Abstract
We present a smooth, everywhere C k, analytic surface representation for closed surfaces of arbitrary topology. We demonstrate fitting this representation to meshes of varying resolutions and sampling quality. The fitting process is adaptive and provides controls for both the average and the maximum allowable error. The representation is suitable for applications which require consistent parameterizations across different surfaces.
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He, Y., Wang, K., Wang, H., Gu, X., Qin, H.: Manifold T-spline. In: GMP ’06, pp. 409–422 (2006)
Zheng, J., Wang, Y., Seah, H.S.: Adaptive T-spline surface fitting to z-map models. In: GRAPHITE ’05, pp. 405–411 (2005)
Li, W.-C., Ray, N., Lévy, B.: Automatic and interactive mesh to T-spline conversion. In: SGP 06: Symposium on Geometry Processing, pp. 191–200, Eurographics Association (2006)
Gu, X., He, Y., Qin, H.: Manifold splines. In: SPM ’05, pp. 27–38 (2005)
Wang, H., He, Y., Li, X., Gu, X., Qin, H.: Polycube splines. In: SPM ’07, pp. 241–251 (2007)
Grimm, C., Hughes, J.: Modeling surfaces of arbitrary topology using manifolds. Comput. Graph. 29 (1995)
Grimm, C.: Spherical manifolds for adaptive resolution surface modeling. In: Graphite, November 2005
Ferguson, H., Rockwood, A.: Multiperiodic functions for surface design. Comput. Aided Geom. Des. 10, 315–328 (1993)
Rockwood, A., Park, H.: Interactive design of smooth genus n objects using multiperiodic functions and applications. Int. J. Shape Model. 5, 135–157 (1999)
Wallner, J., Pottmann, H.: Spline orbifolds. In: Curves and Surfaces with Applications in CAGD, pp. 445–464 (1997)
Gu, X., Yau, S.-T.: Global conformal surface parameterization. In: SGP ’03, pp. 127–137 (2003)
Krishnamurthy, V., Levoy, M.: Fitting smooth surfaces to dense polygon meshes. In: SIGGRAPH ’96, pp. 313–324 (1996)
Shi, X., Wang, T., Wu, P., Liu, F.: Reconstruction of convergent G1 smooth B-spline surfaces. Comput. Aided Geom. Des. 21(9), 893–913 (2004)
Geo: Geomagic commercial software
Lee, A., Moreton, H., Hoppe, H.: Displaced subdivision surfaces. In: SIGGRAPH ’00, pp. 85–94. ACM Press/Addison-Wesley, New York (2000)
Litke, N., Levin, A., Schröder, P.: Fitting subdivision surfaces. In: VIS ’01, pp. 319–324. IEEE Computer Society, Washington (2001)
Jeong, W.-K., Kim, C.-H.: Direct reconstruction of a displaced subdivision surface from unorganized points. Graph. Models 64(2), 78–93 (2002)
Marinov, M., Kobbelt, L.: Optimization methods for scattered data approximation with subdivision surfaces. Graph. Models 67(5), 452–473 (2005)
Halstead, M., Kass, M., DeRose, T.: Efficient, fair interpolation using Catmull–Clark surfaces. In: SIGGRAPH ’93, pp. 35–44 (1993)
Grimm, C., Laidlaw, D., Crisco, J.: Fitting manifold surfaces to 3d point clouds. J. Biomech. Eng. 124, 136–140 (2002)
Ying, L., Zorin, D.: A simple manifold-based construction of surfaces of arbitrary smoothness. ACM Trans. Graph. 23, 271–275 (2004)
Navau, J.C., Garcia, N.P.: Modeling surfaces from meshes of arbitrary topology. Comput. Aided Geom. Des. 17, 643–671 (2000) ISSN: 0167-8396
Grimm, C.: Parameterization using manifolds. Int. J. Shape Model. 10, 51–80 (2004)
Saba, S., Yavneh, I., Gotsman, C., Sheffer, A.: Practical spherical embedding of manifold triangle meshes. In: Shape Modelling International, pp. 256–265, June 2005
Erickson, J., Whittlesey, K.: Greedy optimal homotopy and homology generators. In: SODA, pp. 1038–1046 (2005)
Grimm, C., Hughes, J.: Parameterizing n-holed tori. In: Mathematics of Surfaces X, pp. 14–29, September 17–19, 2003
Sander, P.V., Gortler, S.J., Snyder, J., Hoppe, H.: Signal-specialized parametrization. In: EGRW ’02, pp. 87–98. Eurographics Association, 2002
LLoyd, S.: Least square quantization in pcm. IEEE Trans. Inf. Theory 129–137 (1982)
Marai, G.E., Grimm, C., Laidlaw, D.: Arthrodial joint markerless cross-parameterization and biomechanical visualization. IEEE Trans. Vis. Comput. Graph. (2007)
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Grimm, C., Ju, T., Phan, L. et al. Adaptive smooth surface fitting with manifolds. Vis Comput 25, 589–597 (2009). https://doi.org/10.1007/s00371-009-0334-4
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DOI: https://doi.org/10.1007/s00371-009-0334-4