4707fde8@news.povray.org...
> High!
>
> After a six-week break, I returned to my self portrait project... as I
> firstly try to do a "cheap" (in terms of rendering time) CSG version, I
> started with a "skull ellipsoid" to which I would like to add face with
> upper jaw and an animatable mandible, as displayed in the three
> schematical drawings below.
>
> The radii of the "skull ellipsoid" (centered at the origin) are as
> follows: <0.115, 0.108, 0.138>
>
> To fit the front parts in, I vertically sliced off the skull shell at
> z=-0.097. Now I have to determine the width of the cut surface at y=0.
> With a non-stretched sphere, that would be easy:
> sqrt(radius^2-0.097^2)*2*radius - but how to transfer this to an
> ellipsoid? To determine the exact radius length at the intersection of x
> axis, cutoff box and ellipsoid, I would have to know its angle with the
> z axis...
>
> See you in Khyberspace!
>
> Yadgar
>

Hi Yadgar.

Doesn't seem to difficult (but maybe I missed something?)

The equation of your skull ellipsoid is:
(x/0.115)^2 + (y/0.108)^2 + (z/0.138)^2 - 1 = 0
The cut surface z==-0.097 is an ellipse in the xy plane, with equation:
(x/0.115)^2 + (y/0.108)^2 + (0.097 /0.138)^2 - 1 = 0
the width at y=0 is given by:
(x/0.115)^2 + (0.097 /0.138)^2 - 1 = 0
<=> |x| = 0.115 * sqrt ( 1 - (0.097 /0.138)^2)
so width = 2 * 0.115 * sqrt ( 1 - (0.097 /0.138)^2), no?

Hope this helps...

Xavier

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