Thanks-- that helps a lot, especially since geometry class is a distant memory.

-DZ

(nice signature line by the way)



Ron Parker wrote:

> On Thu, 28 Jun 2001 14:24:43 -0500, deanz wrote:
> >Can anyone help a trig simpleton bisect an angle in POVRay?
> >
> >If I have three points in space (A, B & C), how can I
> >
> >1) Find the angle of ABC
>
> There's stuff you can do with the cross product and the dot product to
> do this, but you don't really need it if all you want to do is bisect
> the angle.  In case you do need it for some other reason, though,
>
> atan2(vdot(A-B,C-B),vlength(vcross(A-B,C-B)))
>
> should give you an answer for non-pathological cases (i.e. those where
> A, B, and C are distinct points.)
>
> >2) Find the point (D) which lies at a point bisecting an arc AC so that
> >line DB equals line AB equals line CB ?
>
> B+vlength(C-B)*vnormalize(A/2+C/2-B);
>
> Just like in geometry class: first bisect the line connecting A and C,
> then project that out to the circle.  Note that this assumes that A and
> C are the same distance from B.  If they aren't, there's no such solution
> (because AB won't equal CB as specified.)
>
> I haven't tested either equation, so there are probably embarrassing
> errors in them.
>
> --
> #local R=rgb 99;#local P=R-R;#local F=pigment{gradient x}box{0,1pigment{gradient
> y pigment_map{[.5F pigment_map{[.3R][.3F color_map{[.15red 99][.15P]}rotate z*45
> translate x]}]#local H=pigment{gradient y color_map{[.5P][.5R]}scale 1/3}[.5F
> pigment_map{[.3R][.3H][.7H][.7R]}]}}}camera{location.5-3*z}//only my opinions

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