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Show 87 The normal to the cross section curve can be taken as just the X and Z components of the normal to the surface Xn Yu Zv - Zu Yv Zn Xu Yv - Yu Xv Thus the silhouette edge trackers are a special case of this definition of iteration points, those pointing directly to the left and right, 0° and 1800 • For the bivariat@ iteration, each point must be defined by a function, G(u,v), which is zero at that point. The angular direction of the normal at each point can be taken as a. = a.(u,v) atan() Then for a desired normal direction, we could define G(u,v) as -. The explicit use of , however, forces us to compute arctangents. A cheaper function to evaluate is G(u,v) sin(e-a.) cosa. sine - sina. cose Xn sine - Zn cose /xn2+zn2 I so for a maximum angular deviation of 1&-1<1/2 have IG(u,v) l<sin(1/2)=.0087 we must In practice, a table is kept of values of cos(ie), sin(i&) for values of i=O,l, •.. ,(2Tf/ 6l7)-1 where so: is the desired angle flagged wi th increment. Each iteration point is then the index into this table which indicates the |
