Beyond developable: computational design and fabrication with auxetic materials

We present a computational method for interactive 3D design and rationalization of surfaces via auxetic materials, i.e., flat flexible material that can stretch uniformly up to a certain extent. A key motivation for studying such material is that one can approximate doubly-curved surfaces (such as the sphere) using only flat pieces, making it attractive for fabrication. We physically realize surfaces by introducing cuts into approximately inextensible material such as sheet metal, plastic, or leather. The cutting pattern is modeled as a regular triangular linkage that yields hexagonal openings of spatially-varying radius when stretched. In the same way that isometry is fundamental to modeling developable surfaces, we leverage conformal geometry to understand auxetic design. In particular, we compute a global conformal map with bounded scale factor to initialize an otherwise intractable non-linear optimization. We demonstrate that this global approach can handle non-trivial topology and non-local dependencies inherent in auxetic material. Design studies and physical prototypes are used to illustrate a wide range of possible applications

Mean curvature flow for generating discrete surfaces with piecewise constant mean curvatures

Piecewise constant mean curvature (P-CMC) surfaces are generated using the mean curvature flow (MCF). As an extension of the known fact that a CMC surface is the stationary point of an energy functional, a P-CMC surface can be obtained as the stationary point of an energy functional of multiple patch surfaces and auxiliary surfaces between them. A new formulation is presented for the MCF as the negative gradient flow of the energy functional for multiple patch continuous surfaces, which are further discretized so as to determine the change in the vertex positions of triangular meshes on the surface as well as along the internal boundaries between patches. Numerical examples show that multiple patch surfaces approximately reach the specified mean curvatures through the proposed method, which can diversify the options for the shape design using CMC surfaces

Automated generation of flat tileable patterns and 3D reduced model simulation

The computational fabrication community is developing an increasing interest in the use of patterned surfaces, which can be designed to show ornamental and unconventional aesthetics or to perform as a proper structural material with a wide range of features. Geometrically designing and controlling the deformation capabilities of these patterns in response to external stimuli is a complex task due to the large number of variables involved. This paper introduces a method for generating sets of tileable and exchangeable flat patterns as well as a model-reduction strategy that enables their mechanical simulation at interactive rates. This method is included in a design pipeline that aims to turn any general flat surface into a pattern tessellation, which is able to deform under a given loading scenario. To validate our approach, we apply it to different contexts, including real-scale 3D printed specimens, for which we compare our results with the ones provided by a ground-truth solver

Quantifying Geometric Changes in BIM-GIS Conversion

Abstract. A conversion process is often carried out to migrate data during BIM and GIS integration, often from the highly detailed BIM to the less detailed GIS environment. Due to the differences between the two systems, information loss occurs during conversion. While research has been focusing on addressing information loss on the semantics, it is also necessary to quantify geometric changes resulted from converting geometry representations used in the two systems. This paper describes a preliminary study which evaluates the geometric changes during conversion for a list of primitives. The outcome shows that the metrics are useful both to those carrying out the conversion to balance between potential information loss and resulting data complexity, and to end users of the converted information to assess the fitness for purpose and impact of the conversion results