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timetaking polygons

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Okay, now a little math, about the algoritm that renders a whole room out environment with a numbers of polygons in it, how does the time it take depend on the number of polygons in it? Say, if there are n polygons in the picture, and the screen has a resolution of a*b pixels, is the time limited by O(a*b*n) or how is it? Anyone who knows how the algorithm works?

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There is no algorithm, per say. The rendering time performance is vendor specific (ATI, nVidia, etc.), and even board specific. The situation is complex, due to pipelining, size of the vertex cache, and the raw capabilities of the card. The performance is also very, very heavily influenced by the manner in which you pack your primitives and send them to the graphics card. The same geometric mesh, represented in a vertex-cache-friendly way vs. a non-vertex-cache-friendly way can produce measurably different performance numbers. If you have lots of objects with different material properties, the way in which you order the objects to minimize state changes between materials can make an absolutely huge difference. It is just not possible to describe by a simple algorithm.

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