PB-Spline Hybrid Surface Fitting Technique

Abstract

This work considers the fitting of data points organized in a rectangular array to parametric spline surfaces. Point Based (PB) splines, a generalization of tensor product splines, are adopted. The basic idea of this paper is to fit large scale data with a tensorial B-spline surface and to refine the surface until a specified tolerance is met. Since some isolated domains exceeding tolerance may result, detail features on these domains are modeled by a tensorial B-spline basis with a finer resolution, superimposed by employing the PB-spline approach. The present method leads to an efficient model of free form surfaces, since both large scale data and local geometrical details can be efficiently fitted. Two application examples are presented. The first one concerns the fitting of a set of data points sampled from an interior car trim with a central geometrical detail. The second one refers to the modification of the tensorial B-spline surface representation of a mould in order to create a local adjustment. Considerations regarding strengths and limits of the approach then follow.

Advances in Vibration Analysis Research

“…B-spline Shell Finite Element Updating by Means of Vibration Measurements 141where the versors ij 3 v and the thickness values ij t can be calculated from the interpolation process proposed in (Carminelli & Catania, 2009). The displacement field can be defined by following the isoparametric approach and enforcing the fiber inextensibility in the thickness direction (Cook et al, 1989):…”

B-spline Shell Finite Element Updating by Means of Vibration Measurements

“…The position vector of the solid shell can be expressed as: (Carminelli & Catania, 2009). The displacement field can be defined by following the isoparametric approach and enforcing the fiber inextensibility in the thickness direction (Cook et al, 1989) (Carminelli & Catania, 2007), u ij , v ij and w ij are translational dofs, α ij and β ij are rotational dofs.…”