Related papers: Real-Time Visualization in Non-Isotropic Geometrie…
Swept volume computation, the determination of regions occupied by moving objects, is essential in graphics, robotics, and manufacturing. Existing approaches either explicitly track surfaces, suffering from robustness issues under complex…
We define the notion of near geodesic between points of a metric space when no geodesic exists, and use this to extend Recio-Mitter's notion of geodesic complexity to non-geodesic spaces. This has potential application to topological…
Data visualization is the process by which data of any size or dimensionality is processed to produce an understandable set of data in a lower dimensionality, allowing it to be manipulated and understood more easily by people. The goal of…
In the last decades cosmological N-body dark matter simulations have enabled ab initio studies of the formation of structure in the Universe. Gravity amplified small density fluctuations generated shortly after the Big Bang, leading to the…
A simple visual representation of Minkowski spacetime appropriate for a student with a background in geometry and algebra is presented. Minkowski spacetime can be modeled with a Euclidean 4-space to yield accurate visualizations as…
This paper is motivated by the real symplectic isotopy problem : does there exists a nonsingular real pseudoholomorphic curve not isotopic in the projective plane to any real algebraic curve of the same degree? Here, we focus our study on…
Geometrical modelling generally provides the geometrical description of a special structure and a set of services to "navigate" through its structure. HEP geometrical modellers are designed to handle high complexity detector geometries and…
We introduce a deep appearance model for rendering the human face. Inspired by Active Appearance Models, we develop a data-driven rendering pipeline that learns a joint representation of facial geometry and appearance from a multiview…
The geometry of three-dimensional (3D) graphs, consisting of nodes and edges, plays a crucial role in many important applications. An excellent example is molecular graphs, whose geometry influences important properties of a molecule…
Neuromorphic engineering is essentially the development of artificial systems, such as electronic analog circuits that employ information representations found in biological nervous systems. Despite being faster and more accurate than the…
This paper introduces a set of numerical methods for Riemannian shape analysis of 3D surfaces within the setting of invariant (elastic) second-order Sobolev metrics. More specifically, we address the computation of geodesics and geodesic…
Electron tomography is becoming an increasingly important tool in materials science for studying the three-dimensional morphologies and chemical compositions of nanostructures. The image quality obtained by many current algorithms is…
Visual localization techniques rely upon some underlying scene representation to localize against. These representations can be explicit such as 3D SFM map or implicit, such as a neural network that learns to encode the scene. The former…
This paper concerns models and convergence principles for dealing with stochasticity in a wide range of algorithms arising in nonlinear analysis and optimization in Hilbert spaces. It proposes a flexible geometric framework within which…
One considers geometry with the intransitive equaivalence relation. Such a geometry is a physical geometry, i.e. it is described completely by the world function, which is a half of the squared distance function. The physical geometry…
Random invariant manifolds are geometric objects useful for understanding complex dynamics under stochastic influences. Under a nonuniform hyperbolicity or a nonuniform exponential dichotomy condition, the existence of random pseudo-stable…
Robust visual localization under a wide range of viewing conditions is a fundamental problem in computer vision. Handling the difficult cases of this problem is not only very challenging but also of high practical relevance, e.g., in the…
Neural implicit functions have emerged as a powerful representation for surfaces in 3D. Such a function can encode a high quality surface with intricate details into the parameters of a deep neural network. However, optimizing for the…
By decomposing the regular representation of a particular (Heisenberg-like) Lie supergroup into irreducible subspaces, we show that not all of them can be obtained by applying geometric quantization to coadjoint orbits with an even…
Black holes and other compact objects are powerful tools to observationally test Einsteins theory of General Relativity. We develop raytracing code to create visual images of compact objects that are solutions of Einsteins field equations.…