Related papers: Real-Time Visualization in Non-Isotropic Geometrie…
Algorithms for the computation of the forward and inverse geodesic problems for an ellipsoid of revolution are derived. These are accurate to better than 15 nm when applied to the terrestrial ellipsoids. The solutions of other problems…
Traditional approaches to the study of the dynamics of spacetime curvature in a very real sense hide the intricacies of the nonlinear regime. Whether it be huge formulae, or mountains of numerical data, standard methods of presentation make…
We discuss the most elementary properties of the hyperbolic trigonometry and show how they can be exploited to get a simple, albeit interesting, geometrical interpretation of the special relativity. It yields indeed a straightforword…
The task of crafting procedural programs capable of generating structurally valid 3D shapes easily and intuitively remains an elusive goal in computer vision and graphics. Within the graphics community, generating procedural 3D models has…
We propose a neural network-based real-time volume rendering method for realistic and efficient rendering of volumetric media. The traditional volume rendering method uses path tracing to solve the radiation transfer equation, which…
Scientific and engineering processes deliver massive high-dimensional data sets that are generated as non-linear transformations of an initial state and few process parameters. Mapping such data to a low-dimensional manifold facilitates…
Artificial Intelligence & Nanotechnology are promising areas for the future of humanity. While Deep Learning based Computer Vision has found applications in many fields from medicine to automotive, its application in nanotechnology can open…
We introduce the notion of a topological geodesic in a 3-manifold. Under suitable hypotheses on the fundamental group, for instance word-hyperbolicity, topological geodesics are shown to have the useful properties of, and play the same role…
Computational topology is an area that revisits topological problems from an algorithmic point of view, and develops topological tools for improved algorithms. We survey results in computational topology that are concerned with graphs drawn…
Traditional visualisations are designed to be shown on a flat surface (screen or page) but most data is not "flat". For example, the surface of the earth exists on a sphere, however, when that surface is presented on a flat map, key…
This paper addresses two problems needed to support four-dimensional ($3d + t$) spacetime numerical simulations. The first contribution is a general algorithm for producing conforming spacetime meshes of moving geometries. Here, the surface…
Researchers have now achieved great success on dealing with 2D images using deep learning. In recent years, 3D computer vision and Geometry Deep Learning gain more and more attention. Many advanced techniques for 3D shapes have been…
The realization of topological states of matter in ultracold atomic gases is currently the subject of intense experimental activity. Using a synthetic dimension, encoded in a non-spatial degree of freedom, can greatly simplify the…
Isoparametric hypersurfaces and their application to special geometries
The ultimate goal of many image-based modeling systems is to render photo-realistic novel views of a scene without visible artifacts. Existing evaluation metrics and benchmarks focus mainly on the geometric accuracy of the reconstructed…
In this work, we obtain isotropic extensions of the usual spherically symmetric vacuum geometries in general relativity. Exact and perturbative solutions are derived. The classes of geometries obtained include black holes in compact and…
An important new trend in additive manufacturing is the use of optimization to automatically design industrial objects, such as beams, rudders or wings. Topology optimization, as it is often called, computes the best configuration of…
In this paper, we study a new model of nonlocal geometric equations which appears in tomographic reconstruction when using the level-set method. We treat two additional difficulties which make the work original. On one hand, the level lines…
The human hand is the main medium through which we interact with our surroundings, making its digitization an important problem. While there are several works modeling the geometry of hands, little attention has been paid to capturing…
This paper is a very brief and gentle introduction to non-commutative geometry geared primarily towards physicists and geometers. It starts with a brief historical description of the motivation for non-commutative geometry and then goes on…