# Download Computational Geometry. Curve and Surface Modeling by Su Bu-Qing, Liu Ding-Yuan, Chang Geng-Zhe PDF

By Su Bu-Qing, Liu Ding-Yuan, Chang Geng-Zhe

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Extra info for Computational Geometry. Curve and Surface Modeling

Example text

2-8): EI- ds2' ds = dN, dN = p* dd, in which p* represents the tension of the rubber band and El is the rigidity of the wooden spline. We call p = \l p*/ El the tension parameter. 1) ds and its solution is a hyperbolic function of the arc length s: k = C0 ch ps + Cx sh ps, where C0 and C, are two constants of integration. 2) 3 35 Spline Function in Tension and Convexity Preserving Property Suppose that a Cartesian coordinate system is chosen. Under the assumption of small deflection, we have the curvature k~y" and the arc length s~jc.

N - 1). Together with the end condition S'(XQ) = y'0 it gives the recursive relations K , i iyt+i-y, y,-yt-i\ C Î+1 = - T — Ci + — — hi+l hi+l\ hi+x ht J ,. Λ ~ 1X (i = l , 2 , . . 9). In the above scheme, only one end condition can be imposed. 9) that the error in y'0, say Δ^ό, will be propagated to the last piece of the spline in equal oscillations, as will the error for the interpolated value yi. Thus the advantage of decayed error propagation for spline functions has been lost. This is certainly not desirable.

3-9 characterized by 0 < A < 3 and 0 < μ < 3 .