Comparing offset curve approximation methods

• Published in: IEEE computer graphics and applications 1997-05, Vol.17 (3), p.62-71
• Main Authors: Elber, G., In-Kwon Lee, Myung-Soo Kim
• Format: Magazinearticle
• Language: English
• Subjects: Approximation error; Approximation methods; Equations; Polynomials; Spline; Surface reconstruction; Surface topography
• ISSN: 0272-1716; 1558-1756
• DOI: 10.1109/38.586019

Offset curves have diverse engineering applications, spurring extensive research on various offset techniques. In a paper on offset curve approximation (Lee et al., 1996), we suggested a new approach based on approximating the offset circle instead of the offset curve itself. To demonstrate the effectiveness of this approach, we compared it extensively with previous methods. To our surprise, Tiller and Hanson's (1984) simple method outperforms other methods for offsetting (piecewise) quadratic curves, even though its performance is not as good for high degree curves. The experimental results revealed other interesting facts, too. Had these details been reported several years ago, we believe offset approximation research might have developed somewhat differently. This article is intended to fill an important gap in the literature. We conducted qualitative as well as quantitative comparisons employing various contemporary offset approximation methods for freeform curves in the plane. We measured the efficiency of the offset approximation in terms of the number of control points generated while making the approximations within a prescribed tolerance.