相关论文: Computational Geometry Column 38
In this paper we collect the main properties of free curves in the complex projective plane and a lot of conjectures and open problems, both old and new. In the quest to understand the mystery of free curves, many tools were developed and…
Some topics from recent progresses in lattice QCD are reviewed.
This article gives an introduction for mathematicians interested in numerical computations in algebraic geometry and number theory to some recent progress in algorithmic number theory, emphasising the key role of approximate computations…
This is a brief survey of recent results related to austere submanifolds, mainly based on the papers [24,25].
In this work, we present a novel approach for reconstructing shape point clouds using planar sparse cross-sections with the help of generative modeling. We present unique challenges pertaining to the representation and reconstruction in…
A numerical scheme for computing arc-length parametrized curves of low bending energy that are confined to convex domains is devised. The convergence of the discrete formulations to a continuous model and the unconditional stability of an…
Submission on request. This Master thesis from 2008 (University of Oslo, Norway) contains no new results, but it provides an overview of plane rational cuspidal curves, in particular curves of low degree. Please note that new results on…
Point cloud reconstruction from raw point cloud has been an important topic in computer graphics for decades, especially due to its high demand in modeling and rendering applications. An important way to solve this problem is establishing a…
In this article, a new method for segmentation and restoration of images on two-dimensional surfaces is given. Active contour models for image segmentation are extended to images on surfaces. The evolving curves on the surfaces are…
The aim of this paper is to report on recent development on the conformal fractional Laplacian, both from the analytic and geometric points of view, but especially towards the PDE community.
We give explicit formulas for the number of points on reductions of elliptic curves with complex multiplication by any imaginary quadratic field. We also find models for CM $\mathbf{Q}$-curves in certain cases. This generalizes earlier…
Quantum Computing promises accelerated simulation of certain classes of problems, in particular in plasma physics. Given the nascent interest in applying quantum computing techniques to study plasma systems, a compendium of the relevant…
In this paper, we present an algorithm for reparametrizing algebraic plane curves from a numerical point of view. That is, we deal with mathematical objects that are assumed to be given approximately. More precisely, given a tolerance…
This chapter reviews some past and recent developments in shape comparison and analysis of curves based on the computation of intrinsic Riemannian metrics on the space of curves modulo shape-preserving transformations. We summarize the…
We recover plane curves from their branch points under projection onto a line. Our focus lies on cubics and quartics. These have 6 and 12 branch points respectively. The plane Hurwitz numbers 40 and 120 count the orbits of solutions. We…
Surface reconstruction from point clouds is a fundamental step in many applications in computer vision. In this paper, we develop an efficient iterative method on a variational model for the surface reconstruction from point clouds. The…
Man-made objects usually exhibit descriptive curved features (i.e., curve networks). The curve network of an object conveys its high-level geometric and topological structure. We present a framework for extracting feature curve networks…
We review recent developments related to jet clustering algorithms and jet reconstruction, with particular emphasis on their implications in heavy ion collisions. These developments include fast implementations of sequential recombination…
Study of methods of resolved top quarks kinematic reconstruction in the $t\bar{t} \rightarrow \ell+$jets channel is presented at the particle level as well as the fast-simulation detector level. Previous and current pseudo-top quark…
We present an approach to inform the reconstruction of a surface from a point scan through topological priors. The reconstruction is based on basis functions which are optimized to provide a good fit to the point scan while satisfying…