-
Notifications
You must be signed in to change notification settings - Fork 0
/
havran_stats_octrees.txt
887 lines (755 loc) · 46.5 KB
/
havran_stats_octrees.txt
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
146
147
148
149
150
151
152
153
154
155
156
157
158
159
160
161
162
163
164
165
166
167
168
169
170
171
172
173
174
175
176
177
178
179
180
181
182
183
184
185
186
187
188
189
190
191
192
193
194
195
196
197
198
199
200
201
202
203
204
205
206
207
208
209
210
211
212
213
214
215
216
217
218
219
220
221
222
223
224
225
226
227
228
229
230
231
232
233
234
235
236
237
238
239
240
241
242
243
244
245
246
247
248
249
250
251
252
253
254
255
256
257
258
259
260
261
262
263
264
265
266
267
268
269
270
271
272
273
274
275
276
277
278
279
280
281
282
283
284
285
286
287
288
289
290
291
292
293
294
295
296
297
298
299
300
301
302
303
304
305
306
307
308
309
310
311
312
313
314
315
316
317
318
319
320
321
322
323
324
325
326
327
328
329
330
331
332
333
334
335
336
337
338
339
340
341
342
343
344
345
346
347
348
349
350
351
352
353
354
355
356
357
358
359
360
361
362
363
364
365
366
367
368
369
370
371
372
373
374
375
376
377
378
379
380
381
382
383
384
385
386
387
388
389
390
391
392
393
394
395
396
397
398
399
400
401
402
403
404
405
406
407
408
409
410
411
412
413
414
415
416
417
418
419
420
421
422
423
424
425
426
427
428
429
430
431
432
433
434
435
436
437
438
439
440
441
442
443
444
445
446
447
448
449
450
451
452
453
454
455
456
457
458
459
460
461
462
463
464
465
466
467
468
469
470
471
472
473
474
475
476
477
478
479
480
481
482
483
484
485
486
487
488
489
490
491
492
493
494
495
496
497
498
499
500
501
502
503
504
505
506
507
508
509
510
511
512
513
514
515
516
517
518
519
520
521
522
523
524
525
526
527
528
529
530
531
532
533
534
535
536
537
538
539
540
541
542
543
544
545
546
547
548
549
550
551
552
553
554
555
556
557
558
559
560
561
562
563
564
565
566
567
568
569
570
571
572
573
574
575
576
577
578
579
580
581
582
583
584
585
586
587
588
589
590
591
592
593
594
595
596
597
598
599
600
601
602
603
604
605
606
607
608
609
610
611
612
613
614
615
616
617
618
619
620
621
622
623
624
625
626
627
628
629
630
631
632
633
634
635
636
637
638
639
640
641
642
643
644
645
646
647
648
649
650
651
652
653
654
655
656
657
658
659
660
661
662
663
664
665
666
667
668
669
670
671
672
673
674
675
676
677
678
679
680
681
682
683
684
685
686
687
688
689
690
691
692
693
694
695
696
697
698
699
700
701
702
703
704
705
706
707
708
709
710
711
712
713
714
715
716
717
718
719
720
721
722
723
724
725
726
727
728
729
730
731
732
733
734
735
736
737
738
739
740
741
742
743
744
745
746
747
748
749
750
751
752
753
754
755
756
757
758
759
760
761
762
763
764
765
766
767
768
769
770
771
772
773
774
775
776
777
778
779
780
781
782
783
784
785
786
787
788
789
790
791
792
793
794
795
796
797
798
799
800
801
802
803
804
805
806
807
808
809
810
811
812
813
814
815
816
817
818
819
820
821
822
823
824
825
826
827
828
829
830
831
832
833
834
835
836
837
838
839
840
841
842
843
844
845
846
847
848
849
850
851
852
853
854
855
856
857
858
859
860
861
862
863
864
865
866
867
868
869
870
871
872
873
874
875
876
877
878
879
880
881
882
883
884
885
886
887
Comparison of Octree Traversal Algorithms
=========================================
Author: Vlastimil Havran
Department of Computer Science and Engineering
Faculty of Electrical Engineering
Czech Technical University in Prague
e-mail: havran@fel.cvut.cz
Date: 05/Aug/1999
This text is additional material to the Ray Tracing News article on
octrees in RTNv12v2
(http://www.acm.org/tog/resources/RTNews/html/rtnv12n2.html#art4).
and follows the article on grid spatial data structures
http://www.acm.org/tog/resources/RTNews/html/rtnv12n1.html#art3 (also
http://www.acm.org/tog/resources/SPD/havran_stats.txt) in the sense
that reported set of parameters parameters is the same, so octrees can
be directly compared with hierarchical grids as well. Interested
reader can find there also the invariants for these measurements and
therefore we will not include these in this text.
We present here statistics for ray tracing octrees based that was
performed on SPD scenes. The algorithms were implemented in C++ in
GOLEM rendering system (http://www.cgg.cvut.cz/GOLEM). Tests were
conducted on an Intel Pentium II, 350MHz, 128 MBytes RAM, running the
Linux operating system, compiler version egcs-1.1.2, compiler option
-O2.
