CPU-GPU Algorithms for Triangular Surface Mesh Simplification

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8 Suzanne M. Shontz and Dragos M. Nistor(a) Armadillo (b) Bunny (c) Gargoyle(d) Hand (e) Horse (f) KittenFig. 3. Initial test meshes.element angles (in degrees), the minimum and average element areas, the meshvolume, and the wall clock time (measured in seconds) for each algorithm. Usingthese metrics, we were able to assess the quality of the meshes and thealgorithmic efficiency. For the wall clock time, we report averages over 100runs of the algorithm. Table 1 contains the values of the metrics for the initialmeshes.mesh # vertices # faces min ∠ max ∠ min area avg area volumearmadillo 172974 345944 0.034750 170.907 7.424e-08 1.840e-1 1.42690e+6bunny 34834 69664 0.494800 177.515 7.925e-08 1.573e-2 7.54700e+3gargoyle 863182 1726364 0.000215 179.820 3.638e-12 4.553e-2 1.63730e+6hand 327323 654666 0.545000 177.995 5.161e-11 1.078e-4 1.64936e+1horse 15366 30728 0.385500 177.119 1.118e-14 2.118e-6 1.58866e-3kitten 137098 274196 0.004609 179.936 1.427e-08 8.846e-2 8.38625e+5Table 1. Metric values for the initial meshes.To examine the effects of splitting the mesh simplification workload betweenthe CPU and the GPU using the naïve marking algorithm, we comparedthe time spent during the simplification process for the following CPU-GPUworkload splits 100-0, 95-5, 90-10, . . . , and 0-100 on each test case. The timetaken in seconds for the tested CPU-GPU splits for the bunny and gargoylemeshes can be seen in Figure 4. Such results are representative of those obtainedon small and large meshes, respectively. The percentage of runningtime spent in the GPU is shown in Table 2; the 100-0 split is not shown since
CPU-GPU Algorithms for Triangular Surface Mesh Simplification 9all of the time is spent on the CPU. The GPU memory usage for the testedsplits is shown in Table 3.(a) Bunny(b) GargoyleFig. 4. The time taken to simplify the bunny and gargoyle meshes for each CPU-GPU split using the CPU-GPU naïve marking algorithm. As the CPU-GPU splitincreases, the CPU workload increases, and the GPU workload decreases.% of GPU timemesh 95-5 90-10 85-15 80-20 75-25 70-30 65-35 60-40 55-45 50-50armadillo 9.2 14.5 19.6 24.6 29.4 34.1 38.6 43.1 47.5 51.7bunny 5.4 8.8 12.1 15.2 18.2 21.1 23.9 26.5 29.0 31.4gargoyle 10.4 15.8 21.1 26.3 31.3 36.1 40.8 45.4 49.9 54.3hand 9.4 14.8 20.0 25.1 29.9 34.7 39.3 43.9 48.4 52.7horse 5.0 8.0 10.9 13.6 16.2 18.7 21.1 23.3 25.4 27.4kitten 8.2 13.4 18.4 23.2 27.9 32.5 36.8 41.2 45.5 49.6mesh 45-55 40-60 35-65 30-70 25-75 20-80 15-85 10-90 5-95 0-100armadillo 55.8 59.8 63.6 67.4 70.9 74.3 77.5 80.6 83.4 86.0bunny 33.6 35.7 37.7 39.5 41.3 42.9 44.4 45.8 47.2 48.5gargoyle 58.6 62.7 66.7 70.5 74.2 77.7 81.0 84.2 87.2 89.1hand 56.9 61.0 64.8 68.7 72.3 75.8 79.0 82.2 84.2 87.8horse 29.2 30.9 32.5 33.9 35.3 36.5 37.6 38.6 39.4 40.1kitten 53.6 57.4 61.1 64.8 68.2 71.4 74.5 77.4 80.1 82.5Table 2. The percentage of time spent on the GPU for various CPU-GPU splitsusing the CPU-GPU naïve marking algorithm.As seen in Figure 4, the gargoyle mesh shows an increase in running time,whereas the bunny mesh exhibits a decrease in running time, with respectto increasing the workload of the GPU. This indicates that if the mesh is
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CPU-GPU Algorithms for Triangular Surface Mesh Simplification

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