This paper provides a new approach to approximate the offset of free-form curves and surfaces with continued fractions. The properties of continued fractions are introduced. The convergence of the approximation is proved and the relationship between accuracy and approximate step is established. It shows that the approximation converges fast and reliably, the error of approximation is easily estimated and controlled, and a unified algorithm can be used to generate the rational offset of non-rational and rational planar curves, spatial curves, and surfaces in CAD/CAM industry.

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