The scenes are generated by using the default size for the Standard
Procedural Databases (http://www.acm.org/tog/resources/SPD/overview.html).
In addition, the "lattice" scene included in this package is also
used, as well as our own "fluid" scene. This is a fluid simulation
around a ball and it has a mirror in the back, so the whole scene is
mirrored for the viewer. We used this scene for testing along with the
SPD scenes, since it has a reasonable number of objects (2514 spheres
and one polygon) and has many reflected rays.
We report here set of parameters that can be expressed for octrees and
for both uniform and hierarchical grids. They are reported in the
following tables. The meaning of parameters is as follows:
N_IN[-] .. the number of hierarchical cells(interior nodes)
N_V[-] .. the number of elementary cells(leaves) in the hierarchy.
These cells contain references to objects.
N_EV[-] .. the number of empty elementary cells
N_OIV[-] .. the number of references to objects in the elementary cells
N_IT[-] .. the number of intersection tests per one ray
N_TS[-] .. the number of traversal steps per one ray
N_ETS[-] .. the number of elementary cells traversed per one ray
N_EETS[-] .. the number of empty elementary cells traversed per one ray
T_B[s] .. the time needed to construct the octree data structure
T_TR[s] .. the time needed to ray trace the whole image, it includes
both ray shooting and color evaluation according to the
Phong shading model.
Execution times were measured using "getrusage" function and process
user time is reported. We do not use additional acceleration tricks
such as mail boxes for objects, shadow cache, etc. The measurements
should thus reflect the properties of octrees as the spatial data
structures well.
General notes:
1) The root node is in the depth zero (depth is in some articles also
called level).
2) XXX-C means center subdivision; when subdividing the node into eight
octants, the subdivision planes are positioned in the center of the bounding
box; all the octants created are thus of the same size.
3) XXX-A means adaptive, cost estimate subdivision. The subdivision
planes are not positioned in the center, but in the minimum of the
cost function estimate along the appropriate axis. This cost function
is according to the article:
K. Y. Whang et al: {Octree-R: an adaptive octree for efficient
ray tracing", IEEE TVCG, Vol. 1, No. 4, pp.343-349, 1995.
or:
MacDonald and Booth {Heuristics for Ray tracing Using Space
Subdivision}, Visual Computer, pp.153-165, Vol 6, No. 6, 1990}.
The $N$ positions between spatial and object median are evaluated
using cost function and the one with the minimum cost is taken, we
chose $N=10$. To be explicit, when the bounding box is of the size
$a x b x c$ and the splitting plane is positioned perpendicular to
the axis of size $a$ creating two children of sizes $ t x b x c $ and
$ (a-t) x b x c $, then cost function estimate is:
C = (left + cut) * (t * 2.0 * (b + c) + b * c) +
(right + cut) * ((a-t) * 2.0 * (b + c) + b * c);
, where $left$ and $right$ is the number of objects on the left and
right of splitting plane respectively, and $cut$ is the number of
objects straddling the splitting plane.
The cost function estimate is evaluated independently for all three
axes.
4) When assigning the objects to the suboctants or to leaves, the decision
if to assign was implemented using bounding boxes of the objects; no exact
object surface with the octant(axis-aligned bounging box) was used.
5) The termination criteria to declare the current node a leaf
were taken the ones mostly used:
a) when the number of objects reffered to the current octree node is
smaller than or equal to a constant MO, then declare this node a
leaf. We chose MO=1.
b) when the depth of the node reached the maximum depth, then also
declare the node a leaf. The maximum depth was set to 4,5,6, and 7,
corresponding results are in the columns.
Statistics:
==========================================================================
Octree84-C
----------
We call by this name the implementation according to the article:
A. S. Glassner: {Space Subdivision for Fast Ray Tracing}, IEEE CG&A,
pp. 15-22, October 1984.
The implementation has been changed in the sense the representation of
the octree does not use hash table, but a node with eight pointers.
The subdivision is in the center of the current bounding box as described
above.
