19 Class II Method 1 Octahedral Coordinates
1Two tables provide Class II Method 1 information for the octa breakdown in the following array of frequencies: . (The reader will remember that all Class II frequencies are even.)
2 For the arctan notation see the introductory page for Class I octa coordinates.
3 To simplify elliptical breakdowns, data for an area equivalent to the entire octa face are given. This consists of the Class II triangle, its downward-pointing reflection below it, and portions to the left Spherical Octa face and right of the latter: see Diagram 19.1. For spheres use only the symmetry triangle (Diagrams 12.4 and 19.2). For ellipsoids of revolution (one cross-section circular) use the left half of the face. When both roofline and floorplan are non-arcular use the entire face.
4 Class II triangle coordinates were obtained by an HP-65 program V using Equations 12.1 and 12.3. A second program then obtained the remaining points by successive rotations using Equations 14.1, 14.2.
64v 8v 16v | 9e | |
100,0 0,0 0,0 | ||
21arctan 72/225 5-3859771 22arctan /2/225 5.3859771 | ||
23O rd CXJ 24c * 25CXJ CXJ CXJ 26O rd 27rd rd | 33arctan /2/49 11.4217537 34arctan 71/49 8.1301024 35arctan /2/49 11.4217537 | |
47arctan 718/169 18.0744548 48arctan 710/169 13.6717877 49arctan 710/169 13.6717877 50arctan 718/169 18.0744548 | ||
51o rd cxj cn-=r 52O rd CXJ 53CXJ CXJ CXJ 54O rd 55rd rd | 63arctan 72/9 25.2394018 64arctan 75/36 20.4393176 65arctan 1/3 18.4349488 66arctan 75/36 20.4393176 67arctan 72/9 25.2394018 | |
83arctan 750/121 32.7338966 84arctan 734/121 27.9274604 85arctan 726/121 24.8699503 86arctan 726/121 24.8699503 87arctan 734/121 27-9274604 88arctan 750/121 32.7338966 | ||
108arctan /18/25 40.3155422 109arctan 713/25 35.7957599 110arctan 7275 32.3115332 111arctan 3/5 30.9637565 112arctan /2/5 32.3115332 113arctan 713/25 35.7957599 114arctan 718/25 40.3155422 | ||
134arctan 798/81 47.7248561 135arctan 774/81 43.7057841 136arctan /58/8I 40.2377996 137arctan 750/81 38.1558065 138arctan 750/81 38.1558065 139arctan /58/81 40.2377996 140arctan 774/81 43.7057841 141arctan 798/81 47.7248561 | ||
155arctan /2 54.7356103 156arctan 5/4 51.3401917 157arctan 7577 48.1896851 158arctan ✓ 17/16 45.8682508 159arctan 1 45.0000000 | ||
1604v | 1618v | 16216v | ||||||
1672,2 | 1684,3 1694,4 | 1708,5 1718,6 1728,7 1738,8 | 174arctan 175arctan 176arctan | 1775/3 1783 1797 | 18059.0362435 18171.5650512 18281.8698976 18390.0000000 | 184arctan 185arctan 186ar ct an 187arctan | 188✓17/16 189/5X 1905/4 191/2 | 19245.8682508 19348.1896851 19451.3401917 19554.7356103 |
1969,0 | 19700.0000000 | 198arctan | 199<32/9 | 20062.0616473 | ||||
2019,1 | 202arctan | 2031/8 | 2047.1250163 | 205arctan | 206<130/49 | 20758.4525461 | ||
2089,2 | 209arctan | 2102/7 | 21115.9453959 | 212arctan | 213✓106/49 | 21455.7882119 | ||
