calculating the new coordinate of a point in the camera field of view after rotating the camera around the z-axis

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caesar 2020-1-23

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https://ww2.mathworks.cn/matlabcentral/answers/501709-calculating-the-new-coordinate-of-a-point-in-the-camera-field-of-view-after-rotating-the-camera-arou

alright, its bit complicated but i hope i will make it as clear as possible.

i have a camera looking straight and based on the distance from the cam to the objects in front of it ,i can calculate the dimentions ( width and height) of the object that appears on the image from the cam acoording to the following equation:

(Sensor Dimention(mm))/(Focal enght (mm))= (Field Dimention (mm))/(Disance to Field (mm))

so, if the sensor has 36 by 24 mm physical dimensions ( width* height), focal length 40 mm and the distance to the object is 1500 mm, we can see that the width and height of captured image is 1350 mm and 900 mm . for example, looking at the attached image ( image 1) the dimention of the point A ( the right edge of the captured plane) will be ( CAMx-1500, CAMy+675, CAMz+450) ; Point E is at (CAMx-1500, CAMy, CAMz) where all units are in mm and the cam is at ( CAMx, CAMy, CAMz) .

my question is : if i wanted to rotate the camera around the z axis lets say 20 degrees ( as shown in image 2), how can i calculate the point A or any other points coordinations ? I have tried to apply rotation matrix around z-axis on the points but the results werent correct as I can check with the simulation in 3d max. x coordination always negative and i guess its related to the fact that the plane is ' behind the cam' where the cam is looking at negative x direction?

I am sure I am missing something here and would appreciate it if anyone can help .