maximum depth
scene: 4 5 6 7
BALLS
N_IN 57 117 304 1108
N_V 400 820 2129 7757
N_EV 300 570 1038 2905
N_OIV 9171 10946 15611 27288
N_IT 1787.00 577.70 209.60 94.75
N_TS 48.53 86.96 123.20 167.00
N_ETS 9.93 15.39 19.88 24.71
N_EETS 3.67 9.52 12.54 16.12
N_B[s] 0.14 0.16 0.20 0.29
N_TR[s] 626.60 227.70 121.80 102.30
FLUID
N_IN 14 35 118 423
N_V 99 246 827 2962
N_EV 35 87 313 1164
N_OIV 2988 3731 5248 9355
N_IT 978.00 246.90 88.15 34.73
N_TS 15.79 22.12 32.09 48.18
N_ETS 3.63 4.48 5.68 7.42
N_EETS 0.78 0.95 1.37 2.44
N_B[s] 0.05 0.06 0.07 0.11
N_TR[s] 218.00 61.68 30.50 22.85
GEARS
N_IN 265 1405 5837 28447
N_V 1856 9836 40860 199130
N_EV 652 4088 10334 28228
N_OIV 39440 85832 235526 879434
N_IT 157.50 71.38 44.22 39.13
N_TS 27.46 46.49 65.25 88.60
N_ETS 5.71 8.33 10.64 13.20
N_EETS 2.07 4.64 5.66 6.27
N_B[s] 0.27 0.46 0.97 2.69
N_TR[s] 316.10 247.00 260.60 339.50
LATTICE
N_IN 585 4681 17993 56235
N_V 4096 32768 125952 393646
N_EV 0 7744 28732 52822
N_OIV 22112 49600 147494 502272
N_IT 28.60 13.80 11.07 10.82
N_TS 22.03 47.88 67.59 77.21
N_ETS 4.41 7.98 10.35 11.36
N_EETS 0.00 1.71 2.91 3.17
N_B[s] 0.23 0.39 0.76 1.90
N_TR[s] 64.53 56.37 61.37 65.65
MOUNT
N_IN 232 1019 4716 22630
N_V 1625 7134 33013 158411
N_EV 777 3060 11720 45049
N_OIV 18107 34351 90456 324918
N_IT 42.53 23.72 18.30 18.52
N_TS 22.43 30.89 43.68 60.08
N_ETS 4.92 6.08 7.64 9.44
N_EETS 1.82 2.33 2.83 3.31
N_B[s] 0.17 0.25 0.49 1.30
N_TR[s] 38.70 32.40 34.76 41.19
RINGS
N_IN 231 1216 6925 38648
N_V 1618 8513 48476 270537
N_EV 416 2127 10281 49888
N_OIV 22505 44555 133929 565631
N_IT 107.80 47.90 35.12 35.20
N_TS 32.34 53.74 81.90 120.80
N_ETS 6.93 9.92 13.38 17.65
N_EETS 2.91 4.98 6.69 8.29
N_B[s] 0.23 0.34 0.64 1.95
N_TR[s] 179.80 113.50 111.80 133.30
TEAPOT
N_IN 227 1001 4100 18066
N_V 1590 7008 28701 126463
N_EV 777 3450 12327 38316
N_OIV 18845 34072 83551 295865
N_IT 184.00 78.30 45.63 40.02
N_TS 33.66 48.74 64.67 83.40
N_ETS 7.61 9.73 11.69 13.75
N_EETS 5.14 7.07 8.61 9.53
N_B[s] 0.18 0.29 0.47 1.14
N_TR[s] 50.55 33.17 30.72 34.12
TETRA
N_IN 305 1369 6189 28413
N_V 2136 9584 43324 198892
N_EV 1072 4764 21100 80444
N_OIV 13312 32768 110592 512000
N_IT 120.00 63.58 46.77 47.07
N_TS 21.54 32.08 44.09 58.09
N_ETS 4.72 6.20 7.67 9.21
N_EETS 3.05 4.48 5.93 7.22
N_B[s] 0.10 0.17 0.40 1.56
N_TR[s] 7.27 6.34 6.79 8.00
TREE
N_IN 53 101 186 352
N_V 372 708 1303 2465
N_EV 278 556 1054 1801
N_OIV 9029 9670 10915 13725
N_IT 8066.00 4201.00 2098.00 741.30
N_TS 63.48 113.60 169.00 219.30
N_ETS 13.10 20.24 27.16 32.74
N_EETS 3.67 9.91 17.67 23.33
N_B[s] 0.16 0.20 0.24 0.29
N_TR[s] 2907.00 1537.00 805.30 338.20
===========================================================================
Octree84-A
----------
We call by this name the implementation according to the article:
A. S. Glassner: {Space Subdivision for Fast Ray Tracing}, IEEE CG&A,
pp. 15-22, October 1984.
The implementation has been changed in the sense the representation of
the octree does not use hash table, but a node with eight pointers.
The subdivision uses cost function estimate as described above.
