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c++ - Changing coordinate system causes clockwise rotations

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The task I need to convert the coordinate system to +X forward, +Y right and +Z up (left-handed, like the one in Unreal Engine). The crucial part is that I want my camera to face its forward axis (

c++ - Changing coordinate system causes clockwise rotations

c++ - Changing coordinate system causes clockwise rotations

c++ - Changing coordinate system causes clockwise rotations

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Figure 1 from Counterclockwise and Clockwise Rotation of QRS
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A 90 clockwise rotation and then a vertical reflection are applied
270 Degree Clockwise Rotation
Use the image to determine the direction and angle of rotation. 90° clockwise rotation 270° clockwise
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