On Mon, 27 Aug 2001 20:34:00 -0400, Alberto <jac### [at] usbve> wrote:

>In your last equation, a and b are the unknowns. Take the inner product
>of this equation with say, AB. You will end with  a scalar equation.
>Take the inner product of your last equation with AD and you'll get a
>second equation. Now you have a pair of equations with two unkowns. This
>system should be soluble.

I can also split the last equation into two, one for the x components
of vectors and one for the y components which is the same as you
suggest, only the unit vectors i and j are used for multipliers
instead of AB and AD. The problem with this approach is that the
system is non-linear due to the term a*b. When extending this
transformation to three dimensions, I get a system of three
third-order equations which, although it has only one set of roots in
the range [0; 1] is too hard for me to solve.

I can describe the UVW transform but I'd rather have this one solved
before the more complex one is tackled.


Peter Popov ICQ : 15002700
Personal e-mail : pet### [at] vipbg
TAG      e-mail : pet### [at] tagpovrayorg

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