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Citation:

Gershon Elber, In-Kwon Lee, and Myung-Soo Kim, "Comparing Offset Curve Approximation Methods", IEEE Computer Graphics and Applications (SCI), Vol. 17, No. 3, pp. 62-71, (May/June 1997), May 1997

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Abstract:

We have compared several contemporary offset approximation techniques for freeform curves in the plane. In general, the least squares methods perform very well. However, for the case of offsetting quadratic curves, the simple method of Tiller and Hanson is the method of choice. Therefore, the least squares methods need further improvement to produce near-optimal solutions in all cases. Some of the current methods have geometric representations of the offset approximation error (in certain Lβ norms), whereas none of the current least squares methods have such geometric interpretation of their respective error bounds. We also pointed out two limitations of the current least squares methods: (i) the L2 norm employed in these methods and (ii) the dependency on the finite sample points used in the optimization. The B-spline interpolation method also needs further investigation to eliminate the curve undulation resulting from the curve speed mismatch between the base curve and the offset curve.