Abstract
Skinning or lofting remains a challenging problem in computer graphics and free-form surface design. Although it was addressed by many researchers, no sufficiently general solution has been proposed yet. In the interpolating approach, the incompatibility of the input NURBS curves are solved by knot insertion. This process leads to an explosion in the number of control points defining the skinned surface. Other methods avoid this problem by generating skinned surfaces that approximate rather than interpolate the input curves. In this paper, we provide a solution to this problem using T-splines. Compared with existing approaches, a T-spline skinned surface interpolates a set of incompatible curves with a control mesh of fewer vertices. Typically, the linear system involved could be solved globally. However, our approach provides a local solution for each skinned curve. As such, local modification could be used to meet additional constraints such as given normal and/or predefined curvature across the skinned curves.
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Notes
We use bold style to distinguish a quintuple knot from a regular knot.
We will assume that the first two columns and rows are not to be considered as skinned curves.
The geometric positions of these vertices will be discussed later.
References
Bajaj, C., Lin, K., Coyle, E.: Arbitrary topology shape reconstruction from planar cross sections. Graph. Models Image Process. 58(6), 524–543 (1996)
Ball, A.: Consurf, part 1: introduction of the conic lofting tile. Comput. Aided Des. 6(4), 243–249 (1974)
Ball, A.: Consurf, part 2: description of the algorithms. Comput. Aided Des. 7, 237–242 (1975)
Boissonnat, J.: Shape reconstruction from planar cross-sections. Comput. Vis. Graph. Image Process. 44(1), 1–29 (1988)
Farin, G., Hansford, D.: The Essentials of CAGD. AK Peters, Wellesley (2000)
Faux, I., Pratt, M.: Computational Geometry for Design and Manufacture. Wiley, New York (1979)
Nasri, A., Abbas, A., Hasbini, I.: Skinning Catmull-Clark subdivision surfaces with incompatible cross-sectional curves. In: Pacific Graphics, pp. 102–111. IEEE Press, Canmore (2003). ISBN 0-7695-2028-6
Park, H.: Lofted B-spline surface interpolation by linearly constrained energy minimization. Comput. Aided Des. 35(14), 1261–1268 (2003)
Piegl, L., Tiller, W.: Surface skinning revisited. Vis. Comput. 18(4), 273–283 (2002)
Sederberg, T., Cardon, D., Finnigan, D., North, N., Zheng, J., Lyche, T.: T-spline simplification and local refinement. ACM Trans. Graph. 23(3), 276–283 (2004) SIGGRAPH 2004
Sederberg, T., Zheng, J., Bakenov, A., Nasri, A.: T-spline and T-NURCCS. ACM Trans. Graph. 22(3), 477–484 (2003) SIGGRAPH 2003
Wang, W.K., Zhang, H., Park, H., Yong, J.H., Paul, J.C.: Reducing control points in lofted B-spline surface interpolation using common knot vector determination. Comput. Aided Des. 40(10–11), 999–1008 (2008)
Woodward, C.D.: Skinning techniques for interactive B-spline surface interpolation. Comput. Aided Des. 20(8), 441–451 (1988)
Acknowledgements
Ahmad Nasri was supported by a URB grant #1799-6071507 from the American University of Beirut, and partially a grant from the Lebanese National Council for Scientific Research LCR111135-522291. Jianmin Zheng was supported by the ARC 9/09 Grant MOE2008-T2-1-075 of Singapore. The scope of this work was initially discussed during a research visit by Ahmad Nasri to Brigham Young University, Utah, USA. The authors are grateful to Thomas Sederberg for his valuable comments. Thanks are also due to Ali Charara and Wajih Bou Karam for their attempts to extend this work.
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Nasri, A., Sinno, K. & Zheng, J. Local T-spline surface skinning. Vis Comput 28, 787–797 (2012). https://doi.org/10.1007/s00371-012-0692-1
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DOI: https://doi.org/10.1007/s00371-012-0692-1