Research On Curve And Surface Reconstruction From Unorganized Points

Curve and surface reconstruction is one of very important problems in reverseengineering. The motivation of this work comes from researchs attempting toreconstruct surfaces of revolution, spiral surfaces, profile surfaces from a set of points.Such problems can be changed into curve reconstruction. In this paper, a study isfocused on the reconstruction of a type of smooth and simple curves withoutself-intersection. Two algorithms, which we call "curve reconstruction algorithmbased on filtering and smoothing"and "incremental algorithm based on controlpoint's perturbation"respectively, are proposed here for curve reconstruction fromunorganized points. Algorithm based on filtering and smoothing constructs a curve byfirstly ordering the point set, while the incremental algorithm imposes slightperturbation on control points by inputting data points one by one to stabilize thecontrol net and thus constructing a spline curve to fitting the whole point set. Somenumerical examples are given here to show its validity and effectivity inreconstructing curves with different shapes. At the end of this paper, a briefintroduction to current methods of surface reconstruction from unorganized points ismade.