Similar articles

Abstract: We propose an angle-based mesh representation, which is invariant under translation, rotation, and uniform scaling, to encode the geometric details of a triangular mesh. Angle-based mesh representation consists of angle quantities defined on the mesh, from which the mesh can be reconstructed uniquely up to translation, rotation, and uniform scaling. The reconstruction process requires solving three sparse linear systems: the first system encodes the length of edges between vertices on the mesh, the second system encodes the relationship of local frames between two adjacent vertices on the mesh, and the third system defines the position of the vertices via the edge length and the local frames. From this angle-based mesh representation, we propose a quasi-angle-preserving mesh deformation system with the least-squares approach via handle translation, rotation, and uniform scaling. Several detail-preserving mesh editing examples are presented to demonstrate the effectiveness of the proposed method.

基于最小二乘方法的拟保角网格变形

研究目的：网格模型的修改与编辑方法在数字娱乐、数值计算等领域有着重要应用。如何在网格编辑过程中更好地保持模型的几何细节，是网格变形方法中富有挑战性的重要问题。本文利用网格模型蕴涵的内在几何信息，提出基于最小二乘方法的拟保角网格变形方法，在变形过程中有效保持网格模型的几何细节。
创新要点：提出一种基于内在角度信息的离散网格表示方法，具有旋转、平移和均匀缩放不变性，是三角离散网格模型的新型表示方法。基于该网格表示形式和最小二乘方法，建立了拟保持网格角度度量的网格变形框架。与基于拉普拉斯微分坐标方法相比，可有效保持网格模型的几何细节特征。
重要结论：若干三角网格模型变形与编辑实例显示，在数字娱乐领域本文算法有效。
网格编辑；网格变形；基于角度的网格表示；拟保角网格变形方法

[1]Alexa, M., 2003. Differential coordinates for local mesh morphing and deformation. Vis. Comput., 19(2):105-114.

[2]Au, O., Tai, C., Liu, L., et al., 2006. Dual Laplacian editing for meshes. IEEE Trans. Visual. Comput. Graph., 12(3):386-395.

[3]Boier-Martin, I., Ronfard, R., Bernardini, F., 2004. Detail-preserving variational surface design with multiresolution constraints. Proc. Shape Modeling Int., p.119-128.

[4]Botsch, M., Kobbelt, L., 2004. An intuitive framework for real-time freeform modeling. SIGGRAPH, p.630-634.

[5]Chen, S.G., Wu, J.Y., 2004. Estimating normal vectors and curvatures by centroid weights. Comput. Aid. Geom. Des., 21(5):447-458.

[6]Coquillart, S., 1990. Extended free-form deformation: a sculpting tool for 3D geometric modeling. SIGGRAPH, p.187-196.

[7]Guskov, I., Sweldens, W., Schroder, P., 1999. Multiresolution signal processing for meshes. SIGGRAPH, p.325-334.

[8]Hsu, W.H., Hughes, J.F., Kaufman, H., 1992. Direct manipulation of free-form deformations. SIGGRAPH, p.177-184.

[9]Hu, J.W., Liu, L.G., Wang, G.Z., 2007. Dual Laplacian morphing for triangular meshes. Comput. Anim. Virt. Worlds, 18(4-5):271-277.

[10]Kobbelt, L., Campagna, S., Vorsatz, J., et al., 1998. Interactive multiresolution modeling on arbitrary meshes. SIGGRAPH, p.105-114.

[11]Lazarus, F., Coquillart, S., Jancne, P., 1994. Axial deformations: an intuitive deformation technique. Comput.-Aid. Des., 26(8):607-613.

[12]Lipman, Y., Sorkine, O., Cohen-Or, D., et al., 2004. Differential coordinates for interactive mesh editing. Proc. Shape Modeling Int., p.181-190.

[13]Lipman, Y., Sorkine, O., Levin, D., et al., 2005. Linear rotation-invariant coordinates for meshes. SIGGRAPH, p.479-487.

[14]Luke, E., Collins, E., Blades, E., 2012. A fast mesh deformation method using explicit interpolation. J. Comput. Phys., 231(2):586-601.

[15]MacCracken, R., Joy, K., 1996. Free-form deformations with lattices of arbitrary topology. SIGGRAPH, p.181-188.

[16]Nealen, A., Sorkine, O., Alexa, M., et al., 2005. A sketch-based interface for detail-preserving mesh editing. SIGGRAPH, p.1142-1147.

[17]Sederberg, T.W., Parry, S.R., 1986. Free-form deformation of solid geometric models. SIGGRAPH, p.151-160.

[18]Singh, K., Fiume, E., 1998. Wires: a geometric deformation technique. SIGGRAPH, p.405-414.

[19]Sorkine, O., Lipman, Y., Cohen-Or, D., et al., 2004. Laplacian surface editing. ACM SIGGRAPH/Eurographics on Geometry, p.179-188.

[20]Toledo, S., 2003. TAUCS: a Library of Sparse Linear Solvers, Version 2.2.

[21]Xu, G., Wang, G.Z., Chen, X.D., 2008. Free form deformation with rational DMS-spline volumes. J. Comput. Sci. Technol., 23(5):862-873.

[22]Xu, G., Hui, K.C., Ge, W.B., et al., 2013. Direct manipulation of free-form deformation using curve-pairs. Comput.-Aid. Des., 45(3):605-614.

[23]Yu, Y., Zhou, K., Xu, D., et al., 2005. Mesh editing with Poisson-based gradient field manipulation. SIGGRAPH, p.496-503.

[24]Zhou, K., Huang, J., Snyder, J., et al., 2004. Large mesh deformation using the volumetric graph Laplacian. SIGGRAPH, p.641-648.

[25]Zhou, X., Li, S., 2013. A new mesh deformation method based on disk relaxation algorithm with pre-displacement and post-smoothing. J. Comput. Phys., 235:199-215.

[26]Zorin, D., Schroder, P., Sweldens, W., 1997. Interactive multiresolution mesh editing. SIGGRAPH, p.259-268.