11 Eylül 2020

Kurgusal Karakter Grafikleri - Aang

 

Hava büken Aang karakterinin Math Wolfram kullanılarak oluşturulmuş grafiği ve denklemi de parametrik olarak şu şekilde verilmiştir:

x(t) = ((-16/29 sin(58/37 - 11 t) - 45/62 sin(217/145 - 9 t) - 19/41 sin(21/22 - 8 t) - 5/36 sin(25/41 - 7 t) - 439/35 sin(32/21 - 3 t) - 69/20 sin(217/145 - 2 t) + 49/27 sin(t + 21/13) + 69/44 sin(4 t + 42/31) + 4/15 sin(5 t + 104/25) + 11/37 sin(6 t + 143/36) + 17/33 sin(10 t + 151/84) + 4/29 sin(12 t + 17/32) - 463/19) θ(83 π - t) θ(t - 79 π) + (-21/25 sin(81/52 - 8 t) - 16/23 sin(14/9 - 7 t) - 3/8 sin(36/23 - 6 t) - 37/53 sin(36/23 - 4 t) - 101/39 sin(25/16 - 3 t) - 1121/102 sin(58/37 - 2 t) + 542/69 sin(t + 113/72) + 14/19 sin(5 t + 63/40) + 1/26 sin(9 t + 45/29) + 1/42 sin(10 t + 50/31) + 1/18 sin(11 t + 96/61) + 3/16 sin(12 t + 146/31) + 2357/36) θ(79 π - t) θ(t - 75 π) + (-1/11 sin(68/47 - 8 t) + 5671/32 sin(t + 74/47) + 10/19 sin(2 t + 143/34) + 271/14 sin(3 t + 41/26) + 21/85 sin(4 t + 219/59) + 531/83 sin(5 t + 52/33) + 1/7 sin(6 t + 36/23) + 140/41 sin(7 t + 49/31) + 122/21) θ(75 π - t) θ(t - 71 π) + (-61/39 sin(42/29 - 8 t) - 19/14 sin(31/26 - 7 t) - 584/67 sin(14/27 - 3 t) + 3273/23 sin(t + 19/20) + 978/25 sin(2 t + 61/13) + 172/19 sin(4 t + 97/34) + 1169/292 sin(5 t + 53/19) + 494/165 sin(6 t + 130/33) + 175/73 sin(9 t + 17/27) + 7/29 sin(10 t + 19/30) + 61/29 sin(11 t + 4/27) + 5/12 sin(12 t + 101/23) + 154/29) θ(71 π - t) θ(t - 67 π) + (1569/4 sin(t + 133/89) + 1295/18 sin(2 t + 64/21) + 399/23 sin(3 t + 94/25) + 853/24 sin(4 t + 13/33) + 229/5 sin(5 t + 119/26) + 299/36 sin(6 t + 16/19) + 1046/35 sin(7 t + 145/33) + 59/9 sin(8 t + 96/31) + 65/4 sin(9 t + 200/49) + 157/26 sin(10 t + 55/23) + 371/36 sin(11 t + 269/62) + 305/59 sin(12 t + 202/67) - 173/21) θ(67 π - t) θ(t - 63 π) + (-19/34 sin(21/62 - 8 t) - 344/115 sin(91/68 - 7 t) - 87/16 sin(6/7 - 6 t) + 14551/73 sin(t + 9/29) + 244/37 sin(2 t + 31/26) + 742/33 sin(3 t + 151/37) + 316/51 sin(4 t + 75/16) + 49/3 sin(5 t + 64/39) + 112/45 sin(9 t + 17/8) + 132/53 sin(10 t + 98/27) + 49/17 sin(11 t + 5/7) + 27/31 sin(12 t + 147/37) + 183/28) θ(63 π - t) θ(t - 59 π) + (-1479/28 sin(13/34 - t) + 44/31 sin(2 t + 67/29) + 131/29 sin(3 t + 59/32) + 15/16 sin(4 t + 86/19) + 30/23 sin(5 t + 73/17) + 19/35 sin(6 t + 55/48) + 27/40 sin(7 t + 3/22) + 323/32) θ(59 π - t) θ(t - 55 π) + (1073/12 sin(t + 38/29) + 244/75 sin(2 t + 18/25) + 76/21 sin(3 t + 137/35) + 78/23 sin(4 t + 11/7) + 31/9 sin(5 t + 103/29) + 145/34 