maximum depth
scene: 4 5 6 7
BALLS
N_IN 131 661 3077 15283
N_V 918 4628 21540 106982
N_EV 214 1202 4233 14059
N_OIV 10160 16289 42107 172506
N_IT 81.20 28.62 16.29 14.85
N_TS 27.73 40.09 52.18 64.91
N_ETS 6.63 8.35 9.83 11.21
N_EETS 3.23 4.62 5.48 6.00
N_B[s] 0.55 0.73 1.06 2.05
N_TR[s] 45.74 35.40 36.88 42.18
FLUID
N_IN 96 414 1676 6709
N_V 673 2899 11733 46964
N_EV 176 844 2941 6844
N_OIV 5059 9850 28281 111566
N_IT 66.83 27.99 16.60 14.40
N_TS 25.20 37.40 51.29 62.20
N_ETS 5.95 7.64 9.32 10.49
N_EETS 1.83 2.87 3.97 4.49
N_B[s] 0.21 0.31 0.49 1.08
N_TR[s] 25.31 20.74 21.88 24.29
GEARS
N_IN 349 1709 10301 59649
N_V 2444 11964 72108 417544
N_EV 580 1120 5300 20092
N_OIV 31144 95016 344580 1737482
N_IT 68.78 41.18 29.43 30.75
N_TS 23.50 31.33 46.99 66.50
N_ETS 5.15 6.18 8.11 10.24
N_EETS 2.60 2.69 2.92 3.24
N_B[s] 0.79 1.26 2.84 9.83
N_TR[s] 206.60 209.70 246.10 330.00
LATTICE
N_IN 585 4681 18218 45496
N_V 4096 32768 127527 318473
N_EV 0 7133 33332 34508
N_OIV 18768 42789 121693 467745
N_IT 24.00 9.97 6.71 6.73
N_TS 22.33 46.89 62.82 64.34
N_ETS 4.47 7.82 9.73 9.87
N_EETS 0.00 2.65 4.55 4.60
N_B[s] 0.86 1.23 2.17 4.35
N_TR[s] 60.03 49.32 51.75 52.90
MOUNT
N_IN 312 1534 7893 42826
N_V 2185 10739 55252 299783
N_EV 866 3615 14018 41862
N_OIV 21489 47351 150938 692664
N_IT 31.38 17.58 14.00 15.77
N_TS 22.61 29.26 38.53 51.66
N_ETS 4.86 5.77 6.90 8.34
N_EETS 1.99 2.51 2.91 3.14
N_B[s] 0.68 1.01 1.86 5.22
N_TR[s] 32.49 28.34 30.23 36.33
RINGS
N_IN 347 2055 12898 73091
N_V 2430 14386 90287 511638
N_EV 406 1718 10688 41430
N_OIV 20867 54320 210965 1175184
N_IT 58.00 32.11 26.16 31.31
N_TS 30.24 44.74 70.31 103.40
N_ETS 6.58 8.55 11.67 15.29
N_EETS 3.39 3.92 5.01 5.84
N_B[s] 0.84 1.21 2.41 7.54
N_TR[s] 109.30 86.47 92.81 119.40
TEAPOT
N_IN 330 1703 9055 49691
N_V 2311 11922 63386 347838
N_EV 853 3462 14005 49218
N_OIV 25332 59058 199511 922951
N_IT 106.30 51.53 36.74 37.72
N_TS 35.82 49.20 63.93 81.95
N_ETS 8.02 9.87 11.66 13.63
N_EETS 5.65 6.77 7.69 8.33
N_B[s] 0.88 1.27 2.36 6.61
N_TR[s] 34.77 27.65 28.56 33.27
TETRA
N_IN 325 1485 6449 30617
N_V 2276 10396 45144 214320
N_EV 1116 5432 20976 77992
N_OIV 13792 34304 120336 587888
N_IT 99.56 45.46 23.03 25.08
N_TS 21.15 27.69 33.72 39.05
N_ETS 4.68 5.56 6.26 6.82
N_EETS 3.40 4.48 5.33 5.70
N_B[s] 0.38 0.61 1.25 3.82
N_TR[s] 6.48 5.31 5.05 5.57
TREE
N_IN 71 278 1130 4300
N_V 498 1947 7911 30101
N_EV 231 837 3511 11205
N_OIV 9489 11352 17245 44516
N_IT 236.40 66.88 30.99 24.33
N_TS 31.83 37.13 42.18 45.84
N_ETS 8.38 9.13 9.75 10.16
N_EETS 5.34 6.01 6.64 6.95
N_B[s] 0.74 0.90 1.09 1.42
N_TR[s] 94.44 44.67 35.33 34.84
===============================================================================
Octree89-C
----------
We call by this name the implementation according to the article:
H. Samet: {Implementing Ray Tracing with Octrees and Neighbor
Finding}, C&G Vol. 13, No. 4, pp.445-460, 1989.
The subdivision is in the center of the current bounding box as
described above.
