基于形状匹配的网格变形与纹理优化算法
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摘要
随着数据采集技术、计算机硬件以及软件的发展,数字多媒体数据在经历—维声音、二维图像、二维视频为表现形式之后,出现了第四代数字多媒体形式---三维数字几何模型。由于其具有强烈的真实感,更符合人类的直观等优点,在影视制作、网络游戏、计算机动画、工业设计、科学计算和文物保护等领域得到了广泛应用。
本文以计算机图形学、微分几何学、计算几何和数字信号处理为坚实的理论基础,对现有的网格变形技术和纹理优化技术进行了总结。针对网格模型的主要变形技术和纹理化模型的纹理空间优化所存在的问题,提出相应的处理方法。主要内容包括：
1)提出了一种基于四面体胞的尽可能刚性网格变形算法。算法首先对网格模型内部进行稀疏四面体化,再通过最小化相应的变形能量函数,得到所需的模型变形结果。同时,针对大尺度编辑可能造成的模型局部塌陷,提出一种简单高效的四面体胞自适应剖分方法,进而消除不正确的变形效果。实验结果表明,该变形算法可以有效保持模型的表面细节以及模型的内部体积,并能够避免模型形状在大尺度变形时的局部退化。
2)提出了一种基于视觉重要性特征图的纹理空间优化算法。算法首先通过考虑三维模型的几何信息和模型对应的纹理图片的视觉属性,计算得出对应模型的重要性特征图。然后,根据模型重要性特征图,对纹理进行松弛操作,以重新分布图像中的信号信息。同时,针对松弛过程中出现的网格严重扭曲现象,提出一种局部最优化形状匹配算法,该算法通过保持网格局部变化区域的刚性,来调整控制网格在大变形时产生的扭曲现象。实验结果表明,该变形算法可以有效节省纹理空间,并能够有效避免映射过程中产生的不连续、走样现象。
Due to the rapid development of data acquisition, computer hardware and software,3D digital geometry models have emerged to be the fourth generation of digital media which had experienced several representations, such as 1D sound,2D image and 2D video. Because of the advantages of high reality and more human-satisfied intuition, this kind of representation has been widely used in those, fields, like video production, network game, computer animation, industry design, scientific computing and cultural relics protection.
Based on the fundamental theories of computer graphics, differential geometry, computational geometry and digital signal processing, the intensive review and comprehensive analyses of various approaches to mesh deformation and texture optimization are presented. Moreover, we propose some solutions aiming at solving problems related to mesh model deformation and texture space optimization. Main contributions of the dissertation include:
1) A novel approach to as-rigid-as-possible mesh deformation based on tetrahedral cells is introduced. First, sets of tetrahedral cells are produced through sparse voxelization. Preserving the rigidity of local transformations of mesh surface and these tetrahedra during deformation is achieved by minimizing the corresponding energy formulation that prevents unnatural artifacts both in the surface and interior of the geometry model. Meantime, in order to avoid the possible collapse emerged under large-scale deformation, we present a simple adaptive tetrahedron decomposition method. In our experiments, we show that the volume and surface details of the whole mesh can be approximately preserved and the local degeneration inside the mesh under large-scale deformation could be efficiently avoided.
2) A texture space optimization algorithm based on perceptual saliency feature map is proposed. First, the corresponding saliency map of textured model is efficiently computed by combining both geometry and texture properties. Then the texture image is highly relaxed according to this saliency map. In other words, the essential signals in the texture image are accordingly redistributed. At the same time, an optimization algorithm is presented to deal with the phenomenon of severe mesh distortion. By preserving the rigidity of local mesh, this algorithm could adjust the positions of control mesh during large-scale deformation and then avoid artifacts when mapped back to the model.
