Skip to Main content Skip to Navigation
Journal articles

A new subdivision based approach for piecewise smooth approximation of 3D polygonal curves

Abstract : This paper presents an algorithm dealing with the data reduction and the approximation of 3D polygonal curves. Our method is able to approximate efficiently a set of straight 3D segments or points with a piecewise smooth subdivision curve, in a near optimal way in terms of control point number. Our algorithm is a generalization for subdivision rules, including sharp vertex processing, of the Active B-Spline Curve developed by Pottmann et al. We have also developed a theoretically demonstrated approach, analysing curvature properties of B-Splines, which computes a near optimal evaluation of the initial number and positions of control points. Moreover, our original Active Footpoint Parameterization method prevents wrong matching problems occurring particularly for self-intersecting curves. Thus, the stability of the algorithm is highly increased. Our method was tested on different sets of curves and gives satisfying results regarding to approximation error, convergence speed and compression rate. This method is in line with a larger 3D CAD object compression scheme by piecewise subdivision surface approximation. The objective is to fit a subdivision surface on a target patch by first fitting its boundary with a subdivision curve whose control polygon will represent the boundary of the surface control polyhedron.
Document type :
Journal articles
Complete list of metadata
Contributor : Équipe Gestionnaire Des Publications Si Liris Connect in order to contact the contributor
Submitted on : Monday, May 29, 2017 - 10:56:17 AM
Last modification on : Tuesday, June 1, 2021 - 2:08:05 PM


  • HAL Id : hal-01528473, version 1


Guillaume Lavoué, Florent Dupont, Atilla Baskurt. A new subdivision based approach for piecewise smooth approximation of 3D polygonal curves. Pattern Recognition, Elsevier, 2005, 8, 38, pp.1139-1151. ⟨hal-01528473⟩



Les métriques sont temporairement indisponibles