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attached to the Institut Mines-Télécom , become internal schools of the Institute just as the telecommunications schools The Ecole des Mines of Douai is merged with Telecom Lille and the Ecole des Mines of Nantes with Telecom Bretagne to create two new schools of the Institute
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The free course in AR technologies with Coursera from the French Institut Mines-Télécom (Coursera, 2017) was gratefully used to add AR skills to the researcher’s wider developer and computer
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May 2018 doc: IEEE 80215 15-18-0206-00-0thz Project: IEEE
•Project start: 1st September 2017 •Duration: 3 years •Total costs/EC contribution: EUR 2 966 268,75 •Eight partners from seven different European countries: Creonic Gmbh , Ericsson AB, IMEC, Institut Mines-Telecom, InterDigital Europe, Polaran, Technikon, Technische Universitaet Kaiserslautern
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Least Squares Affine Transitions for Global
Parameterization
Ana Maria Vintescu
LTCI - Télécom ParisTech -
Institut Mines-Telecom
75013 Paris, France
vintescu@telecom-paristech.frFlorent DupontUniversité de Lyon, CNRS
Université Lyon 1, LIRIS UMR 5205
69622 Villeurbanne, France
florent.dupont@liris.cnrs.frGuillaume LavouéUniversité de Lyon, CNRS
INSA-Lyon, LIRIS UMR 5205
69621 Villeurbanne, France
glavoue@liris.cnrs.frPooran Memari
LIX UMR 7161, CNRS, École
Polytechnique, Université Paris Saclay
91128 Palaiseau Cedex - France
memari@lix.polytechnique.frJulien TiernySorbonne Universités, UPMC Univ Paris
06, CNRS, LIP6 UMR 7606
75005 Paris, France
julien.tierny@lip6.frABSTRACT
This paper presents an efficient algorithm for
a global parameterization of triangular surf acemeshes. In contrastto previous techniques which achieve global parameterization through the optimization of non-linear systems of
equations, our algorithm is solely based on solving at most two linear equation systems, in the least square sense.
Therefore, in terms of running time the unfolding procedure is highly efficient. Our approach is direct - it solves
for the planar UV coordinates of each vertex directly - hence avoiding any numerically challenging planar recon-
struction in a post-process. This results in a robust unfolding algorithm. Curvature prescription for user-provided
cone singularities can either be specified manually , or suggested automatically by our approach. Experiments on avariety of surface meshes demonstrate the runtime efficiency of our algorithm and the quality of its unfolding. To
demonstrate the utility and versatility of our approach, we apply it to seamless texturing.The propos edalgorithm
is computationally efficient, robust and results in a parameterization with acceptable metric distortion.
0.1 Keywords
surface parameterization, geometry processing ,triangular mesh, mesh unfolding1 INTRODUCTION
Surface parameterization represents a main topic in ge- ometry processing and computer graphics fields. It is defined as a one-to-one mapping between a surface and typically a 2D plane , where geometrical tasks can be carried out more efficiently. The most important ap- plication of surface parameterization are texture map- ping, texture synthesis, re-meshing, and morphing. In ordertounfoldasurfacetotheplane, itmusthaveadisk topology; for a closed surface this requirement implies cutting it into a s ingleor multiple disk topology charts.Cutting
can result in visual artif actsdue to the discon- tinuities across the boundaries of the charts. To thisextent, methods forglobal parameterizationof triangu-Permission to make digital or hard copies of all or part of
this work for personal or classroom use is granted without fee provided that copies are not made or distributed for profit or commercial advantage and that copies bear this notice and the full citation on the first page. To copy otherwise, or re- publish, to post on servers or to redistribute to lists, requires prior specific permission and/or a fee.lated surfaces have been proposed.W ithinthis frame- work, the global parameterization of a surface with disk topology can be defined as a homeomorphism from the surface to a subset of the plane, such that the discrete Gaussian curvature, i.e. the difference between 2pand the incident triangles" sum of angles at a v ertex,is zero everywhere except for a few vertices calledcone singu- larities.These can be thought of distortion absorbers, being chosen as vertices of the mesh where large area distortion can be predicted prior to the actual parame- terization, [Kha05]. Several approaches based on metric scaling have been proposed in the past to address global parameterization [Jin08, Yan09]. However, these methods mostly rely on non-linear solvers and are hence computationally ex- pensive. Linearized approximations, although compu- tationally attractive, are imprecise (the target metric is only approximated and therefore is not guaranteed to be flat). More importantly, the planar coordinates of the surface vertices (the actual output) are not the variables that are optimized by this family of techniques . We will refer to those as indirect methods[Ben08].Indeed theyfocus on the surf acemetric, i.e. the edge lengths, and later reconstruct the planar coordinates in a post- process. However, thisreconstructionpost-processmay be computationally expensive and, more importantly, numerically challenging. This paper addresses these nique which is fast by employing linear solvers, which minimizes angular distortion through imposed confor- mality, and reduces the area distortion through the use of cone singularities. Our method issimpleanddirect. It directly solves for the 2D coordinates. Thus, it does not suffer from numerical instabilities due to angle-to- uv or scaling factors-to-uv conversions , as found with indirect approaches, [She06]. In contrast to more com- putationally expensive techniques based on non-linear solvers, thecomputationalspeedofourapproachmakes it a good candidate for interactive applications, such as user-driven parameterization improvement for instance, where the users could interacti velya djustthe number and locations of the cones.