本文以计算机图形学、微分几何学、计算几何和数字信号处理为坚实的理论基础,对现有的网格变形技术和纹理优化技术进行了总结。针对网格模型的主要变形技术和纹理化模型的纹理空间优化所存在的问题,提出相应的处理方法。主要内容包括：
1)提出了一种基于四面体胞的尽可能刚性网格变形算法。算法首先对网格模型内部进行稀疏四面体化,再通过最小化相应的变形能量函数,得到所需的模型变形结果。同时,针对大尺度编辑可能造成的模型局部塌陷,提出一种简单高效的四面体胞自适应剖分方法,进而消除不正确的变形效果。实验结果表明,该变形算法可以有效保持模型的表面细节以及模型的内部体积,并能够避免模型形状在大尺度变形时的局部退化。
2)提出了一种基于视觉重要性特征图的纹理空间优化算法。算法首先通过考虑三维模型的几何信息和模型对应的纹理图片的视觉属性,计算得出对应模型的重要性特征图。然后,根据模型重要性特征图,对纹理进行松弛操作,以重新分布图像中的信号信息。同时,针对松弛过程中出现的网格严重扭曲现象,提出一种局部最优化形状匹配算法,该算法通过保持网格局部变化区域的刚性,来调整控制网格在大变形时产生的扭曲现象。实验结果表明,该变形算法可以有效节省纹理空间,并能够有效避免映射过程中产生的不连续、走样现象。
Due to the rapid development of data acquisition, computer hardware and software,3D digital geometry models have emerged to be the fourth generation of digital media which had experienced several representations, such as 1D sound,2D image and 2D video. Because of the advantages of high reality and more human-satisfied intuition, this kind of representation has been widely used in those, fields, like video production, network game, computer animation, industry design, scientific computing and cultural relics protection.
Based on the fundamental theories of computer graphics, differential geometry, computational geometry and digital signal processing, the intensive review and comprehensive analyses of various approaches to mesh deformation and texture optimization are presented. Moreover, we propose some solutions aiming at solving problems related to mesh model deformation and texture space optimization. Main contributions of the dissertation include:
1) A novel approach to as-rigid-as-possible mesh deformation based on tetrahedral cells is introduced. First, sets of tetrahedral cells are produced through sparse voxelization. Preserving the rigidity of local transformations of mesh surface and these tetrahedra during deformation is achieved by minimizing the corresponding energy formulation that prevents unnatural artifacts both in the surface and interior of the geometry model. Meantime, in order to avoid the possible collapse emerged under large-scale deformation, we present a simple adaptive tetrahedron decomposition method. In our experiments, we show that the volume and surface details of the whole mesh can be approximately preserved and the local degeneration inside the mesh under large-scale deformation could be efficiently avoided.
2) A texture space optimization algorithm based on perceptual saliency feature map is proposed. First, the corresponding saliency map of textured model is efficiently computed by combining both geometry and texture properties. Then the texture image is highly relaxed according to this saliency map. In other words, the essential signals in the texture image are accordingly redistributed. At the same time, an optimization algorithm is presented to deal with the phenomenon of severe mesh distortion. By preserving the rigidity of local mesh, this algorithm could adjust the positions of control mesh during large-scale deformation and then avoid artifacts when mapped back to the model.
引文
[1]Olga, S., Marc, A. As-rigid-as-possible surface modeling[C]Proceedings of the fifth Eurographics symposium on Geometry processing.2007:109-116.
[2]Adobe, Adobe Photoshop CS4. Adobe Corp.2009.
[3]Mario, B. et al. Geometric modeling based on polygonal meshes[C] ACM SIGGRAPH 2007 courses.2007.
[4]许秋儿.网格变形技术研究[D].浙江：浙江大学计算机学院,2009：13-33.
[5]Mario, B., Mark, P., Martin, W., Markus, G., Adaptive Space Deformations Based on Rigid Cells[J]. Computer Graphics Forum 2007,26(3):339-347.
[6]Takeo, I., Tomer, M.,& John, F.H. As-rigid-as-possible shape manipulation[J] ACM SIGGRAPH 2005 Papers.2005,24(3):1134-1141.
[7]Kun, Z. et al. Large mesh deformation using the volumetric graph Laplacian[J] ACM SIGGRAPH 2005 Papers,2005,24(3):496-503.
[8]Yizhou, Y. et al. Mesh editing with poisson-based gradient field manipulation[J] ACM SIGGRAPH 2004 Papers,2004,23(3):644-651.
[9]Sorkine, O. et al. Laplacian surface editing[C]Proceedings of the 2004 Eurographics/ACM SIGGRAPH symposium on Geometry processing,2004:175-184.
[10]Yaron, L., Olga, S., David, L.,& Daniel, C.-O. Linear rotation-invariant coordinates for meshes[J]. ACM SIGGRAPH 2005 Papers,2005,24(3):496-503.
[11]Huang, J. et al. Subspace gradient domain mesh deformation in ACM SIGGRAPH 2006 Papers,2006,25(3):1126-1134.