maximum depth
scene: 4 5 6 7
BALLS
N_IN 57 117 304 1108
N_V 400 820 2129 7757
N_EV 300 570 1038 2905
N_OIV 9171 10946 15611 27288
N_IT 1805.00 567.80 212.50 93.67
N_TS 37.90 59.79 78.10 97.87
N_ETS 9.93 15.40 19.88 24.71
N_EETS 3.67 9.52 12.55 16.12
N_B[s] 0.12 0.16 0.19 0.27
N_TR[s] 627.00 206.30 97.29 67.47
FLUID
N_IN 14 35 118 423
N_V 99 246 827 2962
N_EV 35 87 313 1164
N_OIV 2988 3731 5248 9355
N_IT 993.50 246.20 88.59 34.57
N_TS 13.08 16.90 22.12 29.55
N_ETS 3.63 4.48 5.68 7.43
N_EETS 0.78 0.96 1.37 2.44
N_B[s] 0.04 0.05 0.07 0.09
N_TR[s] 222.40 60.33 28.34 18.80
GEARS
N_IN 265 1405 5837 28447
N_V 1856 9836 40860 199130
N_EV 652 4088 10334 28228
N_OIV 39440 85832 235526 879434
N_IT 153.40 72.33 43.96 39.27
N_TS 22.70 34.16 43.74 54.45
N_ETS 5.70 8.33 10.64 13.20
N_EETS 2.07 4.65 5.66 6.27
N_B[s] 0.25 0.38 0.69 1.91
N_TR[s] 302.70 229.00 236.30 303.40
LATTICE
N_IN 585 4681 17993 56235
N_V 4096 32768 125952 393646
N_EV 0 7744 28732 52822
N_OIV 22112 49600 147494 502272
N_IT 28.91 13.70 11.06 10.83
N_TS 15.97 31.24 41.58 46.42
N_ETS 4.41 7.98 10.35 11.36
N_EETS 0.00 1.71 2.91 3.17
N_B[s] 0.18 0.34 0.65 1.64
N_TR[s] 60.72 45.22 47.68 50.58
MOUNT
N_IN 232 1019 4716 22630
N_V 1625 7134 33013 158411
N_EV 777 3060 11720 45049
N_OIV 18107 34351 90456 324918
N_IT 43.00 23.50 18.44 18.44
N_TS 18.52 23.54 30.12 37.56
N_ETS 4.93 6.09 7.65 9.45
N_EETS 1.82 2.34 2.83 3.31
N_B[s] 0.15 0.22 0.42 1.05
N_TR[s] 35.96 28.27 28.90 32.07
RINGS
N_IN 231 1216 6925 38648
N_V 1618 8513 48476 270537
N_EV 416 2127 10281 49888
N_OIV 22505 44555 133929 565631
N_IT 108.30 47.72 35.12 35.17
N_TS 25.53 38.01 52.46 70.23
N_ETS 6.94 9.92 13.38 17.65
N_EETS 2.91 4.98 6.69 8.30
N_B[s] 0.21 0.32 0.54 1.52
N_TR[s] 173.70 101.80 94.38 107.60
TEAPOT
N_IN 227 1001 4100 18066
N_V 1590 7008 28701 126463
N_EV 777 3450 12327 38316
N_OIV 18845 34072 83551 295865
N_IT 184.50 78.06 45.77 39.95
N_TS 27.22 35.88 43.95 52.40
N_ETS 7.61 9.73 11.70 13.76
N_EETS 5.14 7.07 8.61 9.53
N_B[s] 0.19 0.25 0.45 0.92
N_TR[s] 46.44 27.16 22.97 23.92
TETRA
N_IN 305 1369 6189 28413
N_V 2136 9584 43324 198892
N_EV 1072 4764 21100 80444
N_OIV 13312 32768 110592 512000
N_IT 120.90 63.66 47.05 47.35
N_TS 17.75 23.91 30.14 36.54
N_ETS 4.75 6.23 7.71 9.24
N_EETS 3.07 4.51 5.96 7.24
N_B[s] 0.09 0.16 0.34 1.16
N_TR[s] 6.60 5.23 5.24 5.90
TREE
N_IN 53 101 186 352
N_V 372 708 1303 2465
N_EV 278 556 1054 1801
N_OIV 9029 9670 10915 13725
N_IT 8060.00 4205.00 2096.00 742.00
N_TS 51.49 80.13 107.80 130.10
N_ETS 13.10 20.24 27.16 32.74
N_EETS 3.67 9.91 17.67 23.34
N_B[s] 0.16 0.19 0.24 0.27
N_TR[s] 2887.00 1510.00 769.70 288.50
===============================================================================
Octree93-C
----------
We call by this name the implementation according to the article:
I. Gargantini and H.H. Atkinson: {Ray Tracing and Octree: Numerical
Evaluation of the First Intersection}, CGF, Vol. 12, No. 4,
pp. 199-210, 1993
The subdivision is in the center of the current bounding box as described
above.
