line segments; (3) delete short amplitude irregularities from the set of intersection 

 points, provided resulting deviations from the profile are not excessive. 



Experimental evidence suggests that, in general, a large "thin line" 

 tolerance tends to smooth the data set too much, yielding line sets with excessive 

 overlap. On the other hand, a small value for the "negligible" departure between 

 a regression point and a straight line tends to yield unions of lines consisting of 

 more line segments than are necessary, and excessive values for the "intolerable" 

 departure between a straight line and a data point results, in some instances, in an 

 unacceptable loss of profile regression precision. By varying the ratio of these 

 tolerances it was determined that the ratio finally selected provides advantages of 

 minimum data smoothing (small RMS departures) with gratifying economy in the 

 number of lines selected to represent a profile. 



C. Compromise Regression Points 



The following method is used to calculate a compromise regression point 

 when regression lines on overlapping line sets do not intersect in the range of 

 overlap. !f the depths z-^ and z2 are the limits of the range of overlap, then an 

 estimate for the regression depth is provided: 



z = (zi + z2)/2. (8) 



If the equations of the regression lines are provided, respectively, 



T = Ai + B, • z (9) 



T = A2 + B2-Z (10) 



then the median point in the range of overlap is identified by the coordinates 

 (z , T ), where 



T = 



(Al + Aj) + (Bi + B2) z J /2 



01) 



It may be noted that this method will not under any circumstance yield an 

 error exceeding a thin stylus line departure (±2e) between the regression profile 

 and any profile data point. Hence, this method is consistent with the three 

 level tolerance algorithm that permits the same maximum departure. 



D. Fitting Curvelinear Functions 



The three level tolerance algorithm for fitting lines to points in a plane 

 may be applied with appropriate modifications to the fitting of alternative sets 



18 



