Martin Skrodzki

Delft University of Technology | TU · Faculty of Electrical Engineering, Mathematics and Computer Sciences (EEMCS)

Holonomy is a virtual environment based on the mathematical concept of hyperbolic geometry. Unlike other environments, Holonomy allows users to seamlessly explore an infinite hyperbolic space by physically walking. They use their body as the controller, eliminating the need for teleportation or other artificial VR locomotion methods. This paper dis...

HOLONOMY is a virtual environment based on the mathematical concept of hyperbolic geometry. Unlike other environments, HOLONOMY allows users to seamlessly explore an infinite hyperbolic space by physically walking. They use their body as the controller, eliminating the need for teleportation or other artificial VR locomotion methods. This paper dis...

In this conversation, Milena Damrau and Martin Skrodzki speak with Kevin Walker about the role of mathematics in his artistic practice. Kevin Walker is a Utah-based artist who finds inspiration for his mathematical art in nature.

The need to understand the structure of hierarchical or high-dimensional data is present in a variety of fields. Hyperbolic spaces have proven to be an important tool for embedding computations and analysis tasks as their non-linear nature lends itself well to tree or graph data. Subsequently, they have also been used in the visualization of high-d...

Widely used pipelines for the analysis of high-dimensional data utilize two-dimensional visualizations. These are created, e.g., via t-distributed stochastic neighbor embedding (t-SNE). When it comes to large data sets, applying these visualization techniques creates suboptimal embeddings, as the hyperparameters are not suitable for large data. Cra...

Mathematical understanding is built in many ways. Among these, illustration has been a companion and tool for research for as long as research has taken place. We use the term illustration to encompass any way one might bring a mathematical idea into physical form or experience, including hand-made diagrams or models, computer visualization, 3D pri...

In this conversation, Milena Damrau and Martin Skrodzki speak with Timea Tihanyi about the role of mathematics in her artistic practice. Timea Tihanyi is a Hungarian born interdisciplinary visual artist and ceramist living and working in Seattle, Washington.

In this conversation, Milena Damrau and Martin Skrodzki speak with Dominic Hopkinson about the role of mathematics in his artistic practice. Dominic Hopkinson generates sculptures in stone, wood, plaster, and bronze, attempting to distill these complex concepts into pure visual form. He lives in the UK.

Point clouds arise from acquisition processes applied in various scenarios, such as reverse engineering, rapid prototyping, or cultural preservation. To run various simulations via, e.g., finite element methods, on the derived data, a mesh has to be created from it. In this paper, a meshing algorithm for point clouds is presented, which is based on...

Wooden artworks can be found throughout all art historical periods. Yet, they are scarcely found in the realm of mathematical art. This introductory article briefly presents the contributors and the structure of their contributions. In the following collection, each article exemplifies the interaction of wood as both an artistic medium and a means...

A core assumption often heard in public health discourse is that increasing trust in national political leaders is essential for securing public health compliance during crises such as the COVID-19 pandemic (2019–ongoing). However, studies of national government trust are typically too coarse-grained to differentiate between trust in institutions v...

Recent years saw a rapid increase in conference formats that take place either fully online or in a hybrid fashion with some people on-site and others online. While these formats brought new challenges, they also opened up new opportunities. In the present article, we first outline advantages and disadvantages of different conference formats as dis...

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 subdivi...

The core editorial team of w/k strives to win specialists for certain aspects of the major topic Art and Science, which have not yet been sufficiently presented in the online journal. Recently, Milena Damrau and Martin Skrodzki joined the team, whom we warmly welcome. In their article, they explain their motivation to expand the representation of m...

Das Kernredaktionsteam von w/k ist stets bestrebt, Spezialist*innen für bestimmte Aspekte oder Teilbereiche von Kunst und Wissenschaft zu gewinnen, die in der Online-Zeitschrift noch nicht ausreichend dargestellt werden. Seit kurzem gehören Milena Damrau und Martin Skrodzki zum Team, die wir herzlich willkommen heißen. In ihrem Artikel erläutern si...

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 subdiv...

In this paper, we define and evaluate a weighting scheme for neighborhoods in point sets. Our weighting takes the shape of the geometry, i.e., the normal information, into account. This causes the obtained neighborhoods to be more reliable in the sense that connectivity also depends on the orientation of the point set. We utilize a sigmoid to defin...