maximum depth
scene: 4 5 6 7
BALLS
N_IN 57 117 304 1108
N_V 400 820 2129 7757
N_EV 300 570 1038 2905
N_OIV 9171 10946 15611 27288
N_IT 1794.00 558.80 207.30 89.93
N_TS 20.58 31.68 40.86 50.67
N_ETS 15.65 20.68 26.45 32.34
N_EETS 9.42 14.86 19.25 23.99
N_B[s] 0.13 0.15 0.20 0.25
N_TR[s] 624.90 218.60 116.20 91.43
FLUID
N_IN 14 35 118 423
N_V 99 246 827 2962
N_EV 35 87 313 1164
N_OIV 2988 3730 5247 9353
N_IT 978.80 238.80 82.28 31.21
N_TS 8.21 10.25 12.94 16.65
N_ETS 5.90 7.37 9.26 11.50
N_EETS 3.06 3.89 5.04 6.70
N_B[s] 0.04 0.05 0.07 0.10
N_TR[s] 223.50 61.33 29.87 22.00
GEARS
N_IN 265 1405 5837 28447
N_V 1856 9836 40860 199130
N_EV 652 4088 10334 28228
N_OIV 39440 85832 235526 879434
N_IT 150.10 69.62 39.72 34.50
N_TS 12.86 18.71 23.42 28.49
N_ETS 8.82 11.40 14.68 18.78
N_EETS 5.23 7.80 9.95 12.30
N_B[s] 0.25 0.40 0.73 2.08
N_TR[s] 314.10 246.10 256.60 327.90
LATTICE
N_IN 585 4681 17993 56235
N_V 4096 32768 125952 393646
N_EV 0 7744 28732 52822
N_OIV 22112 49600 147494 502272
N_IT 26.94 12.32 9.52 9.15
N_TS 10.13 17.68 22.60 24.52
N_ETS 7.40 12.46 15.41 16.58
N_EETS 3.29 6.67 8.75 9.46
N_B[s] 0.20 0.38 0.80 1.85
N_TR[s] 65.89 55.45 59.00 62.19
MOUNT
N_IN 232 1019 4716 22630
N_V 1625 7134 33013 158411
N_EV 777 3060 11720 45049
N_OIV 18107 34351 90456 324918
N_IT 41.97 22.61 17.47 17.18
N_TS 10.80 13.37 16.64 20.23
N_ETS 7.35 9.09 11.58 14.44
N_EETS 4.34 5.46 6.95 8.62
N_B[s] 0.15 0.24 0.43 1.07
N_TR[s] 39.72 32.71 34.42 39.12
RINGS
N_IN 231 1216 6925 38648
N_V 1618 8513 48476 270537
N_EV 416 2127 10281 49888
N_OIV 22505 44555 133929 565631
N_IT 108.00 47.48 34.87 34.80
N_TS 14.66 21.14 28.59 37.65
N_ETS 10.37 14.26 19.43 26.30
N_EETS 6.35 9.33 12.78 17.01
N_B[s] 0.20 0.31 0.57 1.66
N_TR[s] 181.10 112.10 108.80 126.30
TEAPOT
N_IN 227 1001 4100 18066
N_V 1590 7008 28701 126463
N_EV 777 3450 12327 38316
N_OIV 18845 34072 83551 295865
N_IT 182.70 76.40 44.21 37.16
N_TS 14.79 19.23 23.31 27.36
N_ETS 9.75 12.02 14.34 17.11
N_EETS 7.30 9.40 11.33 13.17
N_B[s] 0.19 0.25 0.43 1.03
N_TR[s] 48.92 30.82 27.78 29.89
TETRA
N_IN 305 1369 6189 28413
N_V 2136 9584 43324 198892
N_EV 1072 4764 21100 80444
N_OIV 13312 32768 110592 512000
N_IT 117.20 61.11 44.76 44.20
N_TS 9.59 12.70 15.82 18.98
N_ETS 6.18 7.66 9.11 10.80
N_EETS 4.53 5.99 7.45 8.93
N_B[s] 0.09 0.16 0.34 1.24
N_TR[s] 6.93 5.83 6.10 6.96
TREE
N_IN 53 101 186 352
N_V 372 708 1303 2465
N_EV 278 556 1054 1801
N_OIV 9029 9670 10915 13725
N_IT 8057.00 4201.00 2092.00 738.00
N_TS 26.62 41.00 54.87 65.90
N_ETS 22.36 30.41 36.46 41.63
N_EETS 12.93 20.08 26.99 32.40
N_B[s] 0.16 0.20 0.24 0.28
N_TR[s] 2893.00 1501.00 785.80 317.60
===============================================================================
Octree93-A
----------
We call by this name the implementation according to the article:
I. Gargantini and H.H. Atkinson: {Ray Tracing and Octree: Numerical
Evaluation of the First Intersection}, CGF, Vol. 12, No. 4, pp. 199-210,
1993.
The subdivision uses cost function estimate as described above.
