Branch, J.W., Prieto, F., Boulanger, P. (2007) Automated Reverse Engineering
of Free Formed Objects Using MORSE Theory, * In IEEE 3D Imaging and
Modeling Conference, Montreal, Canada *, pp. 21-28.

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 geodesics are then approximated by a B-spline curves creating a quadrilateral network on which a NURBS surface is approximated. The NURBS surfaces are then optimized using evolutive strategies to guaranty the best t as well as C1 continuity between the patches.

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