Ron Parker wrote:
> It's a perspective transformation.  It's not linear, in that
> f(A)+f(B) != f(A+B).  I'm not sure it transforms lines to lines,
> either.

If it's perspective, it does! For example, can you remember of a scene with
a "normal" camera were an object's straight edge turned curved <he he> in
the image? (I know this is no proof, but I know perspective is line-> line).

> Consider the (2d) perspective transformation f(x,y) = xy.
> If you transform a line parallel to the X axis, such as y=2, then
> you get a line in return (y=2x).  If you transform a line parallel
> to the Y axis, you also get a line in return.  But what happens
> when you transform the line y=x?  By my calculations, you get y=x*x,
> which is not a line.

I'll dig in my school notes and find some math about perspective, such as
main properties of transformation, transform matrix (wich is 4x4 with
homogenous coordinates). I'll post that sometime next week...

> For another thought experiment, assume that you have a transformation
> that can turn a cylinder into a cone.  What would it do to the
> resulting cone?  If it leaves it a cone, then the transformation
> isn't invertible, because there's some cylinder that maps to the same
> cone.  If it makes it anything else, then what does it do to a line
> that lies in the surface of that cone?


I think it turns a cone into an _other_ cone. Line-> line.



Povingly


Philippe

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