13 citations · 36 across the 15 of their papers we have counts for
15 papers
Holonomy: A Virtual Reality Exploration of Hyperbolic Geometry
Martin Skrodzki, Scott Jochems, Joris Rijsdijk +2
HOLONOMY is a virtual environment based on the mathematical concept of hyperbolic geometry. Unlike other environments, HOLONOMY allows users to seamlessly explore an infinite hyper…
Accelerating hyperbolic t-SNE
Martin Skrodzki, Hunter van Geffen, Nicolas F. Chaves-de-Plaza +3
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…
Navigating Perplexity: A linear relationship with the data set size in t-SNE embeddings
Martin Skrodzki, Nicolas F. Chaves-de-Plaza, Thomas Höllt +2
Widely used pipelines for analyzing high-dimensional data utilize two-dimensional visualizations. These are created, for instance, via t-distributed stochastic neighbor embedding (…
On the importance of illustration for mathematical research
Rémi Coulon, Gabriel Dorfsman-Hopkins, Edmund Harriss +3
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 illu…
Feature-aware manifold meshing and remeshing of point clouds and polyhedral surfaces with guaranteed smallest edge length
Henriette Lipschütz, Ulrich Reitebuch, Konrad Polthier +1
Point clouds and polygonal meshes are widely used when modeling real-world scenarios. Here, point clouds arise, for instance, from acquisition processes applied in various surround…
Weaving patterns inspired by the pentagon snub subdivision scheme
Henriette Lipschütz, Ulrich Reitebuch, Martin Skrodzki +1
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 doma…
Illustrations of non-Euclidean geometry in virtual reality
Martin Skrodzki
Mathematical objects are generally abstract and not very approachable. Illustrations and interactive visualizations help both students and professionals to comprehend mathematical…
Surface Denoising based on Normal Filtering in a Robust Statistics Framework
Sunil Kumar Yadav, Martin Skrodzki, Eric Zimmermann +1
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 (gi…
Experimental visually-guided investigation of sub-structures in three-dimensional Turing-like patterns
Martin Skrodzki, Ulrich Reitebuch, Eric Zimmermann
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 vali…
Vector Fields and Paul Klee -- A Summer School Course for gifted High-School Students
Martin Skrodzki, Henriette Lipschütz
The artist Paul Klee describes and analyzes his use of symbols and colors in his book "Pädagogisches Skizzenbuch" (pedagogical sketchbook, 1925). He uses arrows for means of illust…
Variational Shape Approximation of Point Set Surfaces
Martin Skrodzki, Eric Zimmermann, Konrad Polthier
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 t…
How the deprecation of Java applets affected online visualization frameworks -- a case study
Martin Skrodzki
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 page…
A Large-Scale Evaluation of Shape-Aware Neighborhood Weights and Neighborhood Sizes
Martin Skrodzki, Eric Zimmermann
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.…
The k-d tree data structure and a proof for neighborhood computation in expected logarithmic time
Martin Skrodzki
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 introdu…
Combinatorial and Asymptotical Results on the Neighborhood Grid
Martin Skrodzki, Ulrich Reitebuch, Alex McDonough
In various application fields, such as fluid-, cell-, or crowd-simulations, spatial data structures are very important. They answer nearest neighbor queries which are instrumental…