Simple and Efficient Mesh Layout with Space-Filling Curves

We present a simple and efficient algorithm to compute cache-friendly layouts of unstructured geometric data. Coherent mesh layouts minimize cache misses and page faults by laying out vertices, triangles or tetrahedra in a spatially structured manner. Recently, Yoon et al. have shown that it is possible to construct an optimal cache-oblivious mesh layout (COML) for surface and volume data. However, their approach is based on an NP-Hard optimization problem, and is thus very computationally expensive. We present a mesh layout based on space-filling curves that has comparable performance to COML and is orders of magnitude faster to compute. We also discuss extending our algorithm to handle extremely large datasets through an out-of-core approach. Finally, we include an analysis that examines a number of different mesh layouts, highlighting their strengths and weaknesses. Our evaluation indicates that space-filling curve layouts can be an order of magnitude faster and less memory-intensive to compute while, in every application, being able to maintain a performance within 5% of the best layout, including those that are specifically tuned for GPU hardware vertex caches in [Lin and Yu 06, Sander et al. 07]. © A K Peters, Ltd. 1 1086-7651/06 $0.50 per page