网格变形技术研究

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1、浙江大学计算机科学与技术学院博士学位论文网格变形技术研究姓名：许秋儿申请学位级别：博士专业：计算机科学与技术指导教师：张三元;叶修梓20090408浙江大学博士学位论文摘要与目标网格的对应关系，无需用户前期对应点的指定。通过均值骨架坐标与微分域坐标变形技术的融合，将目标网格的变形转化为线性的能量约束问题，达到高效计算的同时保持目标网格的几何特征。该方法不仅能够实时地生成视觉真实的变形复制结果，而且操作简单适合动画制作初学者。(4)提出了基于动态轮廓模型的微分域网格变形技术。整个算法的关键是将骨架和体积的特征约束通过动态轮廓模型

2、的形式来进行近似的模拟，从而与微分域上的变形技术结合在一起，通过解线性最小二乘法得到变形后的结果。算法的目的是通过骨架和体积的近似保持将原本非线性的问题转换成线性求解来换取变形的速度，从而平衡了最大限度保持原有网格特征的要求和变形时间复杂度之间的矛盾。关键词：网格，最小二乘网格，自由变形，骨架子空间变形，变形复制，微分域坐标，均值骨架坐标，动态轮廓模型浙江大学博士学位论文AbstractMeshdeformationisthekernelpartofthedigitalgeometryprocessingwhichmorean

3、dmoreresearchersathomeandabroadarefocusingonrecently．Meshdeformationhaswideapplicationsinmanyareassuchasreverseengineering,numericalsimulations，rapidinnovativedesignandcomputeranimation，etc．Basedontheintensivesurveyandcomprehensiveanalysesofvariousapproachestothemes

4、hdeformation，severaldeformationalgorithmshavebeendesigned，implementedandverifiedinthisdissertationwhichmainlyaimsattheweaknessoftheexistingdeformationtechniques．Thetheoriesofcomputergraphics，computer-aidedgeometricdesign，discretedifferentialgeometry,digitalsignalpro

5、cessingandcomputationalgeometryareallincorporatedintoOUralgorithms．Maincontributionsofthedissertationinclude：(1)Anovelfree·formdeformationbasedonleast—squaremeshbasedisproposedinthedissertation．Inordertopreservethegeometrydetailsoftheoriginalmesh，theleast—squaremesh

6、oftheoriginalmeshisusedtoencodethedisplacementbetweentthetwomeshes．Thealgorithmconsistsofthefollowingmainsteps：Firstmean-valuecoordinatesisusedtocontroltheleast-squaremeshinsteadoftheoriginalone；Seconddisplacementvectorsareencodedanddecodedinthelocalframeofthevertic

7、eoftheleast—squaremeshanddrivetheoriginalmeshtodeformaccordingly．Fromtheuser’spointofview,thecontrolandspeedofthealgorithmisthesameastheydointhetraditionalfree—formdeformation．However,thedeformationresultofOUralgorithmisbeaerthanthetraditionalonesespeciallyinpreserv

8、ationofmesh’sgeometrydetails．(2)Localdetailpreservedmeshdeformationbasedonmean-valueskeletonsubspaceisintroducedinthedissertation．Themean—