On Wed, 8 Aug 2001 13:16:49 +0200, Rune wrote:
>Rune wrote:
>> Whenever anyone talks about doing non-linear
>> transformations on meshes, someone jumps in and says
>> it can't be done because it would require curved rays.
>
>Then "Ron Parker" wrote:
>> If they do, they're wrong.  Nonlinear transforms on
>> meshes are about the only kind that don't require
>> curved rays.  But that's off-topic for this group...
>
>I agree with you, but some people claim that real non-linear transforms
>would bend the individual triangles, and this would require curved rays.
>However, I don't see why it would have to bend the individual triangles to
>qualify as a non-linear transform.

Well, it's true that it might have to bend the individual triangles (though 
a perspective transform, for example, would not) but there's no reason you
can't cut a triangle up into as many pieces as necessary and transform those
pieces to do the bending.

-- 
#macro R(L P)sphere{L F}cylinder{L P F}#end#macro P(V)merge{R(z+a z)R(-z a-z)R(a
-z-z-z a+z)torus{1F clipped_by{plane{a 0}}}translate V}#end#macro Z(a F T)merge{
P(z+a)P(z-a)R(-z-z-x a)pigment{rgbt 1}hollow interior{media{emission T}}finish{
reflection.1}}#end Z(-x-x.2y)Z(-x-x.4x)camera{location z*-10rotate x*90}

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