Abstract
This paper addressed the problem of Spherical Mesh parameterization. The main contribution of this work was to propose an effective optimization scheme to compute such parameterization, and to have an algorithm exposing a property of global convergence This is the case of trust region spherical parameterization (TRSP) to minimizing the ratio of inverted triangle, have an efficient spherical parameterization, and to generate bijective and lowly distorted mapping results so the faces have the correct orientation, thus creating a 3d spherical geometry object. Simulation results show that it is possible to achieve a considerable correspondence between the angle and area perspective distortion.
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References
Maillot, J., Yahia, H., Verroust, A.: ACM SIGGRAPH (1993)
Cignoni, P., Montani, C., Rocchni, C., Scopigno, R.: A general method for recovering attributes values on simplified meshes. In: IEEE Visualisation (1998)
Sander, P., Snyder, J., Gortler, S., Hoppe, H.: Texture mapping progressive meshes. In: ACM SIGGRAPH (2001)
Floater, M.S, Hormann, K.: Surface parameterization: a tutorial and survey (2005)
Floater, M.S.: Parameterization and smooth approximation of surface triangulation. Computer Aided Geometric Design 14 (1997)
Levy, B., Petitjean, S.: Least squares conformal maps for automatic texture atlas generation. In: Proceedings of ACM SIGGRAPH (2002)
Isenburg, M., Gumhold, S., Gotsman, C.: Connectivity Shapes. In: Proceedings of IEEE Visualization (2001)
Gu, X., Gortler, S., Hoppe, H.: Geometry images. In: ACM SIGGRAPH (2002)
Praun, Hoppe, H.: Spherical parametrization and remeshing. In: SIGGRAPH 2003 (2003)
Kent, J., Carlson, W., Parent, R.: Shape transformation for polyhedral objects. In: ACM SIGGRAPH 92 (1992)
Alexa, M.: Recent advances in mesh morphing. Computer Graphics Forum (2002)
Grimm, C.: Simple manifolds for surface modeling and parametrization. Shape Modeling International (2002)
Haker, S., Angenent, S., Tannenbaum, S., Kikinis, R., Sapiro, G., Halle, M.: Conformal surface parametrization for texture mapping. In: IEEE TVCG (2000)
Sheffer, A., Gotsman, C., Dyn, N.: Robust spherical parameterization of triangular meshes. In: 4th Israel-Korea Bi-National Conf. on Geometric Modeling and Computer Graphics (2003)
Gotsman, C., Gu, X., Sheffer, A.: Fundamentals of spherical parameterization for 3D meshes. In: ACM SIGGRAPH (2003)
Quicken, M., Brechbuhler, C., Hug, J., Blattmann, H., Székely, G.: Parametrization of closed surfaces for parametric surface description. In: CVPR (2000)
Zayer, R., Rossl, C., Seidel, H.P.: Curvilinear spherical parameterization. In: Proc. IEEE International Conf. on Shape Modeling and Applications (2006)
Sander, P., Snyder, J., Gortler, S., Hoppe: Texture mapping progressive meshes. In: Proceedings of SIGGRAPH (2001)
Gu, X., Yau, S.T.: Global conformal surface parameterization. In: Proc. Symp. of Geometry Processing (2003)
Li, X., He, Y., Gu, X., Qin, H.: Curves-on-surface: a general shape comparison framework. In: Proc. IEEE International Conf. on Shape Modeling and Applications (2006)
Wa, S., Ye, T., Li, M., Zh, H., Li, X., Hu, S.-M., Martin, R.R.: CVM. LNCS. Springer-Verlag, Heidelberg (2012)
Theodoris, A., Ioannis, F., Christophoros, N.: Feature-based 3D Morphing based on Geometrically Constrained Sphere Mapping Optimization (2010)
Sheffer, A., de Sturler, E.: Parameterization of faceted surfaces for meshing using angle based flattening. Engineering with Computers (2001)
Pinkall, U., Polthier, K.: Computing Discrete Minimal Surfaces and Their Conjugates
https://www.ceremade.dauphine.fr/~peyre/numericaltour/tours/meshdeform_2_parameterization_sphere/
Bogdan, CM., Titus, Z.: IA3D Mesh Morphing
Li, S., Moo, C.: Large-Scale Modeling of Parametric Surfaces using Spherical Harmonics
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Dhibi, N., Elkefi, A., Bellil, W., Amar, C.B. (2015). A Trust Region Optimization Method for Fast 3D Spherical Configuration in Morphing Processes. In: Battiato, S., Blanc-Talon, J., Gallo, G., Philips, W., Popescu, D., Scheunders, P. (eds) Advanced Concepts for Intelligent Vision Systems. ACIVS 2015. Lecture Notes in Computer Science(), vol 9386. Springer, Cham. https://doi.org/10.1007/978-3-319-25903-1_47
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DOI: https://doi.org/10.1007/978-3-319-25903-1_47
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