Non-Uniform Rational B-Splines (NURBS) can represent curves and surfaces of any degree. Usually in the same curve, however, the degree is unique. The goal of this work is to identify single and exact corner point of lines represented by cubic or other NURBS. The combination of arcs and lines can then be represented by one NURBS with error not to exceed (10−12). The developed procedure can represent any NURBS curve and surface of any degree with full control on all parameters, control points, weights, knot vectors, and number of segments representing the curve or surface, in addition to, the basis functions examination. The optimization identifies the parameters and geometry to insure any required level of accuracy to represent singular corner solid models to allow a single cubic or other NURBS representing the whole solid. It is concluded that the singular corner point can be identified with cubic NURBS. Applications to several 3D solid CAD models are used to verify such a technique.

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