sin(6 t + 116/93) + 21/23 sin(7 t + 56/15) + 71/28 sin(8 t + 25/33) + 70/51 sin(9 t + 210/47) + 151/15) θ(55 π - t) θ(t - 51 π) + (-13/27 sin(9/28 - 9 t) - 16/17 sin(32/25 - 7 t) - 25/11 sin(19/29 - 5 t) - 14/5 sin(40/53 - 2 t) - 23/22 sin(47/37 - t) + 208/33 sin(3 t + 97/45) + 71/13 sin(4 t + 97/39) + 40/37 sin(6 t + 61/24) + 9/32 sin(8 t + 18/7) + 41/55 sin(10 t + 111/50) + 3/4 sin(11 t + 22/45) + 10/41 sin(12 t + 84/37) - 18572/95) θ(51 π - t) θ(t - 47 π) + (-41/124 sin(43/37 - 12 t) - 9/31 sin(4/9 - 11 t) - 2/7 sin(33/25 - 10 t) - 65/34 sin(41/36 - 6 t) - 73/26 sin(37/32 - 2 t) + 88/19 sin(t + 5/11) + 161/29 sin(3 t + 40/21) + 162/25 sin(4 t + 41/40) + 44/19 sin(5 t + 54/17) + 19/56 sin(7 t + 105/79) + 26/53 sin(8 t + 145/32) + 12/23 sin(9 t + 35/27) + 6405/29) θ(47 π - t) θ(t - 43 π) + (2050/39 sin(t + 39/19) - 3326/17) θ(43 π - t) θ(t - 39 π) + (1184/23 sin(t + 36/25) + 4125/19) θ(39 π - t) θ(t - 35 π) + (7562/65 sin(t + 26/17) + 6098/27) θ(35 π - t) θ(t - 31 π) + (2709/23 sin(t + 46/27) - 5289/26) θ(31 π - t) θ(t - 27 π) + (-16/9 sin(42/29 - 2 t) + 2332/23 sin(t + 43/26) + 222/23 sin(3 t + 43/23) + 790/789 sin(4 t + 115/43) + 139/51 sin(5 t + 55/26) + 11/13 sin(6 t + 103/45) + 33/25 sin(7 t + 19/8) + 13444/53) θ(27 π - t) θ(t - 23 π) + (-43/32 sin(13/12 - 7 t) - 77/29 sin(23/20 - 5 t) - 267/32 sin(17/13 - 3 t) - 1033/11 sin(81/56 - t) + 61/23 sin(2 t + 115/72) + 25/38 sin(4 t + 25/43) + 376/377 sin(6 t + 5/38) + 35/37 sin(8 t + 25/36) - 5869/22) θ(23 π - t) θ(t - 19 π) + (-375/23 sin(18/13 - 3 t) - 93/25 sin(15/13 - 2 t) + 1417/43 sin(t + 151/48) + 125/18 sin(4 t + 69/37) + 38/13 sin(5 t + 29/26) + 37/56 sin(6 t + 47/44) - 4508/9) θ(19 π - t) θ(t - 15 π) + (-150/149 sin(109/219 - 6 t) - 188/31 sin(27/47 - 4 t) - 980/43 sin(18/19 - t) + 229/32 sin(2 t + 141/37) + 283/21 sin(3 t + 260/71) + 113/30 sin(5 t + 51/16) + 52/19 sin(7 t + 167/50) + 16211/31) θ(15 π - t) θ(t - 11 π) + (-38/21 sin(17/12 - 6 t) - 178/51 sin(1/12 - 4 t) + 4913/55 sin(t + 95/33) + 692/51 sin(2 t + 378/89) + 167/25 sin(3 t + 52/31) + 58/21 sin(5 t + 5/12) + 117/58 sin(7 t + 202/49) + 11932/23) θ(11 π - t) θ(t - 7 π) + (-283/39 sin(34/25 - 3 t) - 1770/19 sin(11/43 - t) + 371/32 sin(2 t + 2/3) + 155/37 sin(4 t + 61/19) + 191/45 sin(5 t + 154/39) + 28/29 sin(6 t + 8/13) + 27/26 sin(7 t + 4/3) - 11294/23) θ(7 π - t) θ(t - 3 π) + (35723/71 sin(t + 16/11) + 775/68 sin(2 t + 58/19) + 1119/38 sin(3 t + 321/73) + 92/19 sin(4 t + 84/29) + 192/25 sin(5 t + 186/43) + 97/29 sin(6 t + 71/26) + 66/31 sin(7 t + 33/37) + 22/23 sin(8 t + 178/59) + 64/7) θ(3 π - t) θ(t + π)) θ(sqrt(sgn(sin(t/2))))

