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Replicating actual sized 3D objects

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I am reaching out to the community to get some advice, ideas, or overall techniques that can be used in an interesting task I am researching, any comments, suggestions, or discussions are greatly appreciated. Lastly, I am not posting in hopes to get someone to give me the mathematical equation I am merely looking for additional advice, ideas, and/or different ways readers may accomplish this task.

Using a projection screen I need to represent 3D objects such that they visually appear to be the same size, at distance, as they would normally appear to the human eye in real-life. For example, if a 3D billboard is being rendered onto a projection screen how many pixels (width/height) would the rendering occupy based on the following pieces of information: (values are just examples for discussion)

- Viewer is standing 6' from the screen
- The projected image is 6x8 feet
- The 3D billboard in the real world would be 5' x 5'
- The 3D billboard is placed at 200' from the projection plane (ie. z depth is 200, camera is at 0 z)
- The viewer is looking at the projection screen with a 4x powered rifle scope

Thanks in advance

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