| OCR Text |
Show 94 parallel to the scan plane normal (0 -Z Y). This latter surface, i.e. only at stationary points of the case only occurs when the scan plane is tangent to the (perspective) Y definition function which is, here, Y/Z. The iteration function, G(u,v), is then defined as G(u,v) S(u,v) sine - T(u,v) case in direct analogy to its previous definition in the orthographic case with Xn replaced by Sand Zn replaced by T. In the process of doing the iteration it is necessary to take u and v derivatives of G and therefore of Sand T. For T: aT au (xu Yu zu)· (xn Yn zn) + (x Y z)· (xnu Ynu znu) Due to the definition of the normal vector the first term of this is identically zero. Hence: aT = X Xn + Y Yn + Z Zn au u u u X Xn + Y Yn + Z Zn v v v The derivatives of the S term are unfortunately more complex. = (Mx Myu Mz ). (xn Yn zn) + (MX My MZ) .(Xn Yn zn) au u u u u u where Mx refers to the X component of the vector M, etc. This as a rather imposing calculation to perform for each iteration step. However, by some algebraic shuffling, much |
