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Show 66 e(f,g) h Figure 4.12. Computing curve-curve relations it is not. To find the farthest point of the curve from the surface can be rnore difficult in the cases of ellipse and circle vs. surfaces as shown in Figure 4.13. Example: In Figure 4.13: -1 -1 - vl and v2 are the unit vectors. -1 -1 - V1 is normal vector of the plane Plt that the ellipse is lying on. V1 = v;_ X V2. v;_ and 1f; are as shown in Figure 4.5. -I V2 is normal vector of the plane Pl2 • P1 is the center of the ellipse. P2 is the Base-Point of plane Pl2. Therefore a point M on ellipse , can be represented as M: i\ + M M = R 1 X cosO X v;_ + R 2 x cosO X 11; and: Dp is the distance of P1 to plane Pl2 Dm is the distance of M to plane Pl~. * distance of point on ellipse to plane Pl2 is: __, __, I __, __, I L • V2 ± M • V2 = Dp ± Dm. -+ _., _. -+/ ......; -+/ Dm = M. v2 = Rt X cosO X Vt • v2 + R2 X cosO X v2 • v2 __, __,I __, __,I . I 2 2 let tl = VI • v2 and t2 = v2 • v2 Dm s; v R1 2tl + R22t2 therefore: if J Riti + R~t~ + Dp s; £t + £2 then the ellipse is incident on plane Pl2. |
