Abstract
In CNC machinery, the industrial products and machinery parts are often represented by circular arcs. A new method for representing circular arc based on parametric complex functions is presented in the paper. Since cross ratio is an invariant of the group of all Mobius transformations, and a Mobius transformation maps a circle into another circle, we represent a segment of circular arc with a parametric complex rational function. The representation has no weight factors or control parameters, and it is geometric and affine invariant. Compared with the classical method for representing circular arc, such as NURBS or C-curves, the presented method is much simpler.
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