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- W2271098465 abstract "In this talk we explain method of rational approximation of parallel curve using LN(linear normal) approximation of circular arc. RATIONAL APPROXIMATION OF PARALLEL CURVE BASED ON LN APPROXIMATION OF CIRCLE Parallel curves (or offset curves) and surfaces are widely used in CAD/CAM. The parallel curves of spline (piecewise parametric polynomial) curves are not rational in general, thus most CAD systems must require approximation techniques for constructing and representing parallel curves [4,6]. In the last 30 years, work on spline approximations for parallel curve, has focused on curve and surface fitting for smaller approximation error [9,15,13]. Also there are another two methods using the families of curves that have exact rational parallel curve. One is the family of Pythagorean Hodograph (PH) curves, and the other is the family of linear normal (LN) curves. PH curves were first presented by Farouki [7], and then, many approximation methods and properties of the PH curves have been found [5,8,17]. The curves have been extended to Pythagorean normal (PN) vector surfaces [10,12,14]. LN curves have the property that their convolution with polynomial or rational curve is rational. Quadratic Bezier curves are LN curves so that the convolution of given curve and quadratic approximation of circular arc is an approximation of the parallel curve[11]. The approximation schemes based on LN curves have been extended to LN surfaces, to approximate parallel surfaces [3,4,16]. Ahn et al.[2] presented a G end-point interpolation and is based on an approximation of circular arcs using quadratic Bezier biarcs. They also prove that the Hausdorff distance between two compatible curves is invariant under convolution. Using this elegant fact, the exact Hausdorff distance between the parallel curve and its rational approximation could be obtained. The invariance of Hausdorff distance under convolution can be applied the rational approximation of parallel curve using LN curve approximation of any degree of circular arc[1]. The main contribution of the approximation method is the exact Hausdorff distance between parallel curve and rational approximation, which is equal to the Hausdorff distance between circular arc and LN approximation of any degree." @default.
- W2271098465 created "2016-06-24" @default.
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- W2271098465 date "2013-05-01" @default.
- W2271098465 modified "2023-09-26" @default.
- W2271098465 title "Circular arc, parallel curve, convolution curve and Hausdorff distance" @default.
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