相关论文: Computational Geometry Column 38

We provide an algorithm of constructing a rectifiable curve between two sufficiently close points of a proximally smooth set in a uniformly convex and uniformly smooth Banach space. Our algorithm returns a reasonably short curve between two…

It is hereby established that, in Euclidean spaces of finite dimension, bounded self-contracted curves have finite length. This extends the main result of Daniilidis, Ley, and Sabourau (J. Math. Pures Appl. 2010) concerning continuous…

We survey some of our old results given in [CE95] and [CE10] and present some new ones in the last three sections.We survey some of our old results given in [CE95] and [CE10] and present some new ones in the last three sections.

We discuss reconstructing smooth real algebraic maps onto curves whose Reeb graph is as prescribed. This can be contributed to real algebraic geometry, especially in explicit examples in real algebraic geometry in a new way. The Reeb graph…

We introduce CurveFusion, the first approach for high quality scanning of thin structures at interactive rates using a handheld RGBD camera. Thin filament-like structures are mathematically just 1D curves embedded in R^3, and…

We approach the Torelli problem of recostructing a curve from its Jacobian from a computational point of view. Following Dubrovin, we design a machinery to solve this problem effectively, which builds on methods in numerical algebraic…

Industrial cone-beam X-ray computed tomography (CT) scans of additively manufactured components produce a 3D reconstruction from projection measurements acquired at multiple predetermined rotation angles of the component about a single…

The inversion of linear systems is a fundamental step in many inverse problems. Computational challenges exist when trying to invert large linear systems, where limited computing resources mean that only part of the system can be kept in…

This is an extended version of an invited lecture I gave at the Journees Arithmetiques in St. Etienne in July 2009. We discuss the state of the art regarding the problem of finding the set of rational points on a (smooth projective)…

A short overview of recent developments on resummations in QCD is presented.

Reconstructing the 3D geometry, pose, and motion of animals is a long-standing problem, which has a wide range of applications, from biology, livestock management, and animal conservation and welfare to content creation in digital…

We present two methods that combine image reconstruction and edge detection in computed tomography (CT) scans. Our first method is as an extension of the prominent filtered backprojection algorithm. In our second method we employ…

Implicit curve and surface reconstruction attracts the attention of many researchers and gains a wide range of applications, due to its ability to describe objects with complicated geometry and topology. However, extra zero-level sets or…

We give a combinatorial description of closed curves on oriented surfaces in terms of certain permutations, called charts. We describe automorphisms of curves in terms of charts and compute the total number of curves counted with…

Two conjectures recently proposed by one of the authors are disproved

This article is a survey of recent results about scalar curvature and contractible open $3$-manifolds. It is dedicated to the memory of Professor S. S. Chern.

We derive recursive equations for the characteristic numbers of rational nodal plane curves with at most one cusp, subject to point conditions, tangent conditions and flag conditions, developing techniques akin to quantum cohomology on a…

Recent methods for dynamic human reconstruction have attained promising reconstruction results. Most of these methods rely only on RGB color supervision without considering explicit geometric constraints. This leads to existing human…

We prove the existence of embedded closed constant curvature curves on convex surfaces.

We address the problem of the maximal finite number of real points of a real algebraic curve (of a given degree and, sometimes, genus) in the projective plane. We improve the known upper and lower bounds and construct close to optimal…