Automated Reverse Engineering of Free Form Objects Using Morse Theory

In this paper, a method for surface reconstruction by means of optimized NURBS (non-uniform rational b-splines) patches from complex quadrilateral bases on triangulated surfaces of arbitrary topology is proposed. To decompose the triangulated surface into quadrilateral patches, Morse theory and spectral mesh analysis are used. The quadrilateral regions obtained from this analysis is then regularized by computing the geodesic curves between each corner of the quadrilateral regions. These geodesies are then fitted by a B-splines curves creating a quadrilateral network on which a NURBS surface is fitted. The NURBS surfaces are then optimized using evolutive strategies to guaranty the best fit as well as C¹ continuity between the patches.