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Past approaches for statistical shape analysis of objects have focused mainly on objects within the same topological classes, e.g., scalar functions, Euclidean curves, or surfaces, etc. For objects that differ in more complex ways, the…
The success of denoising diffusion models in representing rich data distributions over 2D raster images has prompted research on extending them to other data representations, such as vector graphics. Unfortunately due to their variable…
Vector fields are one of the fundamental parts of mathematics which are key for modelling many physics phenomena such as electromagnetic fields or fluid and gas flows. Fields found in nature often exhibit complex structures which can be…
Divergence-free (div-free) and curl-free vector fields are pervasive in many areas of science and engineering, from fluid dynamics to electromagnetism. A common problem that arises in applications is that of constructing smooth approximants…
In this article we present pictorially the foundation of differential geometry which is a crucial tool for multiple areas of physics, notably general and special relativity, but also mechanics, thermodynamics and solving differential…
In this paper we give a method for constructing systematically all simple 2-connected graphs with n vertices from the set of simple 2-connected graphs with n-1 vertices, by means of two operations: subdivision of an edge and addition of a…
Visual grounding is a long-lasting problem in vision-language understanding due to its diversity and complexity. Current practices concentrate mostly on performing visual grounding in still images or well-trimmed video clips. This work, on…
Much of arithmetic geometry is concerned with the study of principal bundles. They occur prominently in the arithmetic of elliptic curves and, more recently, in the study of the Diophantine geometry of curves of higher genus. In particular,…
This paper demonstrates that parallel vector curves are piecewise cubic rational curves in 3D piecewise linear vector fields. Parallel vector curves -- loci of points where two vector fields are parallel -- have been widely used to extract…
The traditional study of plane and space algebraic curves by looking at their tangent vectors, curvatures and torsions provides geometric, but unfortunately not sufficient information about individual curves in order to be able to…
One of the most useful techniques to help visual data analysis systems is interactive filtering (brushing). However, visualization techniques often suffer from overlap of graphical items and multiple attributes complexity, making visual…
Scientific data sets continue to increase in both size and complexity. In the past, dedicated graphics systems at supercomputing centers were required to visualize large data sets, but as the price of commodity graphics hardware has dropped…
English abstract: In the "Intuitive Quantum Physics" course, we use graphical interpretations of mathematical equations and qualitative reasoning to develop and teach a simplified model of quantum physics. Our course contains three units:…
Visualisation is often presented as a means of simplifying information and helping people understand complex data. In this paper we describe the design, development and evaluation of an interactive visualisation for spreadsheet formulae…
Existing score-distilling text-to-3D generation techniques, despite their considerable promise, often encounter the view inconsistency problem. One of the most notable issues is the Janus problem, where the most canonical view of an object…
Little is known about how people learn from a brief glimpse of three-dimensional (3D) bivariate vector field visualizations and about how well visual features can guide behavior. Here we report empirical study results on the use of color,…
Many systems comprising entities in interactions can be represented as graphs, whose structure gives significant insights about how these systems work. Network theory has undergone further developments, in particular in relation to…
We present a connection between two seemingly disparate fields: VC-theory and graph theory. This connection yields natural correspondences between fundamental concepts in VC-theory, such as shattering and VC-dimension, and well-studied…
It is hard to imagine curved spacetimes of General Relativity. A simple but powerful way how to achieve this is visualizing them via embedding diagrams of both ordinary geometry and optical reference geometry. They facilitate to gain an…
We present a novel approach to object classification and detection which requires minimal supervision and which combines visual texture cues and shape information learned from freely available unlabeled web search results. The explosion of…