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Calculating relative stage size


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I'm trying to center a 3D object in a scene (for the sake of this question).

Calculating stage size simply according to canvas dimensions doesn't work, e.g. if in PG the canvas width is 960, then the x position of the sphere can be between around -10 to 10 meaning the "screen width" I can play with is around 20.

I imagine I need to somehow take into account the camera z, and possibly other parameters.

Here's a PG where you can see more or less what I'm trying to do:



By the way I'm not looking for some workaround of setting the camera target to an object or something of the sort, I'd like to really understand how to calculate such a thing.

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This is going to involve the camera.FOV since the value assigned affects how far away things look at the same position.  In another thread I took snapshots of the effects of changing this.  Here I was trying to get images of the same size, so I had to move the camera or they would not be.

In your research, FOV plays into defining the frustrum.

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