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1、SIGGRAPH2000As-Rigid-As-PossibleShapeInterpolationMarcAlexa/DanielCohen-Or/DavidLevinAbstractnObject-spacemorphingtechnique을소개함-2차원이나3차원물체에대하여,그것의경계가아닌내부를blend함nMorphing은rigid함-Source에서부터targetconfiguration으로변할때에,지역의부피가최소로왜곡됨nBoundaryvertexcorrespondence가주어지면,source와target형상은isomorphicsimplicialco
2、mplexes(같은구조를가진,간단한삼각형으로이루어진복합체)로분해됨n시간에대한함수로서의closed-formexpression-Simplicialcomplexes에대하여,source로부터target위치까지의경계와내부의모든점에대한경로를할당nKeypoints-최적의simplexmorphing에대한정의(identification)-Errorfunction에대한적절한정의-점의경로를정의하는최소화문제n대응하는simplices의각짝은affinetransformation을정의함nRotation/stretchingtransformation으로분해됨
3、-localtransformation은시간에대하여자연스럽게interpolate됨-globalcoherentleast-distortingtransformation을구성하는데basis로제공됨261.Introductionn하나의그래픽적인물체를다른것으로변형하는기술은최근널리얻어지고있음-Morphing이나blending기술n최초의물체로부터target물체로의부드러운transition을생성하는것과관련됨n이것은시각적효과가강력하다고밝혀졌으며,영화나TV에서놀라운예제도많음n대부분의경우,이러한morphing기술은source와target물체의구조가다소유
4、사한곳에대하여,이미지기반기술을이용하여생성됨-유사하지않으면,처리과정은사용자의노력을더많이필요로하게됨[3,21,30]n이분야의제1의도전과제는,사용자와의상호작용을최소화하면서서로매우다른주어진2개의물체를blend하는알고리즘을고안하는것-그러면서도,중간형상은그것의최초의외양과특성을가능한많이유지해야함n<그림1>에서의Morph예제는이미지기반기술로는얻기힘듦-Foreground와background가서로다르게동작하기때문임nObject-spacemorphing은공간(image,volumes)을이산화하는대신에,물체를explicit한표현으로다룸[14],[20
5、]-물체가다각형(2D)이나다면체(3D)라고가정nMorphing과정은다음으로구성됨nVertexcorrespondenceproblem-표현된기하학적특징사이에서대응을생성하는것[23,19,6,18,14,1,20]nVertexpathproblem-이미결정된경로를따라서경계표현의위치를interpolation하는것[24,25,13,8][23:T.W.Sederberg,APhysicallyBasedApproachto2-DShapeBlending,CG1992]-2D의source와target형상을wire로가정하고,wire의물리적인특성인bending과
6、stretching을최소화함으로써자연스러운blending을만들어내는기법.26-이논문에서는source와target의형상의correspondenceproblem을각각의점에대하여차례로번호를매기는방법으로해결하였으며,source와target의점의개수가다를경우에는중간에점을추가함으로써개수를맞춰주었음(위그림에서source에서5,target에서1번vertex가추가됨)[19:J.R.Kent,ShapeTransformationforpolyhedralobjects,CG1992]-3D의source와target은genus0solid-Source와targ
7、et의좌표를구에projection시켜하나의mergedtopology를만들어냄-Mergedtopology를각형상의표면에mapping하여같은topology를갖도록함[18:T.Kanai,3Dgeometricmetamorphosisbasedonharmonicmaps,PG,1997]-두개의물체는같은topology를가짐-2-manifold(sphereordisk)-두물체는harmonicm