2159,3 | 216arctan | 2171/2 | 21826.5650512 | 219arctan | 220✓90/49 | 22153.5776902 | ||
2229,4 | 223arctan | 2244/5 | 22538.6598083 | 226arctan | 227✓82/49 | 22852.2952350 | ||
2299,5 | 230arctan | 2315/4 | 23251.3401917 | 233arctan | 234✓82/49 | 23552.2952350 | ||
2369,6 | 237arctan | 2382 | 23963.4349488 | 240arctan | 241✓90/69 | 24253.5776902 | ||
2439,7 | 244arctan | 2457/2 | 24674.0546041 | 247arctan | 248✓106/49 | 24955.7882119 | ||
2509,8 | 251arctan | 2528 | 25382.8749836 | 254arctan | 255✓130/49 | 25658.4525461 | ||
2579,9 | 25890.0000000 | 259arctan | 260✓32/9 | 26162.0616473 | ||||
2625,0 | 26310,0 | 26400.0000000 | 265arotan | 266/S’ | 26770.5287793 | |||
26810,1 | 269arctan | 2701/8 | 2717.1250163 | 272arctan | 273<26/5 | 27466.3211550 | ||
2755,1 | 27610,2 | 277arctan | 2781/4 | 27914.0362435 | 280arctan | 281✓34/9 | 28262.7743720 | |
28310,3 | 284arctan | 2853/7 | 28623.1985905 | 287arctan | 288✓29/9 | 28960.8784319 | ||
2905,2 | 29110,4 | 292arctan | 2932/3 | 29433.6900675 | 295arctan | 296✓26/9 | 29759.5296405 | |
29810,5 | 299arctan | 3001 | 30145.0000000 | 302arctan | 303✓25/9 | 30459.0362435 | ||
3055,3 | 30610,6 | 307arctan | 3083/2 | 30956.3099325 | 310arctan | 311✓26/9 | 31259.5296405 | |
31310,7 | 314arctan | 3157/3 | 31666.8014095 | 317arctan | 318✓29/9 | 31960.8784319 | ||
3205,4 | 32110,8 | 322arctan | 3234 | 32475.9637566 | 325arctan | 326✓34/9 | 32762.7743720 | |
32810,9 | 329arctan | 3308 | 33182.8749836 | 332arctan | 333✓26/5 | 33466.3211550 | ||
3355,5 | 33610,10 | 33790.0000000 | 338arctan | 339/b* | 34070.5287793 | |||
34111,0 | 34200.0000000 | 343arctan | 344✓32 | 34579.9750121 | ||||
34611,1 | 347arctan | 3481/8 | 3497.1250163 | 350arctan | 351✓130/9 | 35275.2586068 | ||
35311,2 | 354arctan | 3551/4 | 35614.0362435 | 357arctan | 358✓17/2 | 35971.0681768 | ||
36011,3 | 361arctan | 3623/8 | 36320.5560452 | 364arctan | 365✓146/25 | 36667.5200842 | ||
36711,4 | 368arctan | 3694/7 | 37029.7448813 | 371arctan | 372✓26/5 | 37366.3211550 | ||
37411,5 | 375arctan | 3765/6 | 37739.8055711 | 378arctan | 379✓122/25 | 38065.6447487 | ||
38111,6 | 382arctan | 3836/5 | 38450.1944289 | 385arctan | 386✓122/25 | 38765.6447487 | ||
38811,7 | 389arctan | 3907/4 | 39160.2551187 | 392arctan | 393✓26/5 | 39466.3211550 | ||
39511,8 | 396arctan | 3978/3 | 39869.4439548 | 399arctan | 400✓146/25 | 40167.5200842 | ||
402■11,9 | 403arctan | 4044 | 40575.9637566 | 406arctan | 407<17/2 | 40871.0681768 | ||
40911,10 | 410arctan | 4118 | 41282.8749836 | 413arctan | 414✓130/9 | 41575.2586068 | ||
41611,11 | 41790.0000000 | 418arctan | 419/32 | 42079.9750121 | ||||
4213,0 | 4226,0 | 42312,0 | 42400.0000000 | 42590.0000000 | ||||
42612,1 | 427arctan | 4281/8 | 4297.1250163 | 430arctan | 431/I30 | 43284.9876536 | ||
4336,1 | 43412,2 | 435arctan | 4361/4 | 43714.0362435 | 438arctan | 439✓34 | 44080.2685245 | |