y(t) = ((-7/19 sin(34/27 - 11 t) - 9/16 sin(13/11 - 10 t) - 9/26 sin(49/38 - 9 t) - 25/56 sin(43/28 - 6 t) - 8/23 sin(43/39 - 5 t) - 66/35 sin(139/93 - 4 t) + 75/17 sin(t + 51/32) + 9/17 sin(2 t + 55/31) + 21/29 sin(3 t + 69/44) + 7/10 sin(7 t + 44/25) + 5/33 sin(8 t + 133/59) + 4/25 sin(12 t + 37/18) - 3951/32) θ(83 π - t) θ(t - 79 π) + (-16/45 sin(73/47 - 12 t) - 12/43 sin(54/35 - 11 t) - 18/53 sin(81/52 - 10 t) - 69/62 sin(47/30 - 6 t) - 123/16 sin(58/37 - 2 t) + 54/41 sin(t + 36/23) + 20/27 sin(3 t + 39/25) + 3/8 sin(4 t + 212/45) + 8/19 sin(5 t + 47/30) + 10/51 sin(7 t + 41/26) + 9/32 sin(8 t + 46/29) + 4/13 sin(9 t + 68/43) - 8605/73) θ(79 π - t) θ(t - 75 π) + (-49/48 sin(11/7 - 7 t) + 683/41 sin(t + 52/33) + 239/29 sin(2 t + 41/26) + 267/80 sin(3 t + 113/24) + 71/19 sin(4 t + 30/19) + 11/23 sin(5 t + 38/23) + 65/43 sin(6 t + 107/68) + 44/29 sin(8 t + 65/41) - 6219/25) θ(75 π - t) θ(t - 71 π) + (-43/35 sin(55/49 - 11 t) - 526/27 sin(17/21 - 3 t) - 1149/38 sin(10/61 - 2 t) - 3659/30 sin(26/29 - t) + 211/12 sin(4 t + 8/5) + 89/28 sin(5 t + 52/31) + 37/7 sin(6 t + 23/29) + 64/19 sin(7 t + 136/31) + 81/35 sin(8 t + 89/26) + 49/29 sin(9 t + 93/25) + 13/9 sin(10 t + 110/49) + 3/41 sin(12 t + 33/65) - 21455/36) θ(71 π - t) θ(t - 67 π) + (-53/24 sin(18/19 - 9 t) - 145/26 sin(83/82 - 8 t) - 1069/11 sin(17/67 - t) + 5275/24 sin(2 t + 42/29) + 431/21 sin(3 t + 42/31) + 103/10 sin(4 t + 1/87) + 928/31 sin(5 t + 95/28) + 901/31 sin(6 t + 43/26) + 274/19 sin(7 t + 9/13) + 67/23 sin(10 t + 51/22) + 149/36 sin(11 t + 1/18) + 179/57 sin(12 t + 46/11) - 13073/19) θ(67 π - t) θ(t - 63 π) + (-29/16 sin(8/21 - 9 t) - 99/34 sin(31/21 - 7 t) - 413/17 sin(12/19 - 3 t) - 4997/36 sin(29/24 - t) + 217/24 sin(2 t + 79/17) + 89/18 sin(4 t + 76/23) + 224/39 sin(5 t + 5/33) + 173/52 sin(6 t + 9/28) + 77/15 sin(8 t + 34/25) + 31/17 sin(10 t + 70/41) + 9/16 sin(11 t + 48/29) + 21/46 sin(12 t + 9/4) + 13451/24) θ(63 π - t) θ(t - 59 π) + (-33/31 sin(23/36 - 7 t) + 109/6 sin(t + 91/20) + 59/12 sin(2 t + 149/41) + 89/24 sin(3 t + 5/28) + 24/35 sin(4 t + 151/76) + 17/35 sin(5 t + 34/25) + 49/73 sin(6 t + 179/55) - 2893/9) θ(59 π - t) θ(t - 55 π) + (-77/27 sin(52/37 - 7 t) - 69/17 sin(13/18 - 3 t) - 1033/27 sin(21/46 - t) + 741/29 sin(2 t + 37/41) + 96/19 sin(4 t + 3/35) + 284/49 sin(5 t + 60/13) + 85/64 sin(6 t + 3/5) + 39/20 sin(8 t + 61/22) + 35/52 sin(9 t + 52/21) - 2289/20) θ(55 π - t) θ(t - 51 π) + (-510/77 sin(7/25 - t) + 142/49 sin(2 t + 69/25) + 81/14 sin(3 t + 106/23) + 404/47 sin(4 t + 34/9) + 105/31 sin(5 t + 7/16) + 61/25 sin(6 t + 76/21) + 68/41 sin(7 t + 1/38) + 95/48 sin(8 t + 112/33) + 22/19 sin(9 t + 4/29) + 49/39 sin(10 t + 105/29) + 23/21 sin(11 t + 21/85) + 12/13 sin(12 t + 91/27) + 6503/47) θ(51 π - t) θ(t - 47 π) + (-60/43 sin(4/11 - 2 t) + 39/14 sin(t + 52/23) + 383/58 sin(3 t + 127/35) + 192/25 sin(4 t + 36/13) + 107/42 sin(5 t + 135/29) + 81/82 sin(6 t + 49/36) + 11/24 sin(7 t + 80/27) + 5/14 sin(8 t + 117/25) + 38/51 sin(9 t + 37/43) + 7/22 sin(10 t + 140/43) + 9/19 sin(11 t + 16/35) + 10/59 sin(12 t + 87/26) + 3811/28) θ(47 π - t) θ(t - 43 π) + (2125/39 sin(t + 15/28) + 2705/22) θ(43 π - t) θ(t - 39 π) + (137 - 2014/41 sin(3/17 - t)) θ(39 π - t) θ(t - 35 π) + (1727/17 sin(t + 1/19) + 2376/19) θ(35 π - t) θ(t - 31 π) + (2109/20 sin(t + 4/35) + 6414/53) θ(31 π - t) θ(t - 27 π) + (-61/27 sin(36/29 - 6 t) - 187/14 sin(97/68 - 2 t) - 284/11 sin(52/45 - t) + 59/19 sin(3 t + 29/72) + 185/41 sin(4 t + 134/29) + 79/41 sin(5 t + 7/11) + 70/43 sin(7 t + 109/78) + 12043/31) θ(27 π - t) θ(t - 23 π) + (-59/88 sin(7/32 - 8 t) - 43/33 sin(37/41 - 6 t) - 79/20 sin(116/93 - 4 t) - 211/18 sin(27/19 - 2 t) - 890/29 sin(27/29 - t) + 104/17 sin(3 t + 1/16) + 163/74 sin(5 t + 17/23) + 38/33 sin(7 t + 23/18) + 24587/68) θ(23 π - t) θ(t - 19 π) + (-99/31 sin(29/24 - 6 t) - 128/21 sin(37/33 - 3 t) - 2994/35 sin(11/21 - t) + 841/54 sin(2 t + 11/26) + 494/55 sin(4 t + 102/37) + 63/22 sin(5 t + 169/127) - 3685/56) θ(19 π - t) θ(t - 15 π) + (986/11 sin(t + 13/3) + 187/38 sin(2 t + 51/13) + 198/41 sin(3 t + 112/33) + 326/109 sin(4 t + 223/60) + 79/32 sin(5 t + 13/7) + 213/82 sin(6 t + 107/34) + 34/23 sin(7 t + 1) - 1043/32) θ(15 π - t) θ(t - 11 π) + (-43/34 sin(25/34 - 7 t) - 48/29 sin(7/18 - 6 t) + 5926/37 sin(t + 102/25) + 309/37 sin(2 t + 47/30) + 457/33 sin(3 t + 106/41) + 232/61 sin(4 t + 24/29) + 80/29 sin(5 t + 38/31) - 2171/35) θ(11 π - t) θ(t - 7 π) + (-152/91 sin(11/19 - 7 t) + 1503/10 sin(t + 214/51) + 197/32 sin(2 t + 39/19) + 277/29 sin(3 t + 156/55) + 31/22 sin(4 t + 41/35) + 137/56 sin(5 t + 38/49) + 25/33 sin(6 t + 145/33) - 1043/11) θ(7 π - t) θ(t - 3 π) + (-31/8 sin(15/44 - 7 t) - 31/13 sin(17/16 - 5 t) - 418/45 sin(6/37 - 3 t) + 17636/29 sin(t + 97/32) + 185/24 sin(2 t + 29/16) + 205/34 sin(4 t + 32/7) + 158/49 sin(6 t + 19/14) + 111/41 sin(8 t + 107/26) + 1958/17) θ(3 π - t) θ(t + π)) θ(sqrt(sgn(sin(t/2))))

Wolfram bağlantısı...