[12]Oscar Kin-Chung, A., Hongbo, F., Chiew-Lan, T., Daniel, C.-O. Handle-aware isolines for scalable shape editing[J].ACM SIGGRAPH 2007 papers,2007,26(3):83.
[13]Robert, W.S., Johannes, S.,& Mark, P. Embedded deformation for shape manipulation[J]ACM SIGGRAPH 2007 papers,2007,26(3):80.
[14]Pereberin, A., Hierarchical Approach for Texture Compression[C] Proc. of GraphiCon'99, 1999,195-199.
[15]Beers, A.C., Agrawala, M., Chaddha, N. Rendering from compressed textures[C]. Proceedings of the 23rd annual conference on Computer graphics and interactive techniques, 1996:373-378.
[16]Pedro, V.S., Steven, J.G., John, S.,& Hugues, H. Signal-specialized parametrization[C]. Proceedings of the 13th Eurographics workshop on Rendering,2002.
[17]Laurent, B., Gabriel, T., Fausto, B., Space-Optimized Texture Maps[J]. Computer Graphics Forum,2002,21(3),411-420.
[18]Hunter, A. Cohen, J.D. Uniform frequency images:adding geometry to images to produce space-efficient textures[C]Proceedings of the conference on Visualization'00, IEEE Computer Society Press, Salt Lake City, Utah, United States,2000.
[19]Yang, B., Wang, X.,& Li, F.W.B., Salient region of textured 3D model[C]. Proceedings of Computers Graphics,2010.
[20]Matthias, M., Bruno, H., Matthias, T.,& Markus, G. Meshless deformations based on shape matching[J] ACM SIGGRAPH 2005 Papers,2005,24(3):471-478.
[21]Schaefer, S., McPhail, T.,& Warren, J., Image deformation using moving least squares[J]. ACM Trans. Graph.2006,25 (3):533-540.
[22]James, G. Dominique, B., A survey of spatial deformation from a user-centered perspective[J]. ACM Trans. Graph.2008,27 (4):1-21.
[23]Thomas, W.S. Scott, R.P. Free-form deformation of solid geometric models in Proceedings of the 13th annual conference on Computer graphics and interactive techniques,1986, 20(4):151-160.
[24]Prem, K., Angelo, M., Nadia, M.T., Daniel, T., Simulation of facial muscle actions based on rational free form deformations[J] Computer Graphics Forum,1992,11(3):56-69.
[25]J Griessmair, W.P., Deformation of Solids With Tri-Variate B-Splines[J]. In Proceedings fo Eurographics,1989,137-148.
[26]Lamousin, H.J.& Jr., W.N.W., NURBS-Based Free-Form Deformations[J]. IEEE Comput. Graph. Appl.1994,14(6):59-65.
[27]Wenhao, S.& Xunnian, Y., Free-form deformation with weighted T-spline. Vis. Comput. 2005,21 (3):139-151.
[28]Sabine, C. Extended free-form deformation:a sculpturing tool for 3D geometric modeling[J]. Proceedings of the 17th annual conference on Computer graphics and interactive techniques .1990,24(4):187-196.
[29]Ron, M.& Kenneth, I.J. Free-form deformations with lattices of arbitrary topology[C].Proceedings of the 23rd annual conference on Computer graphics and interactive techniques.1996:181-188.
[30]Feng, J., Ma, L., Peng, Q., A new free-form deformation through the control of parametric surfaces[J]. Computers & Graphics.1996,20(4):531-539.
[31]Feng, J., Heng, P.-A., Wong, T.-T., Accurate B-spline free-form deformation of polygonal objects. J. Graph. Tools.1998,3(3):11-27.
[32]Kazuya, G.K. Katsutoshi, O. t-FFD:free-form deformation by using triangular mesh[J]. Proceedings of the eighth ACM symposium on Solid modeling and applications. 2003:226-234.
[33]Tao, J., Scott, S., Joe, W. Mean value coordinates for closed triangular meshes[C]ACM SIGGRAPH 2005 Papers.2005:561-566.
[34]Yaron, L., David, L., Daniel, C.-O., Green Coordinates[J]. ACM Trans. Graph.2008, 27(3):1-10.
[35]Lazarus, F., Coquillart, S., Jancene, P., Axial deformations:an intuitive deformation technique[J]. Computer Aided Design.1994,26(8):607-613.
