models multiple requirements for an effective placement of detail lenses. We show that our path computation method outperforms recently proposed methods and we evaluate the overall impact of our framework in two user studies.

In this paper we present a novel method for non-linear shape optimization of 3d objects given by their surface representation. Our method takes advantage of the fact that various shape properties of interest give rise to underdetermined design spaces implying the existence of many good solutions. Our algorithm exploits this by performing iterative projections of the problem to local subspaces where it can be solved much more efficiently using standard numerical routines. We demonstrate how this approach can be utilized for various shape optimization tasks using different shape parameterizations. In particular, we show how to efficiently optimize natural frequencies, mass properties, as well as the structural yield strength of a solid body. Our method is flexible, easy to implement, and very fast.

Given the 2-manifold surface of a 3d object, we propose a novel method for the computation of an offset surface with varying thickness such that the solid volume between the surface and its offset satisfies a set of prescribed constraints and at the same time minimizes a given objective functional. Since the constraints as well as the objective functional can easily be adjusted to specific application requirements, our method provides a flexible and powerful tool for shape optimization. We use manifold harmonics to derive a reduced-order formulation of the optimization problem, which guarantees a smooth offset surface and speeds up the computation independently from the input mesh resolution without affecting the quality of the result. The constrained optimization problem can be solved in a numerically robust manner with commodity solvers. Furthermore, the method allows simultaneously optimizing an inner and an outer offset in order to increase the degrees of freedom. We demonstrate our method in a number of examples where we control the physical mass properties of rigid objects for the purpose of 3d printing.

Abstract We present a novel framework for the automatic generation of tourist brochures that include routing instructions and additional information presented in the form of so‐called detail lenses. The first contribution of this paper is the automatic creation of layouts for the brochures. Our approach is based on the minimization of an energy function that combines multiple goals: positioning of the lenses as close as possible to the corresponding region shown in an overview map, keeping the number of lenses low, and an efficient numbering of the lenses. The second contribution is a route‐aware simplification of the graph of streets used for traveling between the points of interest (POIs). This is done by reducing the graph consisting of all shortest paths through the minimization of an energy function. The output is a subset of street segments that enable traveling between all the POIs without considerable detours, while at the same time guaranteeing a clutter‐free visualization.