Model "BCPolyAtnInk.cr2" is a more complicated code variant which seems to work better. To find the tangent, the code calculates points "T" of a second Bezier curve with identical parameters moving a little bit ahead of the first curve. The connecting line between points P and T creates a vector of small constant length along the entire curve which is an approximation to the tangent at points P. The vector is used to derive a rotation angle "alpha" as shown in the picture. The square root implementation is the "Bhaskara-Brouncker" algorithm. Model "BCAtan22.cr2" is the same figure setup, but the Bezier code is based on the so called "de Casteljau" algorithm (instead of the parametric polynomials). The ERC code is less efficient, but the resulting "alpha" angle is much more accurate. You can see the difference, when you set the CPs to a steep pitch tangent ("aa_y" and "bb_y" values). For some unknown reason (maybe a bug in the code), the parametric functions make a noticeable error in this case.