[36]Yu-Kuang, C. Alyn, P.R. A generalized de Casteljau approach to 3D free-form deformation[J]. Proceedings of the 21st annual conference on Computer graphics and interactive techniques 1994.
[37]Karan, S. Eugene, F. Wires:a geometric deformation technique[C]. Proceedings of the 25th annual conference on Computer graphics and interactive techniques.1998:405-414.
[38]Paul, B.& Dominique, B. Deformation of n-dimensional objects[C]. Proceedings of the first ACM symposium on Solid modeling foundations and CAD/CAM applications. 1991:351-369.
[39]Laurent, M.Nadia Magnenat,T. Dirichlet Free-Form Deformations and their Application to Hand Simulation[C]. Proceedings of the Computer Animation,1997.
[40]Shewchuk, J.R., Triangle:Engineering a 2D Quality Mesh Generator and Delaunay Triangulator[J]. Applied Computational Geometry:Towards Geometric Engineering Springer-Verlab 1996,1148:203-222.
[41]Ignacio, L., Byungmoon, K., Joshua, G., Jarek, R., Chris, D.S., Twister:a space-warp operator for the two-handed editing of 3D shapes. ACM Trans. Graph.2003,22(3):663-668.
[42]Botsch, M. Kobbelt, L., Real-Time Shape Editing using Radial Basis Functions[J]. Computer Graphics Forum,2005,24(3):611-621.
[43]Nealen, A., Muller, M., Keiser, R., Boxerman, E.,& Carlson, M., Physically based deformable models in computer graphics[C]. In Eurographics:State of the Art Report.2005.
[44]Alec, R.R.& Doug, L.J. FastLSM:fast lattice shape matching for robust real-time deformation[J]ACM SIGGRAPH 2007 papers,2007,26(3):82.
[45]杨文武.计算机辅助卡通角色动作姿势编辑与插值[D].浙江：浙江大学计算机学院.2009：32-45.
[46]Demetri, T., John, P., Alan, B., Kurt, F. Elastically deformable models[C]. Proceedings of the 14th annual conference on Computer graphics and interactive techniques,1987.
[47]William, W. Andrew, W. Variational surface modeling[C]. Proceedings of the 19th annual conference on Computer graphics and interactive techniques,1992.
[48]Garland, M., Multiresolution modeling:Survey & future opportunities [C]. Eurographics'99, State of the Art Report,1999.
[49]Oscar Kin-Chung, A., Chiew-Lan, T., Ligang, L., Hongbo, F., Dual Laplacian Editing for Meshes. IEEE Transactions on Visualization and Computer Graphics,2006,12(3):386-395.
[50]Xu, W.-W. Zhou, K., Gradient domain mesh deformation-a survey[J]. JOURNAL OF COMPUTER SCIENCE AND TECHNOLOGY,2009,24(1):6-18.
[51]Sorkine, O., Laplacian Mesh Processing[C]. Eurographics STAR-State of The Art Report 2005,15-36.
[52]Mario, B., Mark, P., Markus, G., Leif, K. PriMo:coupled prisms for intuitive surface modeling[C] Proceedings of the fourth Eurographics symposium on Geometry processing. 2006:11-20.
[53]Yanlin, W., Weiwei, X., Yanchen, W., Kun, Z., Baining, G.,2D shape deformation using nonlinear least squares optimization[J]. Vis. Comput.,2006,22 (9):653-660.
[54]Xiaohan, S. et al. Mesh puppetry:cascading optimization of mesh deformation with inverse kinematics[J]. ACM SIGGRAPH 2007 papers,2007,26(3):81.
[55]Kraus, M. Ertl, T. Adaptive texture maps[C]. Proceedings of the ACM SIGGRAPH/EUROGRAPHICS conference on Graphics hardware.2002.
[56]Fenney, S. Texture compression using low-frequency signal modulation[C]. Proceedings of the ACM SIGGRAPH/EUROGRAPHICS conference on Graphics hardware.2003.
[57]Sheffer, A., Praun, E., Rose, K., Mesh parameterization methods and their applications[J]. Found. Trends. Comput. Graph. Vis.2006,2(2)105-171.
[58]Si, H., TETGEN, A Quality Tetrahedral Mesh Generator and 3-Dimensional Delaunay Triangulator. http://tetgen.berlios.de/.
[59]Wenwu, Y, Jieqing, F., Xiaogang, J., Shape deformation with tunable stiffness. Vis. Comput. 2008,24(7):495-503.
