Marco Tarini
Paolo Cignoni
ABSTRACT
We present a method for the global parametrization of meshes that preserves alignment to a cross field in input while obtaining a parametric domain made of few coarse axis-aligned rectangular patches, which form an abstract base complex without T-junctions. The method is based on the topological simplification of the cross field in input, followed by global smoothing.
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- Bommes, D., Zimmer, H., and Kobbelt, L. 2009. Mixed-integer quadrangulation. ACM Trans. Graph. 28, 3, 1--10. Google Scholar
Digital Library
- Bommes, D., Lempfer, T., and Kobbelt, L. 2011. Global structure optimization of quadrilateral meshes. Computer Graphics Forum 30, 2, 375--384.Google ScholarCross Ref
- Chen, G., Mischaikow, K., Laramee, R. S., and Zhang, E. 2008. Efficient morse decompositions of vector fields. IEEE Trans. on Vis. and Comp. Graph. 14, 848--862. Google ScholarDigital Library
- Daniels, J., Silva, C., Shepherd, J., and Cohen, E. 2008. Quadrilateral mesh simplification. ACM Trans. Graph. 27, 5, 148:1--148:9. Google ScholarDigital Library
- Daniels, J., Silva, C. T., and Cohen, E. 2009. Semiregular quadrilateral-only remeshing from simplified base domains. Computer Graphics Forum 28, 5, 1427--1435. Google ScholarDigital Library
- Delmarcelle, T., and Hesselink, L. 1994. The topology of symmetric, second-order tensor fields. In VIS '94: Proceedings of the conference on Visualization '94, 140--147. Google ScholarDigital Library
- Dong, S., Bremer, P.-T., Garland, M., Pascucci, V., and Hart, J. 2006. Spectral surface quadrangulation. ACM Trans. Graph. 25, 3, 1057--1066. Google ScholarDigital Library
- Eppstein, D., Goodrich, M., Kim, E., and Tamstorf, R. 2008. Motorcycle graphs: Canonical quad mesh partitioning. Computer Graphics Forum 27, 5 (July), 1477--1486. Google ScholarDigital Library
- Gu, X., Gortler, S. J., and Hoppe, H. 2002. Geometry images. In SIGGRAPH, ACM, T. Appolloni, Ed., 355--361. Google ScholarDigital Library
- Hormann, K., and Greiner, G. 2000. MIPS: An efficient global parametrization method. In Curve and Surface Design: Saint-Malo 1999, Innovations in Appl. Math. Vanderbilt Univ. Press, 153--162.Google Scholar
- Hormann, K., Polthier, K., and Sheffer, A. 2008. Mesh parameterization: Theory and practice. In SIGGRAPH Asia 2008 Course Notes, ACM Press, Singapore, no. 11, 1--81. Google ScholarDigital Library
- Huang, J., Zhang, M., Ma, J., Liu, X., Kobbelt, L., and Bao, H. 2008. Spectral quadrangulation with orientation and alignment control. ACM Trans. Graph. 27, 5, 147. Google ScholarDigital Library
- Khodakovsky, A., Litke, N., and Schröder, P. 2003. Globally smooth parameterizations with low distortion. ACM Trans. Graph. 22, 3, 350--357. Google ScholarDigital Library
- Klberer, F., Nieser, M., and Polthier, K. 2007. Quadcover - surface parameterization using branched coverings. Computer Graphics Forum 26, 3, 375--384.Google ScholarCross Ref
- Lee, A. W. F., Sweldens, W., Schröder, P., Cowsar, L., and Dobkin, D. 1998. Maps: Multiresolution adaptive parameterization of surfaces. Comp. Graph. Proc., 95--104. Google ScholarDigital Library
- Lin, J., Jin, X., Fan, Z., and Wang, C. 2008. Automatic polycube-maps. In Proc. of the 5th Int. Conf. on Advances in geometric modeling and processing, Springer-Verlag, 3--16. Google ScholarDigital Library
- Myles, A., Pietroni, N., Kovacs, D., and Zorin, D. 2010. Feature-aligned t-meshes. In ACM SIGGRAPH 2010 papers, ACM, New York, NY, USA, SIGGRAPH '10, 117:1--117:11. Google ScholarDigital Library
- Pietroni, N., Tarini, M., and Cignoni, P. 2010. Almost isometric mesh parameterization through abstract domains. IEEE Trans. on Visualization and Comp. Graphics 16, 4, 621--635. Google ScholarDigital Library
- Ray, N., Li, W., Lévy, B., Sheffer, A., and Alliez, P. 2006. Periodic global parameterization. ACM Trans. Graph. 25, 4, 1460--1485. Google ScholarDigital Library
- Ray, N., Vallet, B., Li, W. C., and Lévy, B. 2008. N-symmetry direction field design. ACM Trans. Graph. 27, 2, 1--13. Google ScholarDigital Library
- Sander, P. V., Wood, Z. J., Gortler, S. J., Snyder, J., and Hoppe, H. 2003. Multi-chart geometry images. In Symp. on Geom. Proc., Eurographics Association, vol. 43 of ACM Internat. Conf, Proc. Series, 146--155. Google ScholarDigital Library
- Tarini, M., Hormann, K., Cignoni, P., and Montani, C. 2004. Polycube-maps. In ACM SIGGRAPH 2004 Papers, ACM, New York, NY, USA, SIGGRAPH '04, 853--860. Google ScholarDigital Library
- Tricoche, X., Scheuermann, G., and Hagen, H. 2001. Continuous topology simplification of planar vector fields. In IEEE Visualization. Google ScholarDigital Library
- Zhang, M., Huang, J., Liu, X., and Bao, H. 2010. A wave-based anisotropic quadrangulation method. In ACM SIGGRAPH 2010 papers, ACM, New York, NY, USA, SIGGRAPH '10, 118:1--118:8. Google ScholarDigital Library
Index Terms
- Simple quad domains for field aligned mesh parametrization
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