44112,3 | 442arctan | 4433/8 | 44420.5560452 | 445arctan | 446✓146/9 | 44776.0564504 | ||
4483,1 | 4496,2 | 45012,4 | 451arctan | 4521/2 | 45326.5650512 | 454arctan | 455✓10 | 45672.4515994 |
45712,5 | 458arctan | 4595/7 | 46035.5376778 | 461arctan | 462✓37/4 | 46371.7992398 | ||
4646,3 | 46512,6 | 466arctan | 4671 | 46845.0000000 | 469arctan | 4703 | 47171.5650512 | |
47212,7 | 473arctan | 4747/5 | 47554.4623222 | 476arctan | 477✓37/4 | 47871.7992398 | ||
4793,2 | 4806,4 | 48112,8 | 482arctan | 4832 | 48463.4349488 | 485arctan | 486/io | 48772.4515994 |
48812,9 | 489arctan | 4908/3 | 49169.4439548 | 492arctan | 493✓146/9 | 49476.0564504 | ||
4956,5 | 49612,10 | 497arctan | 4984 | 49975.9637566 | 500arctan | 501✓34 | 50280.2685245 | |
5034v 8v 16v | 5041 | 5058 |
528arctan 1/8 7-1250163 529arctan 1/4 14.0362435 530arctan 3/8 20-5560452 531arctan 1/2 26.5650512 532arctan 5/8 32.0053832 533arctan 6/7 40.6012947 534arctan 7/6 49-3987054 535arctan 8/5 57-9946168 536arctan 2 63.4349488 537arctan 8/3 69-4439548 538arctan 4 75-9637566 539arctan 8 82.8749836 | ||
568arctan 3/8 20.5560452 569arctan 1/2 26.5650512 570arctan 5/8 32.0053832 571arctan 3/4 36.8698976 572arctan 1 45-0000000 573arctan 4/3 53.1301024 574arctan 8/5 57-9946168 575arctan 2 63.4349488 576arctan 8/3 69-4439548 | ||
595arctan 5/8 32.0053832 596arctan 3/4 36.8698976 597arctan 7/8 41.1859252 598arctan 8/7 48.8140748 599arctan 4/3 53.1301024 600arctan 8/5 57.9946168 | ||
614arctan 7/8 41.1859252 615arctan 1 45.0000000 616arctan 8/7 48.8140748 | ||
6216v | 62212v | e | ||||
6250,0 | 6260,0 | 00.0000000 | ||||
6291,0 | 63000.0000000 | 631arctan /2/121 | 6327.3260370 | |||
6331,1 | 63490.0000000 | 635arctan /2/121 | 6367.3260370 | |||
6371,0 | 6382,0 | 63900.0000000 | 640arctan /2/25 | 64115.7931691 | ||
6422,1 | 643arctan | 6441 | 64545.0000000 | 646arctan 1/5 | 64711.3099325 | |
6481,1 | 6492,2 | 65090.0000000 | 651arctan /2/25 | 65215.7931691 | ||
6533,0 | 65400.0000000 | 655arctan Z2/9 | 65625.2394018 | |||
6573,1 | 658arctan | 6591/2 | 66026.5650512 | 661arctan /10/81 | 66219.3596487 | |
6633,2 | 664arctan | 6652 | 66663.4349488 | 667arctan /10/81 | 66819.3596487 | |
6693,3 | 67090.0000000 | 671arctan /2/9 | 67225.2394018 | |||
6732,0 | 6744,0 | 67500.0000000 | 676arctan /1/2 | 67735.2643897 | ||
6784,1 | 679arctan | 6801/3 | 68118.4349488 | 682arctan /5/16 | 68329.2059322 | |
6842,1 | 6854,2 | 686arctan | 6871 | 68845.0000000 | 689arctan 1/2 | 69026.5650512 |
6914,3 | 692ar ct an | 6933 | 69471.5650512 | 695arctan /5/16 | 69629.2059322 | |
6972,2 | 6984,4 | 69990.0000000 | 700arctan /1/2 | 70135.2643897 | ||
7025,0 | 70300.0000000 | 704arctan /50/49 | 70545.2893775 | |||
7065,1 | 707arctan | 7081/4 | 70914.0362435 | 710arctan /§4/49 | 71139.7940655 | |
7125,2 | 713arctan | 7142/3 | 71533.6900675 | 716arctan /26/49 | 71736.0707687 | |
