#
Simple Models of the Impact of Overlap in Bucket Rendering

Milton Chen,
Gordon Stoll,
Homan Igehy,
Kekoa Proudfoot, and
Pat Hanrahan,
*Stanford University*

Appears in the *Proceedings of the 1998 Eurographics/SIGGRAPH Workshop on Graphics Hardware*

### Abstract:

Bucket rendering is a technique in which the framebuffer is subdivided
into coherent regions that are rendered independently. The primary
benefits of this technique are the decrease in the size of the working set
of framebuffer memory required during rendering and the possibility of
processing multiple regions in parallel. The drawbacks of this technique
are the cost of computing the regions overlapped by each triangle and the
redundant work required in processing triangles multiple times when they
overlap multiple regions. Tile size is a critical parameter in bucket
rendering systems: smaller tile sizes allow smaller memory footprints and
better parallel load balancing but exacerbate the problem of redundant
computation.
In this paper, we use mathematical models, instrumentation, and
trace-driven simulation to evaluate the impact of overlap and conclude
that the problem of overlap is limited in scope. If triangles are small,
the overlap factor itself is also small. If triangles are large, overlap
is high but pixel work dominates the rendering time. In pipelined
rendering systems, the worst-case impact of overlap occurs when the area
of an input triangle is equal to the area for which the pipeline is
balanced-that is, the triangle-related computation time is equal to the
pixel-related computation time. Thus, as the current trends of
exponentially increasing triangle rate, slowly increasing screen
resolution, and increasing per-pixel computation continue to push this
balance point toward triangles with smaller area, bucket rendering systems
will be able to utilize smaller tiles efficiently.

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miltchen@graphics.stanford.edu