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We introduce a novel approach to reconstructing 3D objects from cross sections of point clouds acquired by 3D scanning. In this context cross sections are almost planarclusters of 3D points. We first thin each cluster to obtain an ordered one dimensional set of planar points. We then partition the point set to subsets that can be approximated adequately by piecewise quadratic rational Bezier curves using an optimal fitting method. For each curve we select a number of representative points that lie on the fitting curves which are then used for reconstructing the object surface. Inter-cross section and intra-cross section constraints are imposed to support parameterization and editing of the derived model. Shape and topological differences between adjacent object contours pose several issues for the 3D reconstruction process. By using the contour skeleton information we produce intermediate cross sections representing places where ramifications occur to achieve robust covering (meshing) of adjacent slices. Finally, we present a proof of concept implementation of our method and several examples that demonstrate its effectiveness and efficiency.