A core assumption often heard in public health discourse is that increasing trust in national political leaders is essential for securing public health compliance during crises like the Covid-19 pandemic (2019-ongoing). However, studies of national government trust typically are too coarse-grained to differentiate between the trust in institutions...

Surface representations play a major role in a variety of applications throughout a diverse collection of fields, such as biology, chemistry, physics, or architecture. From a simulation point of view, it is important to simulate the surface as good as possible, including the usage of a wide range of different approximating elements. However, when i...

Auf der DMV Jahrestagung 2020 fand das erste Minisymposium im Schnittbereich Mathematik und Kunst statt. Dieser Artikel berichtet kurz von den Ergebnissen und weiteren Planungen.

Turing proposed a reaction-diffusion model for skin coloring which was subsequently discretized by Young as a Cellular Automaton. We investigate the parameter space of the corresponding 3D models.

Mathematical objects are generally abstract and not very approachable. Illustrations and interactive visualizations help both students and professionals to comprehend mathematical material and to work with it. This approach lends itself particularly well to geometrical objects. An example for this category of mathematical objects are hyperbolic geo...

The JavaView visualization framework was designed at the end of the 1990s as a software that provides—among other services—easy, interactive geometry visualizations on web pages. Subsequently, it was widely used in geometry groups around the globe. However, as JavaView’s easy web exports was based on Java Applets, the deprecation of this technology...

During a surface acquisition process using 3D scanners, noise is inevitable and an important step in geometry processing is to remove these noise components from these surfaces (given as points-set or triangulated mesh). The noise-removal process (denoising) can be performed by filtering the surface normals first and by adjusting the vertex positio...

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 stu...

We investigate the quality of weighted neighborhoods with different sizes, see https://arxiv.org/abs/2002.06827 for complete results. The weights are determined by the normal similarity between points and are given by a sigmoid function modeling both continuous and sharp increases. Our large-scale analysis consists of more than 1, 000 point sets, w...

The JavaView visualization framework was designed at the end of the 1990s as a software that provides-among other services- easy, interactive geometry visualizations on web pages.We discuss how this and other design goals were met and present several applications to highlight the contemporary use-cases of the framework. However, as JavaView's easy...

The artist Paul Klee describes and analyzes his use of symbols and colors in his book "P\"adagogisches Skizzenbuch" (pedagogical sketchbook, 1925). He uses arrows for means of illustrations and also discusses the arrow itself as an element of his repertoire of symbols. Interestingly, his point of view on arrows matches the way in which vector field...

In this work, we present a translation of the complete pipeline for variational shape approximation (VSA) to the setting of point sets. First, we describe an explicit example for the theoretically known non-convergence of the currently available VSA approaches. The example motivates us to introduce an alternate version of VSA based on a switch oper...

In this work, we present a translation of the complete pipeline for variational shape approximation (VSA) to the setting of point sets. First, we describe an explicit example for the theoretically known non-convergence of the currently available VSA approaches. The example motivates us to introduce an alternate version of VSA based on a switch oper...

The JavaView visualization framework was designed at the end of the 1990s as a software that provides - among other services - easy, interactive geometry visualizations on web pages. We discuss how this and other design goals were met and present several applications to highlight the contemporary use-cases of the framework. However, as JavaView's e...

Point sets arise naturally in many 3D acquisition processes and have diverse applications in several areas of geometry processing. Besides their advantages---for instance low storage cost---they do not provide connectivity information. Thus, for each point, the notion of its neighborhood has to be defined and computed. Common approaches include com...

Throughout the last years, new methods in artificial intelligence have revolutionized several scientific fields. These developments affect arts twofold. On the one hand, artists discover machine learning as a new tool. On the other hand, researchers apply the new techniques to the creative work of artists to better analyze and understand it. The wo...

Learning mathematics can be supported by technology in various creative ways. Appliances for 3D digital setups are widely available. They have transcended their intended use as simple in- or output devices and nowadays play a part in many artistic setups. Thus, they change the way we both perceive and create (digital) models. In this paper, we exam...

Point Sets are acquired as representations of surfaces in R 3 e.g. via laser-scanning or LiDaR. At first, they are unstructured and neighborhood relations have to be established. Then, noise added during generation has to be removed robustly also on non-uniform input while retaining features. The obtained cleaned point set can then be used for e.g....

