scholarly journals Pair of pants decomposition of 4–manifolds

2017 ◽  
Vol 17 (3) ◽  
pp. 1407-1444
Author(s):  
Marco Golla ◽  
Bruno Martelli
Keyword(s):  
Pants Decomposition

scholarly journals 3D B-Rep meshing for real-time data-based geometric parametric analysis

2021 ◽  
Vol 8 (1) ◽  
Author(s):  
Tristan Maquart ◽  
Thomas Elguedj ◽  
Anthony Gravouil ◽  
Michel Rochette
Keyword(s):  
Real Time ◽  
Surface Topology ◽  
Time Data ◽  
Standard Data ◽  
Input Surface ◽  
Cad Models ◽  
Pants Decomposition ◽  
Parametric Studies ◽  
Geometry Feature ◽  
Complicated Geometry

AbstractThis paper presents an effective framework to automatically construct 3D quadrilateral meshes of complicated geometry and arbitrary topology adapted for parametric studies. The input is a triangulation of the solid 3D model’s boundary provided from B-Rep CAD models or scanned geometry. The triangulated mesh is decomposed into a set of cuboids in two steps: pants decomposition and cuboid decomposition. This workflow includes an integration of a geometry-feature-aware pants-to-cuboids decomposition algorithm. This set of cuboids perfectly replicates the input surface topology. Using aligned global parameterization, patches are re-positioned on the surface in a way to achieve low overall distortion, and alignment to principal curvature directions and sharp features. Based on the cuboid decomposition and global parameterization, a 3D quadrilateral mesh is extracted. For different parametric instances with the same topology but different geometries, the MEG-IsoQuad method allows to have the same representation: isotopological meshes holding the same connectivity where each point on a mesh has an analogous one into all other meshes. Faithful 3D numerical charts of parametric geometries are then built using standard data-based techniques. Geometries are then evaluated in real-time. The efficiency and the robustness of the proposed approach are illustrated through a few parametric examples.

scholarly journals Hyperbolic three-string vertex

2021 ◽  
Vol 2021 (8) ◽  
Author(s):  
Atakan Hilmi Fırat
Keyword(s):  
Boundary Value Problem ◽  
Conservation Laws ◽  
Riemann Surfaces ◽  
Higher Order ◽  
Local Coordinates ◽  
Pants Decomposition ◽  
Fuchsian Equation ◽  
String Amplitudes ◽  
Hyperbolic Riemann Surfaces ◽  
Liouville’S Equation

Abstract We begin developing tools to compute off-shell string amplitudes with the recently proposed hyperbolic string vertices of Costello and Zwiebach. Exploiting the relation between a boundary value problem for Liouville’s equation and a monodromy problem for a Fuchsian equation, we construct the local coordinates around the punctures for the generalized hyperbolic three-string vertex and investigate their various limits. This vertex corresponds to the general pants diagram with three boundary geodesics of unequal lengths. We derive the conservation laws associated with such vertex and perform sample computations. We note the relevance of our construction to the calculations of the higher-order string vertices using the pants decomposition of hyperbolic Riemann surfaces.

scholarly journals Surface Mapping Using Consistent Pants Decomposition

2009 ◽  
Vol 15 (4) ◽  
pp. 558-571 ◽  
Author(s):  
Xin Li ◽  
Xianfeng Gu ◽  
Hong Qin
Keyword(s):  
Surface Mapping ◽  
Pants Decomposition

scholarly journals BERS' CONSTANTS FOR PUNCTURED SPHERES AND HYPERELLIPTIC SURFACES

2012 ◽  
Vol 04 (03) ◽  
pp. 271-296 ◽  
Author(s):  
FLORENT BALACHEFF ◽  
HUGO PARLIER
Keyword(s):  
Upper Bounds ◽  
Lower And Upper Bounds ◽  
Hyperelliptic Surfaces ◽  
Pants Decomposition ◽  
Marked Points

The main goal of this paper is to present a proof of Buser's conjecture about Bers' constants for spheres with cusps (or marked points) and for hyperelliptic surfaces. More specifically, our main result states that any hyperbolic sphere with n cusps has a pants decomposition with all of its geodesics of length bounded by [Formula: see text]. Other results include lower and upper bounds for Bers' constants for hyperelliptic surfaces and spheres with boundary geodesics.

scholarly journals A Note on Toric Varieties Associated with Moduli Spaces

2011 ◽  
Vol 54 (3) ◽  
pp. 561-565
Author(s):  
James J. Uren
Keyword(s):  
Riemann Surface ◽  
Moduli Space ◽  
Moduli Spaces ◽  
Toric Variety ◽  
Toric Varieties ◽  
Pants Decomposition ◽  
Basic Facts ◽  
The Moment ◽  
Moment Polytopes

AbstractIn this note we give a brief review of the construction of a toric variety coming from a genus g ≥ 2 Riemann surface Σg equipped with a trinion, or pair of pants, decomposition. This was outlined by J. Hurtubise and L. C. Jeffrey. A. Tyurin used this construction on a certain collection of trinion decomposed surfaces to produce a variety DMg , the so-called Delzant model of moduli space, for each genus g. We conclude this note with some basic facts about the moment polytopes of the varieties . In particular, we show that the varieties DMg constructed by Tyurin, and claimed to be smooth, are in fact singular for g ≥ 3.

scholarly journals The behaviour of Fenchel–Nielsen distance under a change of pants decomposition

2012 ◽  
Vol 20 (2) ◽  
pp. 369-395 ◽  
Author(s):  
Daniele Alessandrini ◽  
Lixin Liu ◽  
Athanase Papadopoulos ◽  
Weixu Su
Keyword(s):  
Pants Decomposition

scholarly journals Fenchel–Nielsen coordinates on upper bounded pants decompositions

2015 ◽  
Vol 158 (3) ◽  
pp. 385-397 ◽  
Author(s):  
DRAGOMIR ŠARIĆ
Keyword(s):  
Teichmüller Space ◽  
Hyperbolic Surface ◽  
Length Spectrum ◽  
Teichmuller Space ◽  
Closed Geodesics ◽  
Infinite Type ◽  
Pants Decomposition ◽  
Length Spectrum Metric ◽  
Path Connected ◽  
Simple Closed Geodesics

AbstractLet X0 be an infinite-type hyperbolic surface (whose boundary components, if any, are closed geodesics) which has an upper bounded pants decomposition. The length spectrum Teichmüller space Tls(X0) consists of all surfaces X homeomorphic to X0 such that the ratios of the corresponding simple closed geodesics are uniformly bounded from below and from above. Alessandrini, Liu, Papadopoulos and Su [1] described the Fenchel–Nielsen coordinates for Tls(X0) and using these coordinates they proved that Tls(X0) is path connected. We use the Fenchel–Nielsen coordinates for Tls(X0) to induce a locally bi-Lipschitz homeomorphism between l∞ and Tls(X0) (which extends analogous results by Fletcher [9] and by Allessandrini, Liu, Papadopoulos, Su and Sun [2] for the unreduced and the reduced Tqc(X0)). Consequently, Tls(X0) is contractible. We also characterize the closure in the length spectrum metric of the quasiconformal Teichmüller space Tqc(X0) in Tls(X0).

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