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The "Free Transform" feature in Photoshop allows you to not only scale, rotate and skew an image (which are all linear
transformations), but also apply some sort of perspective projection. What I mean is it allows you to move the 4 corners all independently (by dragging them with CTRL pressed). I don’t fully understand the transformation it applies. Can anybody explain what would be the algorithm behind this Free Transform?
It doesn’t seem to apply a linear projection, since a pixel halfway one of the 4 original edges does NOT always end up halfway the edge in the destination! Draw a rectangle with a spot in the bottom middle, and transform it in PS to see what I mean.
In other words my question is: if I have 4 arbitrary coordinates A, B, C and D which represent the new positions for the 4 corner points of the original image, how exactly do I put the image into the new shape? (or rather, how do I correctly obtain the source position in the original image for any point within the new shape)
I understand that certain layouts for the new corner positions A,B,C,D would be impossible or meaningless, so for the sake of simplicity let’s assume the 4 points are positioned "reasonably".
transformations), but also apply some sort of perspective projection. What I mean is it allows you to move the 4 corners all independently (by dragging them with CTRL pressed). I don’t fully understand the transformation it applies. Can anybody explain what would be the algorithm behind this Free Transform?
It doesn’t seem to apply a linear projection, since a pixel halfway one of the 4 original edges does NOT always end up halfway the edge in the destination! Draw a rectangle with a spot in the bottom middle, and transform it in PS to see what I mean.
In other words my question is: if I have 4 arbitrary coordinates A, B, C and D which represent the new positions for the 4 corner points of the original image, how exactly do I put the image into the new shape? (or rather, how do I correctly obtain the source position in the original image for any point within the new shape)
I understand that certain layouts for the new corner positions A,B,C,D would be impossible or meaningless, so for the sake of simplicity let’s assume the 4 points are positioned "reasonably".
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