Weighted area/angle distortion minimization for Mesh Parameterization

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dc.citation.journalTitleEngineering Computations
dc.contributor.authorMejia D.
dc.contributor.authorAcosta D.A.
dc.contributor.authorRuiz-Salguero O.
dc.contributor.departmentUniversidad EAFIT. Departamento de Ingeniería de Procesosspa
dc.contributor.researchgroupProcesos Ambientales (GIPAB)spa
dc.creatorMejia D.
dc.creatorAcosta D.A.
dc.creatorRuiz-Salguero O.
dc.date.accessioned2021-04-16T20:27:38Z
dc.date.available2021-04-16T20:27:38Z
dc.date.issued2017-01-01
dc.description.abstractPurpose: Mesh Parameterization is central to reverse engineering, tool path planning, etc. This work synthesizes parameterizations with un-constrained borders, overall minimum angle plus area distortion. This study aims to present an assessment of the sensitivity of the minimized distortion with respect to weighed area and angle distortions. Design/methodology/approach: A Mesh Parameterization which does not constrain borders is implemented by performing: isometry maps for each triangle to the plane Z = 0; an affine transform within the plane Z = 0 to glue the triangles back together; and a Levenberg-Marquardt minimization algorithm of a nonlinear F penalty function that modifies the parameters of the first two transformations to discourage triangle flips, angle or area distortions. F is a convex weighed combination of area distortion (weight: a with 0 = a = 1) and angle distortion (weight: 1 - a). Findings: The present study parameterization algorithm has linear complexity [O(n), n = number of mesh vertices]. The sensitivity analysis permits a fine-tuning of the weight parameter which achieves overall bijective parameterizations in the studied cases. No theoretical guarantee is given in this manuscript for the bijectivity. This algorithm has equal or superior performance compared with the ABF, LSCM and ARAP algorithms for the Ball, Cow and Gargoyle data sets. Additional correct results of this algorithm alone are presented for the Foot, Fandisk and Sliced-Glove data sets. Originality/value: The devised free boundary nonlinear Mesh Parameterization method does not require a valid initial parameterization and produces locally bijective parameterizations in all of our tests. A formal sensitivity analysis shows that the resulting parameterization is more stable, i.e. the UV mapping changes very little when the algorithm tries to preserve angles than when it tries to preserve areas. The algorithm presented in this study belongs to the class that parameterizes meshes with holes. This study presents the results of a complexity analysis comparing the present study algorithm with 12 competing ones. © Emerald Publishing Limited.eng
dc.identifierhttps://eafit.fundanetsuite.com/Publicaciones/ProdCientif/PublicacionFrw.aspx?id=6995
dc.identifier.doi10.1108/EC-02-2016-0072
dc.identifier.issn02644401
dc.identifier.issn17587077
dc.identifier.otherWOS;000407603800005
dc.identifier.otherSCOPUS;2-s2.0-85027455278
dc.identifier.urihttp://hdl.handle.net/10784/29401
dc.language.isoeng
dc.publisherEMERALD GROUP PUBLISHING LIMITED
dc.relation.urihttps://www.scopus.com/inward/record.uri?eid=2-s2.0-85027455278&doi=10.1108%2fEC-02-2016-0072&partnerID=40&md5=ce2b3fd3dbef3ba4e08af24a90920d6e
dc.rightshttps://v2.sherpa.ac.uk/id/publication/issn/0264-4401
dc.sourceEngineering Computations
dc.subjectAffine transformseng
dc.subjectComputational complexityeng
dc.subjectMathematical transformationseng
dc.subjectMesh generationeng
dc.subjectMotion planningeng
dc.subjectNonlinear analysiseng
dc.subjectNonlinear programmingeng
dc.subjectOptimizationeng
dc.subjectParameter estimationeng
dc.subjectReverse engineeringeng
dc.subjectSensitivity analysiseng
dc.subjectComplexity analysiseng
dc.subjectDesign/methodology/approacheng
dc.subjectDistortion minimizationeng
dc.subjectLevenberg-Marquardteng
dc.subjectLevenberg-Marquardt minimizationeng
dc.subjectMesh parameterizationeng
dc.subjectNon-linear optimizationeng
dc.subjectTheoretical guaranteeseng
dc.subjectParameterizationeng
dc.titleWeighted area/angle distortion minimization for Mesh Parameterizationeng
dc.typeinfo:eu-repo/semantics/articleeng
dc.typearticleeng
dc.typeinfo:eu-repo/semantics/publishedVersioneng
dc.typepublishedVersioneng
dc.type.localArtículospa

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