Fitting of conic sections is used in reflectometry, aircraft industry, metrology, computer vision, astronomy and propagation of sound waves . So far numerical algorithms assume the type of the conic section to be known in advance. We consider the problem of additionally identifying the type during fitting, i.e. deciding whether the given data are better fitted by an ellipse, a hyperbola or a parabola. To solve this problem we apply a well-known descent algorithm [3,4,6] to NURBS of degree two. Numerical examples will be given
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