We present a discrete gyroid surface. The gyroid is a triply periodic minimal surface, our discrete version has the same symmetries as the smooth gyroid and can be constructed from simple translational units.

This work proposes an algorithm for point set segmentation based on the concept of Variational Shape Approximation (VSA), which uses the k-means approach. It iteratively selects seeds, grows at planar proxy regions according to normal similarity, and updates the proxies. It is known that this algorithm does not converge in general. We provide a con...

For practical applications, any neighborhood concept imposed on a finite point set P is not of any use if it cannot be computed efficiently. Thus, in this paper, we give an introduction to the data structure of k-d trees, first presented by Friedman, Bentley, and Finkel in 1977. After a short introduction to the data structure (Section 1), we turn...

The (video) artist Kristina Paustian honored the Russian futurist Velimir Khlebnikov with her solo exhibition “Laws of Time. The future calculations by Velimir Khlebnikov” in Berlin, Germany. Among other aspects, she focused on his poetry and the mathematics used in his works. In this paper, we present the connections of Khlebnikov's writings to ma...

The artist Piet Mondrian (1872-1944) is most famous for his abstract works utilizing primary colors and axes-parallel black lines. A similar structure can be found in visualizations of the KdTree data structure used in computational geometry for range searches and neighborhood queries. In this paper, we systematically explore these visualizations a...

Our point set denoising is an iterative, 3-phase algorithm for noisy point sets. Its parameters offer a variety of tuning opportunities. Used models are the gargoyle (real, noisy, irregular), the Chinese ball and rabbit (real, noisy, many features), the fan disk (sharp features, near-flat areas), the sphere and the cube (sharp features), with the l...

In many applications, point set surfaces are acquired by 3D scanners. During this acquisition process, noise and outliers are inevitable. For a high fidelity surface reconstruction from a noisy point set, a feature preserving point set denoising operation has to be performed to remove noise and outliers from the input point set. To suppress these u...

"Mathe im Advent" ist ein Wettbewerb, der 2008 von der DMV initiiert wurde. Jedes Jahr im Dezember öffnen Schüler*innen 24 virtuelle Türchen, hinter denen sich mathematische Probleme verstecken - verpackt in kurzen Geschichten über Wichtel. Zu jeder Frage gibt es vier Antworten, von denen genau eine richtig ist. Die Teilnehmer*innen werden dazu auf...

With the emergence of affordable 3D scanning and printing devices, processing of large point clouds has to be performed in many applications. Several algorithms are available for surface reconstruction, smoothing, and parametrization. However, many of these require the sampling of the point cloud to be uniform or at least to be within certain contr...

The Neighborhood Grid approximates neighborhood information. A (quadratic) matrix contains the coordinates of the points such that in each row the x-values are increasing while in each column the y-values are increasing. For the algorithm, the order of the points suffices, the exact coordinates are irrelevant. If the above ordering is given, we cal...

The Neighborhood Grid approximates neighborhood information. A (quadratic) matrix contains the coordinates of the points such that in each row the x-values are increasing while in each column the y-values are increasing. For the algorithm, the order of the points suffices, the exact coordinates are irrelevant. If the above ordering is given, we cal...

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 algor...

Computational and Structural Aspects of Point Set Surfaces: - Coordinate Charts and Transition Maps on Point Sets - Efficient Structures for Access of Coordinate Charts - MLS Procedure for Implicit Manifold Reconstruction - The Neighborhood Grid

Based on previous, well-established, and successfully used discretization schemes of differential geometric structures and operators on triangulated meshes, we take the next step and transfer this calculus to point set surface data that arise naturally in 3D acquisition processes. We aim at a theoretical framework, which mimics the most features of...

Beginning with their introduction in 1952 by Alan Turing, Turing-like patterns have inspired research in several different fields. One of these is the field of cellular automata, which have been utilized to create Turing-like patterns by David A. Young and others. In this paper we provide a generalization of these patterns to the third dimension. S...

In his 1802 book ”Acoustics”, Ernst Florens Friedrich Chladni describes how to visualize different vibration modes using sand, a metal plate, and a violin bow. We will review the underlying physical and mathematical formulations and lift them to the third dimension. Finally, we present some of the resulting three dimensional Chladni figures.