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Projection matrix

Hello everyone,

I am currently trying to figure out the full projection matrix P for a given image, such that

w * [u,v,1] = P * [x,y,z,1]

,where P is a 3x4 projection matrix, u and v are the image coordinates and x,y,z are the world coordinates of the imaged point. So I took a photo (small application written with Unity and C#) and tried to get cameraToWorldMatrix as well as projectionMatrix with

photoCaptureFrame.TryGetCameraToWorldMatrix(...);
photoCaptureFrame.TryGetProjectionMatrix(...);

Initially I thought that now P = projectionMatrix * inverse(cameraToWorldMatrix), but this seems not to be correct. Because of the format of the projection matrix (https://developer.microsoft.com/en-us/windows/mixed-reality/locatable_camera) I also end up with a 4x4 matrix instead of the desired 3x4 matrix.

Can anyone give me a hint how to finally compute the matrix P?

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