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Making 3D Object Surfaces Smoother:
May/June 2010 (vol. 12 no. 3)
pp. 44-51
Yonggao Yang, Prairie View A&M University
Jian-ao Lian, Prairie View A&M University

Interpolating subdivision schemes let users adjust coordinates of a 3D object's initial vertices, generate new vertices, and replace the original mesh with more and smaller polygons to make the object's surface smoother. Two new schemes for triangular meshes extend and combine existing schemes to improve the process and its results.

1. E. Catmull and J. Clark, "Recursively Generated B-Spline Surfaces on Arbitrary Topological Meshes," Computer Aided Design, vol. 10, no. 6, 1978, pp. 350–355.
2. T. De Rose, M. Kass, and T. Truong, "Subdivision Surfaces in Character Animation," Proc. Int'l Conf. Computer Graphics and Interactive Techniques, ACM Press, 1998, pp. 85–94.
3. N. Dyn, D. Levin, and J. Gregory, "A Butterfly Subdivision Scheme for Surface Interpolation with Tension Control," ACM Trans. Graphics, vol. 9, no. 2, 1990, pp. 160–169.
4. H. Hoppe et al., "Piecewise Smooth Surface Reconstruction," Computer Graphics, vol. 28, no. 3, 1994, pp. 295–302.
5. M. Kohler, "A Meta Scheme for Iterative Refinement of Meshes," in Mathematical Visualization: Algorithms, Applications, and Numerics, H.C. Hege, and K. Polthier eds., Springer-Verlag, New York, 2002, pp. 45–60.
6. G. Li, W. Ma, and H. Bao, "√2 Subdivision for Quadrilateral Meshes," Visual Computer, vol. 20, no. 2, 2004, pp. 180–198.
7. J.A. Lian, "Refinable Box Splines and Subdivision," in Approximation Theory XII: San Antonio 2007, M. Neamtu, and L.L. Schumaker eds., Nashboro Press, 2008, pp. 229–242.
8. C. Loop, Smooth Subdivision Surfaces Based on Triangles, master's thesis, Dept. of Mathematics, Univ. of Utah, August 1987.
9. P. Oswald, "Designing Composite Triangular Subdivision Schemes," Computer Aided Geometric Design, vol. 22, no. 7, 2005, pp. 659–679.
10. P. Oswald, and P. Schröder, "Composite Primal/Dual √3 Subdivision Schemes," Computer Aided Geometric Design, vol. 20, no. 3, 2003, pp. 135–164.
11. D. Zorin and P. Schroder, "A Unified Framework for Primal/Dual Quadrilateral Subdivision Schemes," Computer Aided Geometric Design, vol. 18, no. 5, 2002, pp. 429–454.
12. D. Zorin, P. Schroder, and W. Sweldens, "Interpolating Subdivision for Mesh with Arbitrary Topology," Proc. 23rd Conf. Computer Graphics and Interactive Techniques, IEEE Press, 1996, pp. 189–192.

Index Terms:
Interpolation, subdivision, surface design, graphics and multimedia
Yonggao Yang, Jian-ao Lian, "Making 3D Object Surfaces Smoother:," Computing in Science and Engineering, vol. 12, no. 3, pp. 44-51, May-June 2010, doi:10.1109/MCSE.2010.66
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