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Does anyone know a Matrix transformation like so?

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Is there a matrix that can tranform an object as shown in the image?


It can be a 2d matrix, but 3d would also be useful.

I realise it looks a bit like a perspective projection. 

But I just mean a matrix, which transforms / enlarges x values depending on their y value.

The higher the y value, the more x gets scaled up.



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No such matrix is possible, because that's not a linear transformation. The reason that projection matrices can get away with that sort of distortion is because of the division by w term, which makes the whole transformation nonlinear.


To see why, assume that M is a matrix that satisfies your desired transformation. It's easy to see that




This is contradicts the fact that your transformation is linear.

Edited by CulDeVu

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No Matrix possible. ok.


I *think* this formula below kind of does what I need.


m_x is the average x value of the mesh.


y_min is the global minimum y value of the mesh.


delta = 1, doesn't change the mesh.

delta = 0, all x values are condensed into one spot the further you go up (maby there's something missing in the formula, I think it still also needs to process the overall height of the mesh somehow.)

delta > 1 expands x values outwards going up the mesh.


But they behave quite unpredictable, when x is changed upwards, the extent of expansion doesn't seem linear.




does anybody know of a better solution?

Edited by teutoburger

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You can always find a projective transformation that transforms one quadrilateral to another one. A projective transformation on the plane is represented by a 3x3 matrix.

See if something like this works:
(1  0 0)   (x)
(0 -1 0) * (y)
(0  1 1)   (1)

Remember that the resulting vector is in projective coordinates, which means approximately that you need to scale it to force the third coordinate to be 1. Edited by Álvaro

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that's just too good to pass :-P
Oh, you added it, instead of multiplying (optionally also multiplying with scale(y)), ie


x' = x * scale(y) * (1 + sin(y)) / 2


You may want to increase "1" slightly, as "1 + sin(y)" touches 0, ie every 2*pi the entire plane becomes a single point.

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