[60]Shoemake, K. Duff, T. Matrix animation and polar decomposition[C]. Proceedings of the conference on Graphics interface'92,1992.
[61]Tim, D., UMFPACK:unsymmetric multifrontal sparse LU factorization package. http://www.cise.ufl.edu/research/sparse/umfpack/Visit on 10.12.2007.
[62]Feng, J., Shao, J., Jin, X., Peng, Q., Forrest, R., Multiresolution Free-form Deformation with Subdivision Surface of Arbitrary Topology. The Visual Computer, Springer,2006,22(1): 28-42.
[63]彭群生,胡国飞.三角网格的参数化[J].计算机辅助设计与图形学学报,2006,16(6)：31-739.
[64]汤颖.纹理映射、合成和压缩[D].浙江：浙江大学计算机学院.2005：6-29.
[65]Lee, C.H., Varshney, A.,& Jacobs, D.W., Mesh saliency. ACM Trans. Graph.2005,24(3): 659-666.
[66]Sykora, D., Dingliana, J.,& Collins, S. As-rigid-as-possible image registration for hand-drawn cartoon animations[C]. Proceedings of the 7th International Symposium on Non-Photorealistic Animation and Rendering,2009:25-33.
[67]杨柏林.移动环境中三维图形传输机制与流水线优化算法研究[D].浙江：浙江大学计算机学院.2007：98-100.
[2]Adobe, Adobe Photoshop CS4. Adobe Corp.2009.
[3]Mario, B. et al. Geometric modeling based on polygonal meshes[C] ACM SIGGRAPH 2007 courses.2007.
[4]许秋儿.网格变形技术研究[D].浙江：浙江大学计算机学院,2009：13-33.
[5]Mario, B., Mark, P., Martin, W., Markus, G., Adaptive Space Deformations Based on Rigid Cells[J]. Computer Graphics Forum 2007,26(3):339-347.
[6]Takeo, I., Tomer, M.,& John, F.H. As-rigid-as-possible shape manipulation[J] ACM SIGGRAPH 2005 Papers.2005,24(3):1134-1141.
[7]Kun, Z. et al. Large mesh deformation using the volumetric graph Laplacian[J] ACM SIGGRAPH 2005 Papers,2005,24(3):496-503.
[8]Yizhou, Y. et al. Mesh editing with poisson-based gradient field manipulation[J] ACM SIGGRAPH 2004 Papers,2004,23(3):644-651.
[9]Sorkine, O. et al. Laplacian surface editing[C]Proceedings of the 2004 Eurographics/ACM SIGGRAPH symposium on Geometry processing,2004:175-184.
[10]Yaron, L., Olga, S., David, L.,& Daniel, C.-O. Linear rotation-invariant coordinates for meshes[J]. ACM SIGGRAPH 2005 Papers,2005,24(3):496-503.
[11]Huang, J. et al. Subspace gradient domain mesh deformation in ACM SIGGRAPH 2006 Papers,2006,25(3):1126-1134.
[12]Oscar Kin-Chung, A., Hongbo, F., Chiew-Lan, T., Daniel, C.-O. Handle-aware isolines for scalable shape editing[J].ACM SIGGRAPH 2007 papers,2007,26(3):83.
[13]Robert, W.S., Johannes, S.,& Mark, P. Embedded deformation for shape manipulation[J]ACM SIGGRAPH 2007 papers,2007,26(3):80.
[14]Pereberin, A., Hierarchical Approach for Texture Compression[C] Proc. of GraphiCon'99, 1999,195-199.
[15]Beers, A.C., Agrawala, M., Chaddha, N. Rendering from compressed textures[C]. Proceedings of the 23rd annual conference on Computer graphics and interactive techniques, 1996:373-378.
[16]Pedro, V.S., Steven, J.G., John, S.,& Hugues, H. Signal-specialized parametrization[C]. Proceedings of the 13th Eurographics workshop on Rendering,2002.
[17]Laurent, B., Gabriel, T., Fausto, B., Space-Optimized Texture Maps[J]. Computer Graphics Forum,2002,21(3),411-420.
[18]Hunter, A. Cohen, J.D. Uniform frequency images:adding geometry to images to produce space-efficient textures[C]Proceedings of the conference on Visualization'00, IEEE Computer Society Press, Salt Lake City, Utah, United States,2000.
