Reconstructing Surfaces and Surfaces on Surfaces from Scattered 3D Data

We present an efficient and uniform approach for the automatic reconstruction of surfaces of CAD (computer aided design) models and scalar fields defined on them, from an unorganized collection of scanned point data. Example applications in the manufacturing domain are the rapid computer model reconstruction of any existing physical part from some three dimensional (3D) points scan of the part’s surface. Color, texture or some scalar material property of the physical part, defines natural scalar fields over the surface of the CAD model. Manufacturers who wish to use existing computer aided design and manufacturing software (CAD/CAM) need to have computer models of these parts. Using these algorithms, existing parts and prototypes can be automatically reconstructed into computer models from 3D scans. Our reconstruction algorithm does not impose any convexity or differentiability restrictions on the surface of the original physical part or the scalar field function, except that it assumes that there is a sufficient sampling of the input point data to unambiguously reconstruct the CAD model. Compared to earlier methods our algorithm has the advantages of simplicity, efficiency and uniformity (both CAD model and scalar field reconstruction). The simplicity and efficiency of our approach is based on several novel uses of appropriate sub-structures (alpha shapes) of a three-dimensional Delaunay Triangulation, and its dual the three-dimensional Voronoi diagram. The boundary of the CAD model and the scalar field are reconstructed using cubic Bernstein-Bézier patches.