Improving framerate of instanced geometry scene

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I'm rendering large amount (millions) of instanced geometry. The geometry itself is simple, a box without bottom face. The rendered scene is actually a 3D graph where boxes are lines (only 3 faces are rendered at a time using culling).

When the scene occupies small area of screen (either zoomed out or small window) the frame rate is alright, but when it becomes larger the frame rate falls below acceptable level. The scene doesn't redraw constantly, just when user changes view (rotation, zoom) and the frame rate is limitted to 60 fps.

First, identifying the issue.. I'm not sure if I'm hitting fill rate limit or pixel shader throughput limit (too few multiprocessors to process all fragments). The pixel shader does nothing, just outputs the color but this should still result in a processor running the code. I'm running this on Nvidia 635m in Optimus architecture and similliar mobile GPUs can be expected to run this. How can I identify which of those is the problem?

And the next step after identifying the issue would be solving it. There is not, generally, a lot of ocluding fragments (like there would be if I rendered a room and then placed wall in front of it) so optimizing in this regard would have marginal improvement. What would be some other ways to improve frame rate?

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