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ComputerAided_Design_Engineering_amp_Manufactur.pdf

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FIGURE 2.12(a) Linear Approximation for Bezier curve A. Tolerance : 0.6, convergence criteria : 0.06, number of<br />

straight lines: 10, processor time: 0.06.<br />

FIGURE 2.12(b) Linear Approximation of Bezier curve B. Tolerance : 0.9, convergence criteria : 0.09, number of<br />

straight lines: 10, processor time: 0.06.<br />

Algorithm for Circular Approximation<br />

Only two points are required to define a linear segment. Three points, however, are required to define a<br />

circular arc. Hence the algorithm for circular approximation is correspondingly more complex than that<br />

for the linear approximation, although the same basic idea is employed. Figure 2.13 illustrates the<br />

procedure for circular approximation.<br />

Initialization: The Bezier curve is first approximated by a single circular arc which passes through three<br />

points, defined by t0 � 0.0, t1 � 0.5 and t2� 1.0, as shown in Figure 2.13(a). Two control brackets (t1l, t1h) and (t2l, t2h) are used. t1l and t2l are initially set to 0, while t1h and t2h are set to 1. d0 is the maximum deviation<br />

© 2001 by CRC Press LLC

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