Reconstruction of a CAD model from the deformed mesh using B-spline surfaces

For several years, researchers have focused on Reverse Engineering techniques, which generate the geometric model of an object from a point set, a mesh, a triangulation, etc. These data are provided by 3D scanners, three-dimensional Coordinate Measuring Machines, finite elements results, deformed meshes, etc. In this field, the reconstruction of the Computer Aided Design (CAD) model from a deformed mesh remains a challenge. This CAD model can be used in order to visualize 3D objects that were scanned and approximate their shapes by mathematical formulations. It can represent the geometric support for many other activities (analysis, manufacturing, assembly, etc.). In this paper, we propose a method to rebuild the CAD geometry model from a deformed mesh. This approach is based on the B-Spline formulation for rebuilding the CAD model entities (faces, edges and vertices) from those extracted from the deformed mesh (triangulations, arcs, nodes). The reconstruction is based on the Levenberg Marquardt algorithm as a method for the interpolation/approximation. An illustration of the developed method is proposed discussed at the end of this paper.