Combinatorial and Asymptotical Results on the Neighborhood Grid

In 2009, Joselli et al introduced the Neighborhood Grid data structure for fast computation of neighborhood estimates in point clouds. Even though the data structure has been used in several applications and shown to be practically relevant, it is theoretically not yet well understood. The purpose of this paper is to present a polynomial-time algorithm to build the data structure. Furthermore, it is investigated whether the presented algorithm is optimal. This investigations leads to several combinatorial questions for which partial results are given. Finally, we present several limits and experiments regarding the quality of the obtained neighborhood relation.Comment: 33 pages, 18 Figure

Experimental visually-guided investigation of sub-structures in three-dimensional Turing-like patterns

In his 1952 paper "The chemical basis of morphogenesis", Alan M. Turing presented a model for the formation of skin patterns. While it took several decades, the model has been validated by finding corresponding natural phenomena, e.g. in the skin pattern formation of zebrafish. More surprising, seemingly unrelated pattern formations can also be studied via the model, like e.g. the formation of plant patches around termite hills. In 1984, David A. Young proposed a discretization of Turing's model, reducing it to an activator/inhibitor process on a discrete domain. From this model, the concept of three-dimensional Turing-like patterns was derived. In this paper, we consider this generalization to pattern-formation in three-dimensional space. We are particularly interested in classifying the different arising sub-structures of the patterns. By providing examples for the different structures, we prove a conjecture regarding these structures within the setup of three-dimensional Turing-like pattern. Furthermore, we investigate - guided by visual experiments - how these sub-structures are distributed in the parameter space of the discrete model. We found two-fold versions of zero- and one-dimensional sub-structures as well as two-dimensional sub-structures and use our experimental findings to formulate several conjectures for three-dimensional Turing-like patterns and higher-dimensional cases

Weaving patterns inspired by the pentagon snub subdivision scheme

Various computer simulations regarding, e.g., the weather or structural mechanics, solve complex problems on a two-dimensional domain. They mostly do so by splitting the input domain into a finite set of smaller and simpler elements on which the simulation can be run fast and efficiently. This process of splitting can be automatized by using subdivision schemes. Given the wide range of simulation problems to be tackled, an equally wide range of subdivision schemes is available. They create subdivisions that are (mainly) comprised of triangles, quadrilaterals, or hexagons. Furthermore, they ensure that (almost) all vertices have the same number of neighboring vertices. This paper illustrates a subdivision scheme that splits the input domain into pentagons. Repeated application of the scheme gives rise to fractal-like structures. Furthermore, the resulting subdivided domain admits to certain weaving patterns. These patterns are subsequently generalized to several other subdivision schemes. As a final contribution, we provide paper models illustrating the weaving patterns induced by the pentagonal subdivision scheme. Furthermore, we present a jigsaw puzzle illustrating both the subdivision process and the induced weaving pattern. These transform the visual and abstract mathematical algorithms into tactile objects that offer exploration possibilities aside from the visual.Comment: Submitted for publication to the Journal of Mathematics and the Arts (2022

Chip-Firing Revisited: A Peek into the Third Dimension

Chip-firing was first introduced as a probabilistic game. Subsequently, it was generalized to arbitrary graph configurations and investigated mostly with regard to two-dimensional quad-grid layouts. In this paper, we lift chip-firing to the third dimension. Aside from the arising three-dimensional shapes, we are interested in the internal, two-dimensional structures. Furthermore, we explore the different shapes obtained by chip firing processes on various neighborhoods, such as the face-centered and the cube-centered grid as well as on a neighborhood inspired by knight moves.Green Open Access added to TU Delft Institutional Repository 'You share, we take care!' - Taverne project https://www.openaccess.nl/en/you-share-we-take-care Otherwise as indicated in the copyright section: the publisher is the copyright holder of this work and the author uses the Dutch legislation to make this work public.Computer Graphics and Visualisatio

Freelence - coding with free valences

We introduce FreeLence, a novel and simple single-rate compression coder for triangle manifold meshes. Our method uses free valences and exploits geometric information for connectivity encoding. Furthermore, we introduce a novel linear prediction scheme for geometry compression of 3D meshes. Together, these approaches yield a significant entropy reduction for mesh encoding with an average of 20-30 % over leading single-rate regiongrowing coders, both for connectivity and geometry

Experimental visually-guided investigation of sub-structures in three-dimensional Turing-like patterns

In this paper, we are interested in classifying the different arising (topological) structures of three-dimensional Turing-like patterns. By providing examples for the different structures, we confirm a conjecture regarding these structures within the setup of three-dimensional Turing-like pattern. Furthermore, we investigate how these structures are distributed in the parameter space of the discrete model. We found twofold versions of so-called "zero-" and "one-dimensional" structures as well as "two-dimensional" structures and use our experimental findings to formulate several conjectures for three-dimensional Turing-like patterns and higher-dimensional cases.Comp Graphics & Visualisatio

(Guest Editors) FreeLence- Coding with Free Valences

We introduce FreeLence, a novel and simple single-rate compression coder for triangle manifold meshes. Our method uses free valences and exploits geometric information for connectivity encoding. Furthermore, we introduce a novel linear prediction scheme for geometry compression of 3D meshes. Together, these approaches yield a significant entropy reduction for mesh encoding with an average of 20-30 % over leading single-rate regiongrowing coders, both for connectivity and geometry. Categories and Subject Descriptors (according to ACM CCS): I.3.3 [Computer Graphics]: Surface mesh compression, connectivity coding, geometry coding. 1

The volcanic ash plume near the Eyjafjallajökull on 1-2 May 2010

This paper describes the analysis of airborne measurements and model simulations of the volcanic ash plume close to Iceland’s Eyjafjallajökull volcano in April/May 2010. In particular we quantify the plume properties for the period of 1 to 2 May, 2010, up to 450 km downstream the volcano. The measurements provide information on the plume width, upper height, mean depth, wind speed profile, attenuated Lidar backscatter profile, plume temperature, ash particle sizes, ash mass concentration, ash particle size distribution, humidity, O3, CO and SO2 mixing ratio, ash optical depth, volume flux, and mass flux. Here we report about analysis of the optical depth from the Lidar observations using the shadow method, and on comparisons of modeled and measured plume properties constraining the ash properties