Aigner, Martin; Jüttler, Bert Hybrid curve fitting. (English) Zbl 1124.65015 Computing 79, No. 2-4, 237-247 (2007). Fitting parameterized curves to a given set of unorganized points – a point cloud – belongs to the challenging problems in the present computer aided geometric modelling area. The authors introduce an abstract framework for fitting a member of a given family of planar curves to a given point cloud which obtains unorganized point data. The presented curve fitting is realized by a true evolution process which generalizes the technique of normal or tangent distance minimization. The suggested procedure of curve fitting can be used to implicitly defined curves, parametric curves and hybrid objects. Hybrid objects are combinations of simple shapes (such as circular arcs) and free-form curves (such as B-spline curves). Reviewer: Ivana Linkeová (Praha) Cited in 1 Document MSC: 65D17 Computer-aided design (modeling of curves and surfaces) 65D10 Numerical smoothing, curve fitting Keywords:curve fitting; hybrid curve; point cloud; approximation; computer aided geometric modelling; normal or tangent distance minimization × Cite Format Result Cite Review PDF Full Text: DOI References: [1] Aigner, M., Jüttler, B.: Robust computation of foot points on implicitly defined curves. In: Mathematical Methods for Curves and Surfaces: Tromsø 2004 (M. Dæhlen et al., eds.). Nashboro Press 2005, pp. 1–10. · Zbl 1080.65523 [3] Blake, A., Isard, M.: Active contours. Springer 2000. [5] Hoff K. E. et al.: Fast computation of generalized Voronoi diagrams using graphics hardware. SIGGRAPH ’99 Proc. pp. 277–286. [6] Hoschek, J., Lasser, D.: Fundamentals of computer aided geometric design. A.K. Peters/Wellesley, Mass. 1996. · Zbl 0788.68002 [10] Osher, S., Fedkiw, R. P.: Level set methods and dynamic implicit surfaces. Springer 2003. · Zbl 1026.76001 [14] Pottmann, H., Leopoldseder, S., Hofer, M.: Approximation with active B-spline curves and surfaces. Proc. Pacific Graphics 2002, IEEE Press, pp. 8–25. [18] Kass, M., Witkin, A., Terzopoulos, D.: Snakes: active contour models. Int. J. Comp. Vision 1.4, 321–331 (1987). [19] Wang, W., Pottmann, H., Liu, Y.: Fitting B-spline curves to point clouds by squared distance minimization. ACM Trans. on Graphics 25.2 (2006). [20] Yang, H. et al.: Evolution of T-spline level sets with distance field constraints for geometry reconstruction and image segmentation (submitted). FSP report no. 1 (2005), available at www.ig.jku.at. This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.