Related papers: Sampling Superquadric Point Clouds with Normals

With the help of hyper-ideal circle pattern theory, we have developed a discrete version of the classical uniformization theorems for surfaces represented as finite branched covers over the Riemann sphere as well as compact polyhedral…

Simplicial complexes are higher-order combinatorial structures which have been used to represent real-world complex systems. In this paper, we concentrate on the local patterns in simplicial complexes called simplets, a generalization of…

Much effort has been put into developing samplers with specific properties, such as producing blue noise, low-discrepancy, lattice or Poisson disk samples. These samplers can be slow if they rely on optimization processes, may rely on a…

It is well known that not every combinatorial configuration admits a geometric realization with points and lines. Moreover, some of them do not even admit realizations with pseudoline arrangements, i.e., they are not topological. In this…

We present new methods for uniformly sampling the solid angle subtended by a disk. To achieve this, we devise two novel area-preserving mappings from the unit square $[0,1]^2$ to a spherical ellipse (i.e. the projection of the disk onto the…

The abstraction of 3D objects with simple geometric primitives like cuboids allows to infer structural information from complex geometry. It is important for 3D shape understanding, structural analysis and geometric modeling. We introduce a…

Bifurcations of classical orbits introduce divergences into semiclassical spectra which have to be smoothed with the help of uniform approximations. We develop a technique to extract individual energy levels from semiclassical spectra…

This is the story of the rediscovery of classical three-dimensional geometry, especially the geometry of quadric surfaces, while studying the semigroup $M_2(\mathbb R)$ of linear endomorphisms of a real plane. One of the surfaces that…

We develop classical globally supersymmetric theories. As much as possible, we treat various dimensions and various amounts of supersymmetry in a uniform manner. We discuss theories both in components and in superspace. Throughout we…

The interest in matching non-rigidly deformed shapes represented as raw point clouds is rising due to the proliferation of low-cost 3D sensors. Yet, the task is challenging since point clouds are irregular and there is a lack of intrinsic…

In this paper we present, using the arithmetic of elliptic curves over finite fields, an algorithm for the efficient generation of a sequence of uniform pseudorandom vectors in high dimensions, that simulates a sample of a sequence of…

Point clouds are a set of data points in space to represent the 3D geometry of objects. A fundamental step in the processing is to identify a subset of points to represent the shape. While traditional sampling methods often ignore to…

Simplified models are an important tool for the interpretation of searches for new physics at the LHC. They are defined by a small number of new particles together with a specific production and decay pattern. The simplified models adopted…

We perceive the world through images formed by scattering. The ability to interpret scattering data mathematically has opened to our scrutiny the constituents of matter, the building blocks of life, and the remotest corners of the universe.…

Hypergraphs offer a generalized framework for understanding complex systems, covering group interactions of different orders beyond traditional pairwise interactions. This modelling allows for the simplified description of simultaneous…

Over the past two decades, we have seen an exponentially increased amount of point clouds collected with irregular shapes in various areas. Motivated by the importance of solid modeling for point clouds, we develop a novel and efficient…

The concept of a Point Cloud has played an increasingly important role in many areas of Engineering, Science, and Mathematics. Examples are: LIDAR, 3D-Printing, Data Analysis, Computer Graphics, Machine Learning, Mathematical Visualization,…

Point clouds provide a flexible and natural representation usable in countless applications such as robotics or self-driving cars. Recently, deep neural networks operating on raw point cloud data have shown promising results on supervised…

The curse of dimensionality presents a pervasive challenge in optimization problems, with exponential expansion of the search space rapidly causing traditional algorithms to become inefficient or infeasible. An adaptive sampling strategy is…

In this paper, we propose a framework to reconstruct 3D models from raw scanned points by learning the prior knowledge of a specific class of objects. Unlike previous work that heuristically specifies particular regularities and defines…