摘要
Thissurveyreviewstherecentdevelopmentofgradientdomainmeshdeformationmethod.Differenttootherdeformationmethods,thegradientdomaindeformationmethodisasurface-based,variationaloptimizationmethod.Itdirectlyencodesthegeometricdetailsindifferentialcoordinates,whicharealsocalledLaplaciancoordinatesinliterature.BypreservingtheLaplaciancoordinates,themeshdetailscanbewellpreservedduringdeformation.DuetothelocalityoftheLaplaciancoordinates,thevariationaloptimizationproblemcanbecastedintoasparselinearsystem.Fastsparselinearsolvercanbeadoptedtogeneratedeformationresultinteractively,oreveninreal-time.Thenonlinearnatureofgradientdomainmeshdeformationleadstothedevelopmentoftwocategoriesofdeformationmethods:linearizationmethodsandnonlinearoptimizationmethods.Basically,thelinearizationmethodsonlyneedtosolvethelinearleast-squaressystemonce.Theyarefast,easytounderstandandcontrol,whilethedeformationresultmightbesuboptimal.Nonlinearoptimizationmethodscanreachoptimalsolutionofdeformationenergyfunctionbyiterativeupdating.Sincethecomputationofnonlinearmethodsisexpensive,reduceddeformablemodelsshouldbeadoptedtoachieveinteractiveperformance.Thenonlinearoptimizationmethodsavoidtheuserburdentoinputtransformationatdeformationhandles,andtheycanbeextendedtoincorporatevariousnonlinearconstraints,likevolumeconstraint,skeletonconstraint,andsoon.Wereviewrepresentativemethodsandrelatedapproachesofeachcategorycomparativelyandhopetohelptheuserunderstandthemotivationbehindthealgorithms.Finally,wediscusstherelationbetweenphysicalsimulationandgradientdomainmeshdeformationtorevealwhyitcanachievephysicallyplausibledeformationresult.
出版日期
2009年01月11日（中国期刊网平台首次上网日期，不代表论文的发表时间）