maximum depth
scene: 4 5 6 7
BALLS
N_IN 131 661 3077 15291
N_V 918 4628 21540 107038
N_EV 214 1202 4233 14103
N_OIV 10160 16289 42109 172555
N_IT 84.31 26.38 15.25 13.58
N_TS 12.95 16.64 19.75 22.53
N_ETS 9.45 11.41 13.33 15.27
N_EETS 6.10 7.77 9.16 10.39
N_B[s] 0.65 0.83 1.23 2.35
N_TR[s] 47.05 33.80 34.99 38.86
FLUID
N_IN 96 414 1675 6706
N_V 673 2899 11726 46943
N_EV 176 844 2933 6834
N_OIV 5059 9850 28280 111558
N_IT 62.24 24.61 14.06 11.90
N_TS 11.81 15.36 18.72 20.85
N_ETS 9.31 11.42 13.25 14.57
N_EETS 5.30 6.87 8.33 9.24
N_B[s] 0.24 0.34 0.58 1.25
N_TR[s] 24.51 19.57 20.16 21.74
GEARS
N_IN 349 1709 10301 59649
N_V 2444 11964 72108 417544
N_EV 580 1120 5300 20092
N_OIV 31144 95016 344580 1737490
N_IT 65.44 39.09 24.59 26.25
N_TS 11.70 14.29 17.89 22.09
N_ETS 7.11 8.96 11.85 15.51
N_EETS 4.63 5.60 7.17 9.16
N_B[s] 0.92 1.46 3.30 10.51
N_TR[s] 210.90 212.00 245.50 323.60
LATTICE
N_IN 585 4681 18218 45496
N_V 4096 32768 127527 318473
N_EV 0 7133 33332 34508
N_OIV 18768 42789 121693 467745
N_IT 23.05 8.99 5.67 5.66
N_TS 10.27 17.62 21.50 21.80
N_ETS 7.71 11.25 12.55 12.67
N_EETS 3.44 6.48 8.06 8.14
N_B[s] 0.97 1.45 2.53 4.57
N_TR[s] 62.33 50.15 51.39 52.36
MOUNT
N_IN 311 1531 7889 42809
N_V 2178 10718 55224 299664
N_EV 861 3605 14020 41864
N_OIV 21484 47338 150888 692494
N_IT 30.89 16.56 13.14 14.47
N_TS 10.71 12.72 15.07 17.89
N_ETS 7.07 8.30 10.01 12.40
N_EETS 4.28 5.15 6.21 7.52
N_B[s] 0.82 1.18 2.17 5.77
N_TR[s] 33.76 29.24 30.51 35.16
RINGS
N_IN 347 2055 12900 73091
N_V 2430 14386 90301 511638
N_EV 406 1718 10700 41425
N_OIV 20867 54320 210963 1175103
N_IT 57.85 31.81 25.99 30.83
N_TS 13.98 18.65 25.54 33.30
N_ETS 9.17 12.56 17.68 24.00
N_EETS 6.00 7.96 11.06 14.64
N_B[s] 0.94 1.38 2.65 8.03
N_TR[s] 111.30 87.69 92.60 115.90
TEAPOT
N_IN 330 1703 9053 49684
N_V 2311 11922 63372 347789
N_EV 853 3460 13985 49191
N_OIV 25332 59055 199518 922872
N_IT 103.20 47.91 33.59 33.90
N_TS 15.42 19.16 22.89 26.82
N_ETS 9.76 11.91 14.41 17.45
N_EETS 7.56 9.19 10.90 12.74
N_B[s] 1.02 1.46 2.68 7.25
N_TR[s] 33.05 25.33 25.67 29.27
TETRA
N_IN 325 1485 6413 30521
N_V 2276 10396 44892 213648
N_EV 1116 5468 20784 77404
N_OIV 13792 34112 120048 587504
N_IT 97.06 44.97 24.08 28.24
N_TS 9.59 11.89 13.85 15.60
N_ETS 5.76 6.63 7.36 8.40
N_EETS 4.49 5.53 6.38 7.14
N_B[s] 0.45 0.70 1.42 4.17
N_TR[s] 6.21 5.09 4.94 5.60
TREE
N_IN 71 278 1130 4301
N_V 498 1947 7911 30108
N_EV 231 837 3509 11205
N_OIV 9489 11352 17247 44514
N_IT 235.20 66.38 30.38 23.79
N_TS 14.83 16.37 17.64 18.46
N_ETS 11.23 12.05 12.67 13.12
N_EETS 8.21 8.95 9.57 9.96
N_B[s] 0.84 1.02 1.26 1.65
N_TR[s] 91.05 40.57 30.88 29.90
==============================================================================
Octree comparison
-----------------
In the following table we report the best results for all the octrees
above, so these can be compared for one scene at the same line. As in
the previous article, we let the reader to make conclusion himself, we
presented our opinion in our RTNews article.
md .. the maximum depth setting for the best performance and octree algorithm.