7185,3 | 719arctan | 7203/2 | 72156.3099325 | 722arctan /26/49 | 72336.0707687 | |
7245,4 | 725arctan | 7264 | 72775.9637566 | 728ar’ctan /34/49 | 72939.7940655 | |
7305,5 | 73190.0000000 | 732arctan /5O/49 | 73345.2893775 | |||
7343,0 | 7356,0 | 73600.0000000 | 737arctan /T | 73854.7356103 | ||
7396,1 | 740arctan | 7411/5 | 74211.3099325 | 743arctan /13/9 | 74450.2378408 | |
7453,1 | 7466,2 | 747arctan | 7481/2 | 74926.5650512 | 750arctan /10/9 | 75146.5084806 |
7526,3 | 753arctan | 7541 | 75545.0000000 | 756arctan 1 | 75745.0000000 | |
7583,2 | 7596,4 | 760arctan | 7612 | 76263.4349488 | 763arctan /10/9 | 76446.5084806 |
7656,5 | 766arctan | 7675 | 76878.6900675 | 769arctan /13/9 | 77050.2378408 | |
7713,3 | 7726,6 | 77390.0000000 | 774arctan /2 | 77554.7356103 | ||
7767,0 | 77700.0000000 | 778arctan /9/2 | 77964.7605982 | |||
7807,1 | 781arctan | 7821/6 | 7839.4623222 | 784arctan Z74/25 | 78559.8332100 | |
7867,2 | 787arctan | 7882/5 | 78921.8014095 | 790arctan /8/25 | 79156.7138133 | |
7927,3 | 793arctan | 7943/4 | 79536.8698976 | 796arctan /2 | 79754.7356103 | |
7987,4 | 799arctan | 8004/3 | 80153.1301024 | 802arctan /2 | 80354.7356103 | |
8047,5 | 805arctan | 8065/2 | 80768.1985905 | 808arctan 758/25 | 80956.7138133 | |
8107,6 | 811arctan | 8126 | 81380.5376778 | 814arctan /74/25 | 81559.8332100 | |
8167,7 | 81790.0000000 | 818arctan 79/2 | 81964.7605982 | |||
8204,0 | 8218,0 | 82200.0000000 | 823arctan /18 | 82476.7373240 | ||
8258,1 | 826arctan | 8271/6 | 8289.4623222 | 829arctan 72.4/9 | 83070.7741443 | |
8314,1 | 8328,2 | 833arctan | 8341/3 | 83518.4349488 | 836arctan 75 | 83765.9051575 |
8388,3 | 839arctan | 8403/5 | 84130.9637565 | 842arctan 717/4 | 84364.1233099 | |
8444,2 | 8458,4 | 846arctan | 8471 | 84845.0000000 | 849arctan 2 | 85063.4349488 |
8518,5 | 852arctan | 8535/3 | 85459.0362435 | 855arctan 717/4 | 85664.1233099 | |
8576v 12v | ||
8604,3 8,6 8618,7 8624,4 8,-8 | 867arctan 65.9051575 868arctan /74/9 70.7741443 869arctan /18 76.7373240 | |
8709,0 8719,1 8729,2 8739,3 8749,4 8759,5 8769,6 8779,7 8789,8 8799,9 | ||
90410,1 9055,1 10,2 90610,3 9075,2 10,4 90810,5 9095,3 10,6 91010,7 9115,4 10,8 91210,9 | 913arctan 1/6 9.4623222 914arctan 1/3 18.4349488 915arctan 1/2 26.5650512 916arctan 2/3 33-6900675 917arctan 1 45.0000000 918arctan 3/2 56.3099325 919arctan 2 63.4349488 920arctan 3 71.5650512 921arctan 6 80.5376778 | |
93311,3 93411,4 93511,5 93611,6 93711,7 93811,8 | 939arctan 1/2 26.5650512 940arctan 2/3 33.6900675 941arctan 5/6 39-8055711 942arctan 6/5 50.1944289 943arctan 3/2 56.3099325 944arctan 2 63.4349488 | |
95312,5 9546,6 12,6 95512,7 | 956arctan 5/6 39.8055711 957arctan 1 45.0000000 958arctan 6/5 50.1944289 | |
964 4: 0 = 36
9650 = 180° - fl, (when
966 A #2 is viewed
967 upside down: see
968 5:
969 Fjg. 15.4).
970 0 = + 36°
971 fl = same as A #4.
972 6: </> = 72°+0,
973 0=0,.