Full text: Commissions III (Part 5)

7 
2 — In each control the points situated in one side are separated from those situated 
in the other side of the axis of the strip. 
The average of the corrections of X and Y is taken for each one of those 
groups of points. 
For each control two sets of values are obtained: 
Cx+ Cy+ Xp+ Yp+ 
Cx~ Cy~ Xp~ Yp~ 
defining corrections Cx+, Cy+ and Cx~, Cy~ in fictitious points, situated 
respectively in Xp+, Yp+ and Xp-, Yp~. 
By means of linear interpolation, the correction and the value of Xp over the 
line Yp = 0 is calculated. 
We shall have in each control i 
Cxi Cyi Xpi 
The parameters a 1, a2 and a3 are obtained by resolution of the systems: 
| Cxl = a‘2 Xp 2 1 + al Xpl 
[ Cx2 = a2 Xp 2 2 + al Xp2 
in the case of one intermediary control, or 
Cxi — a3 X 3 p 1 +a2 X 2 pl + al Xpl 
Cx2 = a3 X 3 p2 + a2 X 2 p2 + al Xp2 
Cx3 = a3 X 3 p3 + a2 X 2 p3 + al Xp3 
in the case of two intermediary controls. 
The parameters dl, d2 and d3 are then obtained by resolution of the systems: 
Cxl + -Cxl-~a2 [(Xpl+) 2 - {Xpl~) 2 ]-al Xpi+-Xpl~)-Al= (d2 Xp\ + 
+ dl Xpi) (Ypi + -Ypl ~) 
Cx2+ - Cx2~ -a2 [ {Xp2+) 2 - {Xp2~) 2 ] - al (Xp2+-Xp2~) = A2 = (d2 Xp 2 2 + 
+ dl Xp2) (Yp2+ - Yp2~) 
in the case of one intermediary control, or 
Cxl + -Cxl~-a3 [{Xpl+y- {Xpi-) 3 ] - a2 [(Xpl + ) 2 -{Xpi~) 2 ]- 
-al(Xpl+-Xpl~)=Xl=(d3 Xp 3 1 + d2 Xp 2 1 + dl Xpl) (Ypl + ~Ypl-) 
Cx2+-Cx2~-a3 [(Xp2 + ) 3 -(Xp2~) 3 ] -a2 r L (Xp2+) 2 -(Xp2~) 2 ]- 
-al (Xp2+ -Xp2~) = A2= (d3 Xp\ + d2 Xp 2 2 + dl Xp2) (Yp2 + -Yp2~) 
Cx3 + — Cx3~ — a3 [{Xp3+) 3 -{Xp3~) 3 ]-a2 [(Xp3+) 2 -(Xp3~) 2 ]- 
-al(Xp3+-Xp3~)=\3=(d3 Xp\ + d2 Xp 2 3 + dl Xp3)(Yp3+-Yp3~) 
in the case of two intermediary controls.
	        
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