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I'm having trouble interpreting projective transformations. Let's confine ourselves to the projective plane [itex]P(\mathbb{R}_0^3)[/itex].

The transformations of the projective plane are [itex]GL(\mathbb{R}, 3) / \sim[/itex]. But these include things like reflections in planes and lines through the origin.

I don't see how that corresponds to anything useful. Perhaps it'll help if I explain what I think a projective transformation should do, so you ca correct me.

A scene in [itex]\mathbb{R}^3[/itex] consists of some points [itex]p_1, p_2, ..., p_n[/itex]. There is a plane in space, say [itex]\alpha \leftrightarrow x=1[/itex] on which we project the scene from the origin. Now we move the origin, or equivalently the scene and the plane, and do the projection again. The projective points will have changed and a projective transformation describes this change.

Thanks

A_B

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# What are projective transformations?

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