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3D engine, vertex consideration

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Does a 3D graphics engine consider the screen coordinates of all offscreen vertices (provided the vertex in question is onscreen in terms of depth)? Or is there some clever way of deciding not to calculate a certain vertex's onscreen coordinate as you can already tell it is not necessary? I'm sorry that when I read back my question it seems hard to understand, I have difficulty in communicating my ideas and questions :P

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Frustum Culling ...
basically you find the area that it viewable through the camera and test to see if a vertex, or better yet some sort of bounds ( sphere, box... ) for a bunch of vertices is in side the view frustum.... if it is you render it...

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You might also want to look into Octrees, BSP-Trees, Portals and other space partitioning techniques, so that you can eliminate a large portion of vertices (wich are out of the view-volume) with few tests/ operations.

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