Peter, you're reading waaaay too much into it.  The point of
origins aren't the same so all you're doing is lighting up a cone
with a spotlight from the top and making the cone slightly
transpaerent so it mimics the appearence of a "cone of light."

all your proofs are great, but ultimately inapplicable because:
I've done it. :o)  I understand what you've written below, it
really doesn't apply here, because you don't line them up
perfectly to match, as I said (about 4x now) make the cone
*slightly* smaller than the spot light.

-peter

Peter Popov wrote:
> 
> On Mon, 14 Jan 2002 14:31:59 -0800, Dearmad <dea### [at] applesnakenet>
> wrote:
> 
> >no, they'll intersect.  I meant to say the light should be
> >slightly *larger* than the cone so that the cone is sure to be
> >hit by the matching light.
> 
> A cone is defined as the locus of all lines passing through a point
> (vertex) and forming the same angle with a given line (the axis) also
> passing through above point. Another way to define a cone is to rotate
> a line (ruler) about another line (axis), whereas the two lines
> intersect, and the surface formed by above rotation (ruled surface, in
> this case also surface of revolution) is a cone.
> 
> You can easily see that if you place your cone so that the vertex is
> at the location of the light source, be it point or spot, the rays of
> light will be either inside the cone, outside the cone or coincident
> with it. The latter is highly unlikely due to numeric inaccuracies
> inherent to the way computers treat floating point numbers, so in
> practice no way will intersect the cone's surface (except the base),
> and that's what really counts in raytracing.
> 
> Peter Popov ICQ : 15002700
> Personal e-mail : pet### [at] vipbg
> TAG      e-mail : pet### [at] tagpovrayorg

-- 
Current obsession: "Ballet pour ma fille."
http://www.applesnake.net

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