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An approximation approach of the clothoid curve defined in the interval [0, π/2] and its offset by free-form curves |
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| Authors: | L Z K T E T and T J |
| Affiliation: | a Realistic Modeling Laboratory, Department of Mechanical Engineering, Shizuoka University, 3-5-1, Johoku, Hamamatsu, Shizuoka 432-8561, Japan b Sanei Co. Ltd, Hiroshima, 3-26 Kami-Nobori-machi, Hiroshima 730-0014, Japan c Raindrop Geomagic Inc., Research Triangle Park, NC 27709, USA |
| Abstract: | We propose an algorithm to approximate the clothoid curve defined in the interval 0, π/2] and its offset curves with Bézier curves and the approximation errors converge to zero as the degree of the Bézier curves is increased. Secondly, we discuss how to approximate the clothoid curve by B-spline curves of low degrees. By employing our method, the clothoid curve and its offset can be efficiently incorporated into CAD/CAM systems, which are important for the development of 3D civil engineering CAD systems, especially for 3D highway road design systems. The proposed method has been implemented on AutoCAD R14. |
| Keywords: | Clothoid curve Bézier curve NURBS curve |
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