CPU-GPU Algorithms for Triangular Surface Mesh Simplification

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12 Suzanne M. Shontz and Dragos M. NistorSimplification PercentageSimplification PercentageNaïve Marking Algorithm Inverse Reduction Algorithmiter # vertices # faces %v simp %f simp # vertices # faces %v simp %f simp0 863182 1726364 — — 863182 1726364 — —1 735345 1470688 14.8 14.8 779354 1558590 9.7 9.72 646764 1292036 25.1 25.2 704379 1408640 18.4 18.43 573431 1142601 33.6 33.8 639370 1276589 25.9 26.14 512166 1042650 40.7 39.6 581774 1161369 32.6 32.75 458718 952966 46.9 44.8 531048 1059586 38.5 38.66 412135 872794 52.3 49.4 486874 970716 43.6 43.87 371523 801356 57.0 53.6 446693 889413 48.3 48.58 336120 737405 61.1 57.3 410960 816781 52.4 52.79 305243 680268 64.6 60.6 379788 753007 56.0 56.410 278305 629188 67.8 63.6 351150 693992 59.3 59.8Table 6. The simplification percentage of the gargoyle mesh over multiple iterationsof the CPU-GPU naïve marking algorithm and the CPU-GPU inverse reductionalgorithm.too much loss of detail. This reinforces the notion that larger meshes can besimplified more without seeing any visible effects.(a) Armadillo (b) Bunny (c) Gargoyle(d) Hand (e) Horse (f) KittenFig. 6. The resulting meshes after 10 iterations of the CPU-GPU naïve markingalgorithm.Tables 5 and 6 show the vertex and face simplification percentages as afunction of iteration in each mesh. Note that %v simp and %f simp represent
CPU-GPU Algorithms for Triangular Surface Mesh Simplification 13the percentages of vertex and face simplification, respectively, in these tables.The amount of simplification performed each iteration decreases. This suggeststhat as the vertex and element counts increase, the decrease in runningtime achieved by using the GPU simplification algorithm instead of the CPUsimplification algorithm increases as well.To examine the effects of splitting the mesh simplification workload betweenthe CPU and the GPU using the inverse reduction algorithm, werecorded the time spent during the simplification process for various CPU-GPU splits on all test cases. We tested the following CPU-GPU workloadsplits: 100-0, 95-5, 90-10, . . . , and 0-100. The time taken in seconds for theCPU-GPU splits can be seen in Figure 7. The proportion of running timespent in the GPU for the tested is shown in Table 7. The GPU memory usagefor the tested splits is shown in Table 3.(a) Bunny(b) GargoyleFig. 7. The time taken to simplify each test case for every split using the CPU-GPUinverse reduction algorithm. As the CPU-GPU split increases, the CPU workloadincreases, and the GPU workload decreases.The CPU-GPU inverse reduction algorithm shows an increase in runningtime on the horse mesh, whereas it shows a decrease in running time onthe armadillo, bunny, gargoyle, hand, and kitten meshes with respect to anincreasing workload on the GPU. If the mesh is large, the time taken decreasesas the GPU workload increases. If the mesh is small, the reverse trend holds.This is due to the extra time taken for memory allocation in the GPU andfor copying the data from main memory to the GPU cache, shown in Table 3,in addition to the time required for simplification. Also, because the inversereduction algorithm is more efficient than the naïve marking algorithm, wesee that the time taken to simplify the bunny mesh decreases as the GPUworkload increases, now decreasing anywhere between 5.55% for the bunnymesh to 11.48% for the gargoyle mesh when the GPU is given the full workloadwhen compared to the naïve algorithm.
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CPU-GPU Algorithms for Triangular Surface Mesh Simplification

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