Octree method
-----------------------------------------------------------------------
------ Octree84-C Octree84-A Octree89-C Octree93-C Octree93-A
scene:
BALLS md = 7 md = 5 md = 7 md = 7 md = 5
N_IN 1108 661 1108 1108 661
N_V 7757 4628 7757 7757 4628
N_EV 2905 1202 2905 2905 1202
N_OIV 27288 16289 27288 27288 16289
N_IT 94.75 28.62 93.67 89.93 26.38
N_TS 167.00 40.09 97.87 50.67 16.64
N_ETS 24.71 8.35 24.71 32.34 11.41
N_EETS 16.12 4.62 16.12 23.99 7.77
N_B[s] 0.29 6.17 0.27 0.25 0.83
N_TR[s] 102.30 35.40 67.47 91.43 33.80
FLUID md = 7 md = 5 md = 7 md = 7 md = 5
N_IN 423 414 423 423 414
N_V 2962 2899 2962 2962 2899
N_EV 1164 844 1164 1164 844
N_OIV 9355 9850 9355 9353 9850
N_IT 34.73 27.99 34.57 31.21 24.61
N_TS 48.18 37.40 29.55 16.65 15.36
N_ETS 7.42 7.64 7.43 11.50 11.42
N_EETS 2.44 2.87 2.44 6.70 6.87
N_B[s] 0.11 2.54 0.09 0.10 0.34
N_TR[s] 22.85 20.74 18.80 22.00 19.57
GEARS md = 5 md = 5 md = 5 md = 5 md = 4
N_IN 1405 349 1405 1405 349
N_V 9836 2444 9836 9836 2444
N_EV 4088 580 4088 4088 580
N_OIV 85832 31144 85832 85832 31144
N_IT 71.38 68.78 72.33 69.62 65.44
N_TS 46.49 23.50 34.16 18.71 11.70
N_ETS 8.33 5.15 8.33 11.40 7.11
N_EETS 4.64 2.60 4.65 7.80 4.63
N_B[s] 0.46 0.79 0.38 0.40 0.92
N_TR[s] 247.00 206.60 229.00 246.10 210.90
LATTICE md = 5 md = 5 md = 7 md = 5 md = 4
N_IN 4681 4681 4681 4681 4681
N_V 32768 32768 32768 32768 32768
N_EV 7744 7133 7744 7744 7133
N_OIV 49600 42789 49600 49600 42789
N_IT 13.80 9.97 13.70 12.32 8.99
N_TS 47.88 46.89 31.24 17.68 17.62
N_ETS 7.98 7.82 7.98 12.46 11.25
N_EETS 1.71 2.65 1.71 6.67 6.48
N_B[s] 0.39 1.23 0.34 0.38 1.45
N_TR[s] 56.37 49.32 45.22 55.45 50.15
MOUNT md = 6 md = 5 md = 6 md = 5 md = 4
N_IN 1019 1534 1019 1019 1531
N_V 7134 10739 7134 7134 10718
N_EV 3060 3615 3060 3060 3605
N_OIV 34351 47351 34351 34351 47338
N_IT 23.72 17.58 23.50 22.61 16.56
N_TS 30.89 29.26 23.54 13.37 12.72
N_ETS 6.08 5.77 6.09 9.09 8.30
N_EETS 2.33 2.51 2.34 5.46 5.15
N_B[s] 0.25 1.01 0.22 0.24 1.18
N_TR[s] 32.40 28.34 28.27 32.71 29.24
RINGS md = 6 md = 5 md = 6 md = 4 md = 5
N_IN 6925 2055 6925 6925 2055
N_V 48476 14386 48476 48476 14386
N_EV 10281 1718 10281 10281 1718
N_OIV 133929 54320 133929 133929 54320
N_IT 35.12 32.11 35.12 34.87 31.81
N_TS 81.90 44.74 52.46 28.59 18.65
N_ETS 13.38 8.55 13.38 19.43 12.56
N_EETS 6.69 3.92 6.69 12.78 7.96
N_B[s] 0.64 1.21 0.54 0.57 1.38
N_TR[s] 111.80 86.47 94.38 108.80 87.69
TEAPOT md = 6 md = 6 md = 6 md = 6 md = 5
N_IN 4100 4100 4100 4100 1703
N_V 28701 28701 28701 28701 11922
N_EV 12327 12327 12327 12327 3460
N_OIV 83551 83551 83551 83551 59055
N_IT 45.63 45.63 45.77 44.21 47.91
N_TS 64.67 64.67 43.95 23.31 19.16
N_ETS 11.69 11.69 11.70 14.34 11.91
N_EETS 8.61 8.61 8.61 11.33 9.19
N_B[s] 0.47 0.47 0.45 0.43 1.46
N_TR[s] 30.72 30.72 22.97 27.78 25.33
TETRA md = 5 md = 6 md = 5(6) md = 5 md = 5
N_IN 1369 6449 1369 1369 6413
N_V 9584 45144 9584 9584 44892
N_EV 4764 20976 4764 4764 20784
N_OIV 32768 120336 32768 32768 120048
N_IT 63.58 23.03 63.66 61.11 24.08
N_TS 32.08 33.72 23.91 12.70 13.85
N_ETS 6.20 6.26 6.23 7.66 7.36
N_EETS 4.48 5.33 4.51 5.99 6.38
N_B[s] 0.17 1.25 0.16 0.16 1.42
N_TR[s] 6.34 5.05 5.23 5.83 4.94
TREE md = 7 md = 7 md = 7 md = 7 md = 7
N_IN 352 4300 352 352 4301
N_V 2465 30101 2465 2465 30108
N_EV 1801 11205 1801 1801 11205
N_OIV 13725 44516 13725 13725 44514
N_IT 741.30 24.33 742.00 738.00 23.79
N_TS 219.30 45.84 130.10 65.90 18.46
N_ETS 32.74 10.16 32.74 41.63 13.12
N_EETS 23.33 6.95 23.34 32.40 9.96
N_B[s] 0.29 1.42 0.27 0.28 1.65
N_TR[s] 338.20 34.84 288.50 317.60 29.90
------------------
END