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- Thread starter swampwiz
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Isn't this exactly the definition?

https://en.wikipedia.org/wiki/Homothetic_transformation

https://en.wikipedia.org/wiki/Homothetic_transformation

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It does say it. They define a homothetic transformation as ##M \mapsto \lambda \cdot \stackrel{\longrightarrow}{SM}##. That's exactly what a perspective does to a point ##M## as seen from ##S##.

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That's what I thought.It does say it. They define a homothetic transformation as ##M \mapsto \lambda \cdot \stackrel{\longrightarrow}{SM}##. That's exactly what a perspective does to a point ##M## as seen from ##S##.

Now, what about affine transformations? Is the set of all Homothetic transformations also affine transformations? or vice-versa? It seems that since lines are preserved in a homothetic transformation, it is also an affine transformation.

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They are affine transformations. The difference to linear transformations is only whether ##S=0## or ##S\neq 0##.That's what I thought.

Now, what about affine transformations? Is the set of all Homothetic transformations also affine transformations? or vice-versa? It seems that since lines are preserved in a homothetic transformation, it is also an affine transformation.

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In reality there is something like resolution. Although it might not exist theoretically, there is a real margin below which we have indistinguishability.I will need to look at it along the line in the exact same direction of the line, so there should never be a vanishing point, ...

No, it's affine linear, i.e. the origin is the center of projection and not the origin of the coordinate system.... and essentially that a proper perspective projection is not linear.

I got the impression, that a perspective in your view is one whose center is at infinity, the other way around so to say. In this case the center does indeed not exist as part of the screen. A concept which deals with those infinite points is projective geometry where the horizon has a coordinate representation.

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