Thorsten Froehlich wrote:
> 

> Skiba <abx### [at] babilonorg>  wrote:
> 
> >   splines:      news.povray.org/m4f7cug9ch19jbve8m8prf4vl8ima0rsma@4ax.com
> >                 when point is added then type of spline is overwritten
> >                 so bottom, second from right is wrong
> 
> I don't get what you want to say in the sentence above.
> 
> >   bounding:     news.povray.org/2g0dcu8kasg84pqde8hdq9d60nkoa1cvka@4ax.com
> >                 sphere-sweeps are still clipped
> 
> Yes, and this will remain the way it is unless someone comes up with code to
> determine the bounding box of a Catmull-Rom spline segment.  It turns out the
> original sphere_sweep code simply adds a bit to the control point bounding
> box.  The problem appears only for Catmull-Rom splines because they may exceed
> their control points which the code uses to find the bounding...

I have not looked very closely at this, but I don't
think it that it should be very difficult to find an
analytical solution to this.

As I understand it, there should be 3 cubic polynomials
that controls the x, y and z components for each segment.

Just differentiate these (to quadratic polynomials) and
solve for zero to find the max and min points of the
cubic polynomials. The values of the cubic polynomials
at these points will give the components for the
bounding box.

If any of the cubic polynomials has no real roots, then
I think that values at the endpoints of the cubic will
polynomials give the max and min points for the spline
segment.


Tor Olav

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