1 Using Voxelization and Ray-Tracing to Identify Wall Thinness of ...
1 Using Voxelization and Ray-Tracing to Identify Wall Thinness of ...
1 Using Voxelization and Ray-Tracing to Identify Wall Thinness of ...
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39Table 4 Sphere results with Resolution <strong>of</strong> .5mmRadius# <strong>of</strong>TrianglesTotal # <strong>of</strong>voxels Safe voxelsSafe ByProxyvoxelsBorderlineSafeUnsafevoxelsUnsafeDistance2Runtime(secs)10cm 10000 33742755 32989507 748570 508 4170 0 430.84120cm 10000 268100817 265086977 2997490 1244 15106 0 492.52430cm 10000 904216581 897435203 6744076 2841 34460 1 616.35640cm 10000 2139962700 2127907452 11987554 5054 62640 0 797.90010cm 20164 33768872 33015368 749038 320 4146 0 430.26420cm 20164 268349533 265334953 2999022 1092 14466 0 492.30030cm 20164 905006877 898223840 6746808 2418 33809 2 613.89740cm 20164 2141705359 2129646691 11991576 4437 62623 32 791.75710cm 50176 33779009 33025369 749174 260 4206 0 428.89120cm 50176 268506348 265491124 2999544 1128 14552 0 491.96330cm 50176 905350606 898565912 6748014 2435 34244 1 606.32540cm 50176 2142791504 2130729584 11994780 5152 61988 0 783.72810cm 101124 33795016 33041352 749204 220 4240 0 426.50020cm 101124 268535011 265519603 2999708 1028 14672 0 489.15430cm 101124 905490427 898705274 6748734 2040 34379 0 608.16640cm 101124 2143028408 2130965900 11995180 4787 62529 12 784.33710cm 200704 33801385 33047673 749276 236 4200 0 428.11120cm 200704 268596315 265580723 2999830 1106 14656 0 486.82930cm 200704 905647554 898861993 6749042 2250 34269 0 603.96940cm 200704 2143367865 2131304937 11995805 4422 62701 0 792.71410cm 300304 33809661 33055981 749364 186 4130 0 430.32620cm 300304 268619550 265603910 2999865 1120 1120 0 488.67030cm 300304 905626414 898840953 6748944 2161 34356 0 604.40640cm 300304 2143429699 2131366507 11996323 4000 62869 0 785.550These results were tested on a Dell Inspiron 1720 with an Intel ® Core 2 Duo CPUT8300 @2.40 GHz, 3.0 GB RAM, using the 32-bit Windows Vista operating system.What is most interesting about these results is the consistency <strong>of</strong> algorithmic runtime,regardless <strong>of</strong> the triangle count. For instance, all the spheres with radius equal <strong>to</strong> ten centimeters<strong>to</strong>ok roughly a minute <strong>to</strong> run. Clearly, the limiting fac<strong>to</strong>r with our voxel-based approach is notnumber <strong>of</strong> triangles but rather number <strong>of</strong> voxels. As the previous tables show, the algorithm ranfor about 70 seconds on spheres with a 20 centimeter radius, <strong>and</strong> it ran for about 100 seconds onspheres with a 30 centimeter radius, <strong>and</strong> it ran for about 135 seconds on spheres with a 40centimeter radius. Note the consistency <strong>of</strong> this runtime increase, strongly indicating thecorrelation between number <strong>of</strong> voxels <strong>and</strong> runtime.These results mean that this approach would be particularly valuable for identifyingnarrow areas <strong>of</strong> small yet highly complex 3D models. The application is ideal for processingcomplex, highly tessellated input since large numbers <strong>of</strong> vertices do not have a significant effec<strong>to</strong>n runtime. However, the algorithm is less suited <strong>to</strong> processing models with large physical
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