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Backgrounds for full 3D camera rotation

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What is the most efficient and preferred way to implement static backgrounds involving full 3D camera rotation? For example, space and aquatic sims environments. The background is exactly that, just a backdrop to create the overall encapsulating environment allowing the character to explore the 3D universe unhindered.

I was thinking there are two general approaches:

1) Use a 3D model that encapsulates the universe (like a box) with the inside of the model textured; or

2) Use a 2D sprite sheet that maps coordinates on the sheet to the camera position.

The downside to 1) is that because it is a 3D model (needless) collision calculations would constantly be performed. The downside to 2) is that the engine has to constantly perform the mapping calculations and reload the sprite sheet accordingly.

Which of these two approaches is preferred? Are there any other approaches used?

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#1 is the most efficient and what you described is called a skybox. However, there should be no collision detection applied to the cube.

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Perfect! Skybox is exactly what I was looking for. Thanks! About the collision detection, I'm guessing I'll have to create a new content pipeline processor specifically for skyboxes, since my current implementation processes all 3D models with their corresponding hitboxes.

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