Analysis of a Reduced-Order Model for the Simulation of Elastic Geometric Zigzag-Spring Meta-Materials

We analyze the performance of a reduced-order simulation of geometric meta-materials based on zigzag patterns using a simplified representation. As geometric meta-materials we denote planar cellular structures which can be fabricated in 2d and bent elastically such that they approximate doubly-curved 2-manifold surfaces in 3d space. They obtain their elasticity attributes mainly from the geometry of their cellular elements and their connections. In this paper we focus on cells build from so-called zigzag springs. The physical properties of the base material (i.e., the physical substance) influence the behavior as well, but we essentially factor them out by keeping them constant. The simulation of such complex geometric structures comes with a high computational cost, thus we propose an approach to reduce it by abstracting the zigzag cells by a simpler model and by learning the properties of their elastic deformation behavior. In particular, we analyze the influence of the sampling of the full parameter space and the expressiveness of the reduced model compared to the full model. Based on these observations, we draw conclusions on how to simulate such complex meso-structures with simpler models.Comment: 14 pages, 12 figures, published in Computers & Graphics, extended version of arXiv:2010.0807

Topology-Aware Surface Reconstruction for Point Clouds

We present an approach to inform the reconstruction of a surface from a point scan through topological priors. The reconstruction is based on basis functions which are optimized to provide a good fit to the point scan while satisfying predefined topological constraints. We optimize the parameters of a model to obtain likelihood function over the reconstruction domain. The topological constraints are captured by persistence diagrams which are incorporated in the optimization algorithm promote the correct topology. The result is a novel topology-aware technique which can: 1.) weed out topological noise from point scans, and 2.) capture certain nuanced properties of the underlying shape which could otherwise be lost while performing surface reconstruction. We showcase results reconstructing shapes with multiple potential topologies, compare to other classical surface construction techniques, and show the completion of real scan data

Sampling Gabor noise in the spatial domain

Figure 1: Examples of a snake model with Gabor noise sampled on it. The bottom row shows the noise components and the control maps used to weight particular parameters of the noise. The left-most example shows standard Gabor noise, in the middle the frequency of the harmonic is weighted by a hat-profile, and in the right example the noise scale and the frequency are weighted by respective profiles. In all three cases the noise is evaluated in the model’s uv-domain. Gabor noise is a powerful technique for procedural texture gener-ation. Contrary to other types of procedural noise, its sparse con-volution aspect makes it easily controllable locally. In this paper, we demonstrate this property by explicitly introducing spatial vari-ations. We do so by linking the sparse convolution process to the parameterization of the underlying surface. Using this approach, it is possible to provide control maps for the parameters in a natural and convenient way. In order to derive intuitive control of the re-sulting textures, we accomplish a small study of the influence of the parameters of the Gabor kernel with respect to the outcome and we introduce a solution where we bind values such as the frequency or the orientation of the Gabor kernel to a user-provided control map in order to produce novel visual effects