Muyang Zhang
Abstract
This paper proposes a new method for remeshing a surface into anisotropically sized quads. The basic idea is to construct a special standing wave on the surface to generate the global quadrilateral structure. This wave based quadrangulation method is capable of controlling the quad size in two directions and precisely aligning the quads with feature lines. Similar to the previous methods, we augment the input surface with a vector field to guide the quad orientation. The anisotropic size control is achieved by using two size fields on the surface. In order to reduce singularity points, the size fields are optimized by a new curl minimization method. The experimental results show that the proposed method can successfully handle various quadrangulation requirements and complex shapes, which is difficult for the existing state-of-the-art methods.
Supplemental Material
- Alliez, P., Cohen-Steiner, D., Devillers, O., Lévy, B., and Desbrun, M. 2003. Anisotropic polygonal remeshing. ACM Transactions on Graphics 22, 3, 485--493. Google Scholar
Digital Library
- Alliez, P., Ucelli, G., Gotsman, C., and Attene, M. 2005. Recent advances in remeshing of surfaces. Research report, AIM@SHAPE Network of Excellence.Google Scholar
- Ben-Chen, M., Gotsman, C., and Bunin, G. 2008. Conformal flattening by curvature prescription and metric scaling. Computer Graphics Forum 27, 2, 449--458.Google ScholarCross Ref
- Blackstock, D. T. 2000. Fundamentals Of Physical Acoustics. Wiley-interscience.Google Scholar
- Boier-Martin, I., Rushmeier, H., and Jin, J. 2004. Parameterization of triangle meshes over quadrilateral domains. In Eurographics Symposium on Geometry Processing, ACM, New York, NY, USA, 193--203. Google ScholarDigital Library
- Bommes, D., Zimmer, H., and Kobbelt, L. 2009. Mixed-integer quadrangulation. ACM Transactions on Graphics 28, 3, 1--10. Google ScholarDigital Library
- Bremer, P.-T., Edelsbrunner, H., Hamann, B., and Pascucci, V. 2004. A topological hierarchy for functions on triangulated surfaces. IEEE Transactions on Visualization and Computer Graphics 10, 385--396. Google ScholarDigital Library
- Cohen-Steiner, D., and Morvan, J.-M. 2003. Restricted delaunay triangulations and normal cycle. In Symposium on Computational geometry, 312--321. Google ScholarDigital Library
- Dong, S., Kircher, S., and Garland, M. 2005. Harmonic functions for quadrilateral remeshing of arbitrary manifolds. Comput. Aided Geom. Des. 22, 5, 392--423. Google ScholarDigital Library
- Dong, S., Bremer, P.-T., Garland, M., Pascucci, V., and Hart, J. C. 2006. Spectral surface quadrangulation. ACM Transactions on Graphics 25, 3, 1057--1066. Google ScholarDigital Library
- Edelsbrunner, H., Harer, J., and Zomorodian, A. 2001. Hierarchical morse complexes for piecewise linear 2-manifolds. In Symposium on Computational geometry, ACM, New York, NY, USA, 70--79. Google ScholarDigital Library
- Hormann, K., Polthier, K., and Sheffer, A. 2008. Mesh parameterization: theory and practice. In SIGGRAPH Asia courses, ACM, New York, NY, USA, 1--87. 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 Transactions on Graphics 27, 5, 1--9. Google ScholarDigital Library
- Kälberer, F., Nieser, M., and Polthier, K. 2007. Quadcover - surface parameterization using branched coverings. Computer Graphics Forum.Google Scholar
- Lai, Y.-K., Kobbelt, L., and Hu, S.-M. 2008. An incremental approach to feature aligned quad dominant remeshing. In ACM symposium on Solid and physical modeling, ACM, New York, NY, USA, 137--145. Google ScholarDigital Library
- Marinov, M., and Kobbelt, L. 2006. A robust two-step procedure for quad-dominant remeshing. Computer Graphics Forum 25, 3 (Sept.), 537--546.Google ScholarCross Ref
- Meyer, M., Desbrun, M., Schröder, P., and Barr, A. H. 2002. Discrete differential-geometry operators for triangulated 2-manifolds. In Visualization and Mathematics III, H.-C. Hege and K. Polthier, Eds. Springer-Verlag, 35--57.Google Scholar
- Palacios, J., and Zhang, E. 2007. Rotational symmetry field design on surfaces. ACM Transactions on Graphics 26, 3, 55. Google ScholarDigital Library
- Polthier, K., and Preuss, E. 2003. Identifying vector field singularities using a discrete hodge decomposition. In Visualization and Mathematics III, H.-C. Hege and K. Polthier, Eds. Springer Verlag, Heidelberg, Germany, 113--134.Google Scholar
- Ray, N., Li, W. C., Lévy, B., Sheffer, A., and Alliez, P. 2006. Periodic global parameterization. ACM Transactions on Graphics 25, 4, 1460--1485. Google ScholarDigital Library
- Ray, N., Vallet, B., Li, W. C., and Lévy, B. 2008. Nsymmetry direction field design. ACM Transactions on Graphics 27, 2, 1--13. Google ScholarDigital Library
- Tong, Y., Alliez, P., Cohen-Steiner, D., and Desbrun, M. 2006. Designing quadrangulations with discrete harmonic forms. In Eurographics Symposium on Geometry Processing, Eurographics Association, Aire-la-Ville, Switzerland, 201--210. Google ScholarDigital Library
- Zhang, E., Mischaikow, K., and Turk, G. 2006. Vector field design on surfaces. ACM Transactions on Graphics 25, 4, 1294--1326. Google ScholarDigital Library
Index Terms
- A wave-based anisotropic quadrangulation method
Recommendations
Quadrangulation through morse-parameterization hybridization
We introduce an approach to quadrilateral meshing of arbitrary triangulated surfaces that combines the theoretical guarantees of Morse-based approaches with the practical advantages of parameterization methods. We first construct, through an eigensolver ...
Spectral surface quadrangulation
Resampling raw surface meshes is one of the most fundamental operations used by nearly all digital geometry processing systems. The vast majority of this work has focused on triangular remeshing, yet quadrilateral meshes are preferred for many surface ...
A wave-based anisotropic quadrangulation method
SIGGRAPH '10: ACM SIGGRAPH 2010 papersThis paper proposes a new method for remeshing a surface into anisotropically sized quads. The basic idea is to construct a special standing wave on the surface to generate the global quadrilateral structure. This wave based quadrangulation method is ...
Comments