# Calculate corners locations from known dimensions and 1st corner's location

Hello,

I have a board with known dimensions (50cm along x-axis and 30 cm along y-axis). Now i have an Aruco marker taped to the top left corner of the board. I can detect the marker and get its location in the image through aruco::detectMarkers, location in the world coordinates through triangulatePoints and orientation through estimatePoseSingleMarker perfectly.

Now I have the location of the 1st corner and I want to calculate the locations of the other 3 corners of the board w.r.t my world origin. the problem is that the board can be in any orientation so i cannot add 50cm to the x of the 1st corner and 30 to the y. The known dimensions are w.r.t my world coordinate system.

My question is, How can i scale these dimensions depending on the board's orientation and then calculate the 2D/3D locations of the other corners?

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