bottom 1d from 2d

Problem

1. radial thinning disregard neighboring azimuths and creates choppy line
2. tangential thinning tends to drift apart, i.e., deviate from the ideal center of groove bottom

Solution

1. somehow combine the two: weighted average of the two results.

Analysis

1. what we do NOT want to see: a locally(at its own azimuth) optimized btm-pos that disintegrates from its context.
   
1. 1D-btm(a) deviates to the back or front (tangential error): goes behind the previous point or beyond the next point.
2. 1D-btm(a) deviates to the left or right (radial error): causes w/z to fluctuate (stylus shape distorted).
   
2. what we want the 1D-btm(a) to provide: 
1. a(i) > a(i-1)
2. abs(r(i)-r(i-1))<e, e.g. 2pixels
   
3. dr_btm is similar to dr_in, dr_out
4. abs(w2z(i) - w2z(i-1)) < e

Imp

1. #1 elem: 1D-btm(1) is chosen according to any of : 1) lowest, 2) middle, 3) equal w/z for in/out.
2. #2+ elems:
   1. vp = closest_to_line(e_in(a), e_out(a))
   2. vpp = find(vp(a)>a(i-1))
   3. p = min(abs(r(a) - r(a-1))) or
      
   4. p = P * min( (w2z_out(a) - w2z_out(a-1)) / w2z_out(a-1) ) + Q * min(.... w2z_in....)