Triangle Mesh Deformation Based On Generalized Barycentric Coordinates

Mesh deformation is an important component of the digital geometry pro-cessing,being widely applied in many computer graphics feld,such as3D modeling,computer animation,physical simulation and so on.Mesh deformation based gener-alized barycentric coordinates has some remarkable performance including highertime efciency,more convenient interactive interface,non-retricted mesh structureand has come more and more attention by researchers.The basic procedure of mesh deformation based generalized barycentric coor-dinates is as follows: Firstly a coarse controlled mesh,named Cage, is created to thesource mesh; Secondly generalized barycentric coordinates is able to describe the re-lation between controlled mesh and source mesh; Finally when the user manipulatethe vertex of controlled mesh, source mesh also deform following the deformation ofthe controlled mesh. So the generalized barycentric coordinates directly infuencethe performance of mesh deformation. Recently years,researchers have proposedmany novel generalized barycentric coordinates with good properties,namely meanvalue coordinates,harmonic coordinates and green coordinates as representative.This paper studies three form generalized barycentric coordinates and the mainworks are as follows:This paper analyze the mathematical deduction of the mean value coordinates,harmonic coordinates and green coordinates in detail and describe the difer-ence in properties for three coordinate’s form leading to the diference on perfor-mance of mesh deformation based on three coordinate’s form.So this paper com-pare methods in detail from computing time,smoothness,non-negative,detailpreserving.The comparison can provide the theoretical basis in the selection ofgeneralized barycentric coordinates.The development of the experimental system of digital geometry processing.In the research work,some basic algorithm, data structure and interactiveinterface are often coded repeatedly.For this phenomenon, this paper willdevelop the experimental system of digital geometry processing,named Magine.The Magine system provide some basic algorithm,data structure, interactiveinterface and the plug-in module that make researchers break away from theheavy encoding task and devote themselves to the research and innovation on academic feld.