Abstract
This paper presents a new curve fitting framework for styling design data. Given a data set that represents a filleted-like curve, underlying curves (U-curves) and styling radius corners (SR-corners) are generated by fitting to low curvature parts and highly curved ones, respectively. A set of U-curves are firstly reconstructed as a unique \(C^0\) composite B-spline curve, and then an SR-corner is reconstructed for each \(C^0\) corner. This approach guarantees that U-curves can be smoothly connected through convex SR-corners while enabling full editing of the smooth corners up to sharp ones. Compared with existing schemes that naively fit a curve to each part, the proposed framework provides a guiding principle for the generation of curves, which is more suitable for styling design. Experimental results demonstrate that high-quality curves can be generated even from real-world scanned data.





















Similar content being viewed by others
Explore related subjects
Discover the latest articles, news and stories from top researchers in related subjects.References
Attneave, F.: Some informational aspects of visual perception. Psychol. Rev. 61(3), 183–193 (1954)
Baran, I., Lehtinen, J., Popović, J.: Sketching clothoid splines using shortest paths. Comput. Graphics Forum 29(2), 655–664 (2010)
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)
Cao, J., Wang, G.: A note on class A Bézier curves. Comput. Aided Geom. Des. 25(7), 523–528 (2008)
Douglas, D., Peucker, T.: Algorithms for the reduction of the number of points required to represent a digitized line or its caricature. Can. Cartogr. 10(2), 112–122 (1973)
Duda, R.O., Hart, P.E.: Pattern Classification and Scene Analysis. Wiley, New York (1973)
Farin, G.: Class A Bézier curves. Comput. Aided Geom. Des. 23(7), 573–581 (2006)
Guiqing, L., Xianmin, L., Hua, L.: 3D discrete clothoid splines. In: Proceedings of the International Conference on Computer Graphics, pp. 321–324 (2001)
Hosaka, M.: Modeling of Curves and Surfaces in CAD/CAM. Springer, Berlin (1992)
Hoschek, J., Lasser, D.: Fundamentals of Computer Aided Geometric Design. A K Peters Ltd, Natick (1993)
Lai, Y.K., Jin Liu, Y., Zang, Y., Hu, S.M.: Fairing wireframes in industrial surface design. In: IEEE International Conference on Shape Modeling and Applications, pp. 29–35 (2008)
Li, W., Xu, S., Zhao, G., Goh, L.P.: Adaptive knot placement in \(b\)-spline curve approximation. Comput. Aided Des. 37(8), 791–797 (2005)
Lloyd, S.P.: Least squares quantization in pcm. IEEE Trans. Inf. Theory 28(2), 129–137 (1982)
McCrae, J., Singh, K.: Sketching piecewise clothoid curves. Comput. Graphics 33(4), 452–461 (2009)
Moreton, H.P., Séquin, C.H.: Functional optimization for fair surface design. Comput. Graphics 26(2), 167–176 (1992)
NLopt (Nonlinear optimization library): http://ab-initio.mit.edu/wiki/index.php/NLopt. Accessed 15 June 2016
Okaniwa, S., Nasri, A., Lin, H., Abbas, A., Kineri, Y., Maekawa, T.: Uniform \(b\)-spline curve interpolation with prescribed tangent and curvature vectors. IEEE Trans. Vis. Comput. Graphics 18(9), 1474–1487 (2012)
Piegl, L., Tiller, W.: The NURBS Book, 2nd edn. Springer, New York (1997)
Ramer, U.: An iterative procedure for the polygonal approximation of plane curves. Comput. Graphics Image Process. 1(3), 244–256 (1972)
Schnieder, R., Kobbelt, L.: Discrete fairing of curves and surfaces based on linear curvature distribution. In: Curve and Surface Design, Saint-Malo, pp. 371–380 (1999)
Tsuchie, S., Hosino, T., Higashi, M.: High-quality vertex clustering for surface mesh segmentation using student-\(t\) mixture model. Comput. Aided Des. 46, 69–78 (2014)
Tsuchie, S., Okamoto, K.: High-quality quadratic curve fitting for scanned data of styling design. Comput. Aided Des. 71, 39–50 (2016)
Wallner, J., Pottmann, H., Hofer, M.: Fair webs. Vis. Comput. 23(1), 83–94 (2007)
Yang, H., Wang, W., Sun, J.: Control point adjustment for \(b\)-spline curve approximation. Comput. Aided Des. 36, 639–652 (2004)
Yoshida, N., Saito, T.: Interactive aesthetic curve segments. Vis. Comput. 22(9–11), 896–905 (2006)
Zang, Y., Liu, Y.J., Lai, Y.K.: Note on industrial applications of Hu’s surface extension algorithm. In: Advances in Geometric Modeling and Processing (GMP 2008), LNCS, vol. 4975, pp. 304–314 (2008)
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)
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Tsuchie, S. Reconstruction of underlying curves with styling radius corners. Vis Comput 33, 1197–1210 (2017). https://doi.org/10.1007/s00371-016-1282-4
Published:
Issue Date:
DOI: https://doi.org/10.1007/s00371-016-1282-4