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Oribt camera - calculate new point?

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I'm creating a star field simulator where the user can click a star then use the mouse to 'orbit' the camera around the star. I can detect when the mouse moves in a certain direction - either up/down/left or right. The part I need help with is calculating the new camera position if the mouse moves in any of those directions. In my mind, to do this, I can imagine a large sphere, with the center of it being the point the camera is orbitting. I just don't know how to calculate the new camera position based on the direction the mouse moved. Any help? Thanks

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