For CNC cutter path generation of nonlinear curves or surfaces, curve fitting using circular arc segments can be more efficient than linear segments. This paper presents a new algorithm for approximating large sets of points using a spline of biarcs, each of which consists of two circular arcs connected in tangent-continuous manner. The approach proposed in this paper differs from the previous work in that it does not require to pre-determine the number of arc segments, and yet all the family of biarcs between two points can be used, not only the ones which minimize the curvature difference or radii ratio. Combining the merits of least-square algorithms and binary search methods, this approach is capable of producing the minimum, or near minimum number of biarcs needed to approximate points within specified accuracy.

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