相关论文: Computational Geometry Column 38
In this paper, as a result of a theorem of Serre on congruence properties, a complete solution is given for an open question (see the text) presented recently by Kim, Koo and Park. Some further questions and results on similar types of…
This paper extends previous research in that sense that for orthogonal projections of rigid smooth (true-3D) curves moving totally free it reduces the number of required traceable points to two only (the best results known so far to the…
Point cloud surface reconstruction has improved in accuracy with advances in deep learning, enabling applications such as infrastructure inspection. Recent approaches that reconstruct from small local regions rather than entire point clouds…
This is a survey paper that also contains some new results. It will appear in the proceedings of the AMS summer research institute on Algebraic Geometry at Santa Cruz.
Currently, the area of geometric modeling and the construction of 3D models based on point clouds from laser sensors is actively developing. One of the basic tasks of geometric modeling is the reconstruction of a surface from a cloud of…
We describe our recent work on deformations of hyperelliptic curves by means of integrable hierarchy of hydrodynamic type (nlin.SI/0205012). We also discuss a further extension to the case of non-hyperelliptic curves.
This is a work in progress, far from being in its final form whose purpose is to investigate thoroughly the structure of Berkovich analytic curves and its relation with the semi-stable reduction theorem (of which a new proof is given here,…
Reconstructing a complete object from its parts is a fundamental problem in many scientific domains. The purpose of this article is to provide a systematic survey on this topic. The reassembly problem requires understanding the attributes…
It has recently been established by Below, De Loera, and Richter-Gebert that finding a minimum size (or even just a small) triangulation of a convex polyhedron is NP-complete. Their 3SAT-reduction proof is discussed.
Full jet reconstruction in heavy-ion collisions is expected to provide more sensitive measurements of jet quenching in hot QCD matter at RHIC. In this paper we review recent studies of jets utilizing modern jet reconstruction algorithms and…
We propose a new algorithm to the problem of polygonal curve approximation based on a multiresolution approach. This algorithm is suboptimal but still maintains some optimality between successive levels of resolution using dynamic…
We survey recent developments on the Restriction conjecture.
In this note we study the Petty projection of a log-concave function, which has been recently introduced in [9]. Moreover, we present some new inequalities involving this new notion, partly complementing and correcting some results from…
This note completes a talk given at the conference Curves over Finite Fields: past, present and future celebrating the publication the book {\em Rational Points on Curves over Finite Fields by J.-P. Serre and organised at Centro de ciencias…
A $\textit{polygonal curve}$ is a collection of $m$ connected line segments specified as the linear interpolation of a list of points $\{p_0, p_1, \ldots, p_m\}$. These curves may be obtained by sampling points from an oriented curve in…
We study how an irreducible closed algebraic curve X embedded in CP^3 can be recovered using its projections from points onto embedded projective planes. The different embeddings are unknown. The only input is the defining equation of each…
Computing occluding contours is a key building block of non-photorealistic rendering, but producing contours with consistent visibility has been notoriously challenging. This paper describes the first general-purpose smooth surface…
Recent advances in the 3-D reconstruction of planetary nebulae are reviewed. We include not only results for 3-D reconstructions, but also the current techniques in terms of general methods and software. In order to obtain more accurate…
In this paper we show how, under surprisingly weak assumptions, one can split a planar curve into three arcs and rearrange them (matching tangent directions) to obtain a closed curve. We also generalize this construction to curves split…
Quantum computation with quantum data that can traverse closed timelike curves represents a new physical model of computation. We argue that a model of quantum computation in the presence of closed timelike curves can be formulated which…