point outside image with getPerspectiveTransform

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Hi all,

I try to make a perspective transform, all works fine if I use 4 points and if this 4 points are in the picture, but I have a question, is it possible to give one or two point outside image? for example with this image :

I would like to do somthing like this when I take coordinates point:

Like you can see on the above image P1 and P4 are outside image, if I want to have a good quadrilateral. Is there solution to solve this problem ? And I have another question, what is the maximum angle (between camera and plane, it's call FOV I'm not sure...) before opencv makes a bad image ?