[19]Yang, B., Wang, X.,& Li, F.W.B., Salient region of textured 3D model[C]. Proceedings of Computers Graphics,2010.
[20]Matthias, M., Bruno, H., Matthias, T.,& Markus, G. Meshless deformations based on shape matching[J] ACM SIGGRAPH 2005 Papers,2005,24(3):471-478.
[21]Schaefer, S., McPhail, T.,& Warren, J., Image deformation using moving least squares[J]. ACM Trans. Graph.2006,25 (3):533-540.
[22]James, G. Dominique, B., A survey of spatial deformation from a user-centered perspective[J]. ACM Trans. Graph.2008,27 (4):1-21.
[23]Thomas, W.S. Scott, R.P. Free-form deformation of solid geometric models in Proceedings of the 13th annual conference on Computer graphics and interactive techniques,1986, 20(4):151-160.
[24]Prem, K., Angelo, M., Nadia, M.T., Daniel, T., Simulation of facial muscle actions based on rational free form deformations[J] Computer Graphics Forum,1992,11(3):56-69.
[25]J Griessmair, W.P., Deformation of Solids With Tri-Variate B-Splines[J]. In Proceedings fo Eurographics,1989,137-148.
[26]Lamousin, H.J.& Jr., W.N.W., NURBS-Based Free-Form Deformations[J]. IEEE Comput. Graph. Appl.1994,14(6):59-65.
[27]Wenhao, S.& Xunnian, Y., Free-form deformation with weighted T-spline. Vis. Comput. 2005,21 (3):139-151.
[28]Sabine, C. Extended free-form deformation:a sculpturing tool for 3D geometric modeling[J]. Proceedings of the 17th annual conference on Computer graphics and interactive techniques .1990,24(4):187-196.
[29]Ron, M.& Kenneth, I.J. Free-form deformations with lattices of arbitrary topology[C].Proceedings of the 23rd annual conference on Computer graphics and interactive techniques.1996:181-188.
[30]Feng, J., Ma, L., Peng, Q., A new free-form deformation through the control of parametric surfaces[J]. Computers & Graphics.1996,20(4):531-539.
[31]Feng, J., Heng, P.-A., Wong, T.-T., Accurate B-spline free-form deformation of polygonal objects. J. Graph. Tools.1998,3(3):11-27.
[32]Kazuya, G.K. Katsutoshi, O. t-FFD:free-form deformation by using triangular mesh[J]. Proceedings of the eighth ACM symposium on Solid modeling and applications. 2003:226-234.
[33]Tao, J., Scott, S., Joe, W. Mean value coordinates for closed triangular meshes[C]ACM SIGGRAPH 2005 Papers.2005:561-566.
[34]Yaron, L., David, L., Daniel, C.-O., Green Coordinates[J]. ACM Trans. Graph.2008, 27(3):1-10.
[35]Lazarus, F., Coquillart, S., Jancene, P., Axial deformations:an intuitive deformation technique[J]. Computer Aided Design.1994,26(8):607-613.
[36]Yu-Kuang, C. Alyn, P.R. A generalized de Casteljau approach to 3D free-form deformation[J]. Proceedings of the 21st annual conference on Computer graphics and interactive techniques 1994.
[37]Karan, S. Eugene, F. Wires:a geometric deformation technique[C]. Proceedings of the 25th annual conference on Computer graphics and interactive techniques.1998:405-414.
[38]Paul, B.& Dominique, B. Deformation of n-dimensional objects[C]. Proceedings of the first ACM symposium on Solid modeling foundations and CAD/CAM applications. 1991:351-369.
[39]Laurent, M.Nadia Magnenat,T. Dirichlet Free-Form Deformations and their Application to Hand Simulation[C]. Proceedings of the Computer Animation,1997.
[40]Shewchuk, J.R., Triangle:Engineering a 2D Quality Mesh Generator and Delaunay Triangulator[J]. Applied Computational Geometry:Towards Geometric Engineering Springer-Verlab 1996,1148:203-222.
[41]Ignacio, L., Byungmoon, K., Joshua, G., Jarek, R., Chris, D.S., Twister:a space-warp operator for the two-handed editing of 3D shapes. ACM Trans. Graph.2003,22(3):663-668.
[42]Botsch, M. Kobbelt, L., Real-Time Shape Editing using Radial Basis Functions[J]. Computer Graphics Forum,2005,24(3):611-621.
