Skip Talbot wrote:
> Is there a built in function that I'm overlooking that would allow me to 
> compute a normal and tangent vector to a given point on a spline?  I saw 
> that Chris Colefax's spline macro can do this but is there something I can 
> use with POV's built in splines?  I'm looking at approximating the vectors 
> by using adjacent points, but I was hoping there might be something a little 
> more accurate.
> 
> Skip 
> 
> 

You could work out the polynomials that controls the
spline and then differentiate those.

Or you could use numerical methods to calculate the
tangent-, normal- and binormal-vectors.

Some keywords for Google:

"Frenet frame"
"TNB frame"

"Tangent vector"
"Normal vector"
"Binormal vector"

"Numerical differentiaton"
"Vector valued function"


While working on the tools for my POVCOMP image I made
macros that will produce a set of frenet frame functions
for my NURBS functions (and other functions).

-- 
Tor Olav
http://subcube.net
http://subcube.com

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