POV-Ray : Newsgroups : povray.pov4.discussion.general : Suggest v4.0 f_kappa_2d() function. (yuqk R19 v0.6.13.0) : Suggest v4.0 f_kappa_2d() function. (yuqk R19 v0.6.13.0) Server Time
23 Feb 2025 14:56:49 EST (-0500)
  Suggest v4.0 f_kappa_2d() function. (yuqk R19 v0.6.13.0)  
From: William F Pokorny
Date: 23 Feb 2025 08:43:28
Message: <67bb2600$1@news.povray.org>
Adding the inbuilt f_kappa_2d() function to the upcoming release (R19) 
of yuqk).

This a general helper function / technique to match any two curves at 
their endpoints given you have the means to calculate the first and 
second derivatives for both curves being glued together at (t).

The function will calculate and return 'k(t)' or the 'radius of 
curvature' (1.0/k(t)).

Attaching images showing on the left k(t), and on the right the 'radius 
of curvature' at t, as the length of the normal vectors for a 
f_bezier_2d_cubic() curve.

Bill P.


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