[43]Nealen, A., Muller, M., Keiser, R., Boxerman, E.,& Carlson, M., Physically based deformable models in computer graphics[C]. In Eurographics:State of the Art Report.2005.
[44]Alec, R.R.& Doug, L.J. FastLSM:fast lattice shape matching for robust real-time deformation[J]ACM SIGGRAPH 2007 papers,2007,26(3):82.
[45]杨文武.计算机辅助卡通角色动作姿势编辑与插值[D].浙江：浙江大学计算机学院.2009：32-45.
[46]Demetri, T., John, P., Alan, B., Kurt, F. Elastically deformable models[C]. Proceedings of the 14th annual conference on Computer graphics and interactive techniques,1987.
[47]William, W. Andrew, W. Variational surface modeling[C]. Proceedings of the 19th annual conference on Computer graphics and interactive techniques,1992.
[48]Garland, M., Multiresolution modeling:Survey & future opportunities [C]. Eurographics'99, State of the Art Report,1999.
[49]Oscar Kin-Chung, A., Chiew-Lan, T., Ligang, L., Hongbo, F., Dual Laplacian Editing for Meshes. IEEE Transactions on Visualization and Computer Graphics,2006,12(3):386-395.
[50]Xu, W.-W. Zhou, K., Gradient domain mesh deformation-a survey[J]. JOURNAL OF COMPUTER SCIENCE AND TECHNOLOGY,2009,24(1):6-18.
[51]Sorkine, O., Laplacian Mesh Processing[C]. Eurographics STAR-State of The Art Report 2005,15-36.
[52]Mario, B., Mark, P., Markus, G., Leif, K. PriMo:coupled prisms for intuitive surface modeling[C] Proceedings of the fourth Eurographics symposium on Geometry processing. 2006:11-20.
[53]Yanlin, W., Weiwei, X., Yanchen, W., Kun, Z., Baining, G.,2D shape deformation using nonlinear least squares optimization[J]. Vis. Comput.,2006,22 (9):653-660.
[54]Xiaohan, S. et al. Mesh puppetry:cascading optimization of mesh deformation with inverse kinematics[J]. ACM SIGGRAPH 2007 papers,2007,26(3):81.
[55]Kraus, M. Ertl, T. Adaptive texture maps[C]. Proceedings of the ACM SIGGRAPH/EUROGRAPHICS conference on Graphics hardware.2002.
[56]Fenney, S. Texture compression using low-frequency signal modulation[C]. Proceedings of the ACM SIGGRAPH/EUROGRAPHICS conference on Graphics hardware.2003.
[57]Sheffer, A., Praun, E., Rose, K., Mesh parameterization methods and their applications[J]. Found. Trends. Comput. Graph. Vis.2006,2(2)105-171.
[58]Si, H., TETGEN, A Quality Tetrahedral Mesh Generator and 3-Dimensional Delaunay Triangulator. http://tetgen.berlios.de/.
[59]Wenwu, Y, Jieqing, F., Xiaogang, J., Shape deformation with tunable stiffness. Vis. Comput. 2008,24(7):495-503.
[60]Shoemake, K. Duff, T. Matrix animation and polar decomposition[C]. Proceedings of the conference on Graphics interface'92,1992.
[61]Tim, D., UMFPACK:unsymmetric multifrontal sparse LU factorization package. http://www.cise.ufl.edu/research/sparse/umfpack/Visit on 10.12.2007.
[62]Feng, J., Shao, J., Jin, X., Peng, Q., Forrest, R., Multiresolution Free-form Deformation with Subdivision Surface of Arbitrary Topology. The Visual Computer, Springer,2006,22(1): 28-42.
[63]彭群生,胡国飞.三角网格的参数化[J].计算机辅助设计与图形学学报,2006,16(6)：31-739.
[64]汤颖.纹理映射、合成和压缩[D].浙江：浙江大学计算机学院.2005：6-29.
[65]Lee, C.H., Varshney, A.,& Jacobs, D.W., Mesh saliency. ACM Trans. Graph.2005,24(3): 659-666.
[66]Sykora, D., Dingliana, J.,& Collins, S. As-rigid-as-possible image registration for hand-drawn cartoon animations[C]. Proceedings of the 7th International Symposium on Non-Photorealistic Animation and Rendering,2009:25-33.
[67]杨柏林.移动环境中三维图形传输机制与流水线优化算法研究[D].浙江：浙江大学计算机学院.2007：98-100.