Abstract
This study presents a new method for reconstructing an adaptive underlying surface, \(\tilde{\varvec{S}}\), from scanned data for styling design objects. \(\tilde{\varvec{S}}\) is usually generated by sweeping a curve that varies its shape gradually while being swept. However, when \(\tilde{\varvec{S}}\) is reconstructed from a segmented part of the scanned data, it is generally more difficult to control the gradual variation as the ratio of the segmented part to the area of \(\tilde{\varvec{S}}\) becomes smaller. Therefore, this study represents \(\tilde{\varvec{S}}\) by the sum of two surfaces, \(\tilde{\varvec{S}}={\varvec{S}}^{\mathrm{U}}+{\varvec{S}}^\Delta \). Here, an underlying surface \({\varvec{S}}^{\mathrm{U}}\) is generated by the standard sweep method and the difference surface \({\varvec{S}}^\Delta \) not only compensates for the error between \(\tilde{\varvec{S}}\) and the scanned data but also exhibits monotonous change in the curvatures. Consequently, the gradual change in a curve being swept is represented by \({\varvec{S}}^\Delta \), which does not encounter the aforementioned problem because it is intended to control the deviation from the “reference” \({\varvec{S}}^{\mathrm{U}}\) under the constraint of “curvature monotonicity.” The experimental results demonstrate the validity of surface reconstruction from real-world scanned data as well as an application of the proposed method.
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Brent, R.P.: Algorithms for Minimization Without Derivatives. Prentice-Hall, Englewood Cliffs, New Jersey (1973)
Burchard, H., Ayers, J., Frey, W., Sapidis, N.: Approximation with aesthetic constraints. In: Sapidis, N.S. (ed.) Designing Fair Curves and Surfaces, pp. 3–28. SIAM, Philadelphia (1994)
Farin, G.: Class A Bézier curves. Computer Aided Geometric Design 23(7), 573–581 (2006). https://doi.org/10.1016/j.cagd.2006.03.004
Hildebrandt, K., Polthier, K., Wardetzky, M.: Smooth feature lines on surface meshes. In: Eurographics Symposium on Geometry Processing pp. 85–90 (2005)
Hosaka, M.: Modeling of Curves and Surfaces in CAD/CAM. Springer-Verlag, Berlin Heidelberg (1992)
Hoschek, J., Lasser, D.: Fundamentals of computer aided geometric design. A K Peters, Ltd (1993)
Inoue, J., Harada, T., Hagihara, T.: An algorithm for generating log-aesthetic curved surfaces and the development of a curved surfaces generation system using VR. In: International Association of Societies of Design Research, Seoul, Korea pp. 2513–2522 (2009)
Joshi, P., Séquin, C.: Energy minimizers for curvature-based surface functionals. Comput. Aided Des. Appl. 4(5), 607–617 (2007). https://doi.org/10.1080/16864360.2007.10738495
Mehlum, E., Tarrou, C.: Invariant smoothness measures for surfaces. Adv. Comput. Math. 8(1), 49–63 (1998). https://doi.org/10.1023/A:1018931910836
Meier, H., Nowacki, H.: Interpolating curves with gradual changes in curvature. Comput. Aided Geom. Des. 4, 297–305 (1987). https://doi.org/10.1016/0167-8396(87)90004-5
Moreton, H.P., Séquin, C.H.: Functional optimization for fair surface design. Comput. Gr. 26(2), 167–176 (1992). https://doi.org/10.1145/142920.134035
Nelder, J.A., Mead, R.: A simplex method for function minimization. Comput. J. 7(4), 308–313 (1965)
NLopt (Nonlinear optimization library, 2.4.2): (2014). http://ab-initio.mit.edu/wiki/index.php/NLopt
Piegl, L., Tiller, W.: The NURBS Book, 2nd edn. Springer, Berlin (1997)
Tsuchie, S.: Reconstruction of underlying curves with styling radius corners. Vis. Comput. 9(33), 1197–1210 (2017). https://doi.org/10.1007/s00371-016-1282-4
Tsuchie, S.: Reconstruction of underlying surfaces from scanned data using line of curvature. Comput. Gr. 68, 108–118 (2017). https://doi.org/10.1016/j.cag.2017.08.015
Tsuchie, S.: Reconstruction of intersecting surface models from scanned data for styling design. Eng. Comput. (2019). https://doi.org/10.1007/s00366-019-00817-x
Tsuchie, S., Okamoto, K.: High-quality quadratic curve fitting for scanned data of styling design. Comput. Aided Des. 71, 39–50 (2016). https://doi.org/10.1016/j.cad.2015.09.004
Várady, T.: Automatic procedures to create cad models from measured data. Comput. Aided Des. Appl. 5(5), 577–588 (2008). https://doi.org/10.3722/cadaps.2008.577-588
Weiss, V., Andor, L., Renner, G., Várady, T.: Advanced surface fitting techniques. Comput. Aided Geom. Des. 19(1), 19–42 (2002)
Westgaard, G., Nowacki, H.: Construction of fair surfaces over irregular meshes. In: Proceedings of the 6th ACM Symposium on Solid Modeling and Applications, pp. 88–98. (2001). https://doi.org/10.1145/376957.376969
Yamada, Y.: Clay Modeling: Techniques for Giving Three-Dimensional Form to Idea. Sanéishobo Publishing, Shinjuku-ku (1993)
Ziatdinov, R.: Family of superspirals with completely monotonic curvature given in terms of gauss hypergeometric function. Comput. Aided Geom. Des. 29(7), 510–518 (2012). https://doi.org/10.1016/j.cagd.2012.03.006
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Tsuchie, S. Reconstruction of adaptive swept surfaces from scanned data for styling design. Vis Comput 38, 493–507 (2022). https://doi.org/10.1007/s00371-020-02030-0
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DOI: https://doi.org/10.1007/s00371-020-02030-0