v1.1.0

Downloads

• 📦 Download for macOS (Apple silicon)
• 📦 Download for Windows

Changes

• Significantly improved the performance of plotting relations involving if expressions. 🚀
• Add Transparent background option to image export. 🧊
• Fixed an issue where parametric relations with if expressions may not be plotted. 🐞
• Fixed an issue where long relations may not be plotted on Windows. 🐞

Gallery

owl curve

x = −1/2 sin(1/3 − 140 t) − sin(15/14 − 122 t)/4 − sin(3/4 − 121 t)/6 − sin(5/11 − 119 t)/7 − (7 sin(5/8 − 116 t))/13 − sin(5/7 − 113 t)/3 − (13 sin(30/29 − 112 t))/14 − (2 sin(3/8 − 107 t))/5 − (3 sin(3/5 − 103 t))/10 − (2 sin(4/5 − 101 t))/9 − (4 sin(1/5 − 94 t))/9 − (3 sin(11/10 − 93 t))/2 − (2 sin(11/10 − 89 t))/3 − (5 sin(1 − 87 t))/6 − (13 sin(29/30 − 83 t))/10 − (2 sin(1/10 − 82 t))/9 − (8 sin(6/7 − 79 t))/9 − (2 sin(23/22 − 77 t))/7 − (10 sin(1/28 − 74 t))/9 − (19 sin(18/17 − 64 t))/7 − sin(4/7 − 63 t)/3 − (11 sin(7/13 − 60 t))/7 − (2 sin(15/11 − 59 t))/7 − (7 sin(3/5 − 55 t))/3 − sin(6/7 − 50 t)/4 − (25 sin(11/7 − 47 t))/6 − (45 sin(5/6 − 46 t))/13 − (9 sin(7/5 − 45 t))/7 − (7 sin(6/5 − 40 t))/2 − (29 sin(7/6 − 39 t))/8 − (21 sin(1/2 − 33 t))/4 − (44 sin(1/8 − 32 t))/15 − (69 sin(4/5 − 26 t))/17 − (283 sin(11/8 − 19 t))/9 − (481 sin(3/7 − 17 t))/20 − (71 sin(1/2 − 7 t))/5 − (219 sin(2/3 − 5 t))/8 + (167 sin(18 t))/8 + (4061 sin(5/8 + t))/5 + (1888 sin(2/5 + 2 t))/7 + (1052 sin(3/2 + 3 t))/13 + (749 sin(7/5 + 4 t))/10 + (342 sin(13/9 + 6 t))/5 + (503 sin(3/7 + 8 t))/7 + (242 sin(51/11 + 9 t))/5 + (155 sin(37/8 + 10 t))/4 + (166 sin(44/15 + 11 t))/5 + (254 sin(9/8 + 12 t))/11 + (146 sin(5/9 + 13 t))/5 + (58 sin(18/11 + 14 t))/9 + (469 sin(9/10 + 15 t))/36 + (8 sin(29/8 + 16 t))/3 + (171 sin(35/8 + 20 t))/10 + (227 sin(35/8 + 21 t))/11 + (92 sin(17/6 + 22 t))/9 + (8 sin(23/7 + 23 t))/5 + (247 sin(46/15 + 24 t))/15 + (47 sin(7/5 + 25 t))/6 + (23 sin(11/3 + 27 t))/6 + (61 sin(12/5 + 28 t))/5 + (138 sin(3 + 29 t))/11 + (77 sin(13/6 + 30 t))/6 + (16 sin(7/10 + 31 t))/3 + (13 sin(1/6 + 34 t))/3 + (6 sin(40/13 + 35 t))/5 + (13 sin(7/10 + 36 t))/5 + (26 sin(5/11 + 37 t))/9 + (18 sin(11/5 + 38 t))/5 + (22 sin(22/7 + 41 t))/9 + (25 sin(23/9 + 42 t))/6 + (4 sin(28/11 + 43 t))/5 + (29 sin(1 + 44 t))/7 + (10 sin(47/10 + 48 t))/9 + (17 sin(30/7 + 49 t))/8 + sin(41/21 + 51 t) + (6 sin(21/5 + 52 t))/5 + (8 sin(23/5 + 53 t))/5 + (28 sin(13/14 + 54 t))/11 + sin(21/5 + 56 t)/2 + (22 sin(29/9 + 57 t))/7 + (9 sin(43/22 + 58 t))/7 + (22 sin(5/9 + 61 t))/15 + (5 sin(17/5 + 62 t))/8 + (11 sin(18/7 + 65 t))/8 + (17 sin(13/7 + 66 t))/6 + (12 sin(8/5 + 67 t))/7 + sin(20/9 + 68 t) + (3 sin(7/2 + 69 t))/4 + (12 sin(12/7 + 70 t))/11 + (19 sin(2 + 71 t))/13 + (13 sin(35/17 + 72 t))/6 + (38 sin(2/5 + 73 t))/15 + (6 sin(2/5 + 75 t))/5 + (11 sin(41/10 + 76 t))/9 + (7 sin(15/7 + 78 t))/5 + (4 sin(75/19 + 80 t))/5 + (9 sin(4 + 81 t))/10 + (5 sin(4 + 84 t))/4 + (11 sin(61/20 + 85 t))/12 + (28 sin(2/5 + 86 t))/29 + (11 sin(22/7 + 88 t))/12 + (4 sin(26/7 + 90 t))/7 + (10 sin(3/10 + 91 t))/11 + (21 sin(5/7 + 92 t))/20 + (25 sin(8/3 + 95 t))/24 + sin(19/8 + 96 t) + (2 sin(23/6 + 97 t))/7 + sin(7/6 + 98 t)/3 + (6 sin(14/9 + 99 t))/7 + (4 sin(8/9 + 100 t))/7 + sin(15/7 + 102 t)/6 + (2 sin(1/8 + 104 t))/5 + (3 sin(57/14 + 105 t))/5 + (2 sin(5/7 + 106 t))/5 + (2 sin(28/11 + 108 t))/3 + (3 sin(19/5 + 109 t))/7 + (4 sin(85/21 + 110 t))/7 + (9 sin(3/8 + 111 t))/10 + (6 sin(23/12 + 114 t))/11 + (11 sin(1/3 + 115 t))/10 + sin(133/44 + 117 t)/7 + (4 sin(1/7 + 118 t))/9 + (2 sin(1/7 + 120 t))/7 + (2 sin(32/7 + 123 t))/5 + sin(2/3 + 124 t)/4 + (5 sin(21/8 + 125 t))/7 + sin(25/9 + 126 t) + (2 sin(4/7 + 127 t))/7 + sin(14/15 + 128 t)/2 + (3 sin(17/5 + 129 t))/7 + sin(12/5 + 130 t)/5 + sin(26/7 + 131 t)/3 + sin(11/8 + 132 t)/6 + sin(13/6 + 133 t)/4 + (2 sin(7/9 + 134 t))/5 + (3 sin(25/8 + 135 t))/7 + sin(22/5 + 136 t)/4 + (4 sin(4 + 137 t))/7 + (5 sin(8/3 + 138 t))/7 + (2 sin(14/3 + 139 t))/5 && y = −1/7 sin(10/7 − 140 t) − (4 sin(3/7 − 135 t))/7 − sin(7/8 − 133 t)/6 − (3 sin(4/5 − 132 t))/8 − sin(5/9 − 129 t)/3 − (3 sin(23/15 − 120 t))/7 − (4 sin(11/9 − 117 t))/7 − (13 sin(1/18 − 116 t))/14 − (23 sin(1/9 − 114 t))/24 − (7 sin(8/7 − 112 t))/13 − (3 sin(6/7 − 109 t))/5 − (3 sin(12/11 − 108 t))/8 − (9 sin(14/9 − 105 t))/10 − (21 sin(13/10 − 104 t))/22 − (13 sin(1/5 − 87 t))/7 − (13 sin(1/11 − 85 t))/8 − (4 sin(5/6 − 84 t))/3 − sin(3/2 − 83 t) − (3 sin(7/5 − 80 t))/8 − (11 sin(4/5 − 79 t))/9 − (17 sin(11/8 − 78 t))/11 − (11 sin(4/3 − 74 t))/6 − sin(15/11 − 71 t)/2 − sin(7/10 − 64 t)/2 − (7 sin(10/7 − 58 t))/4 − (12 sin(4/3 − 54 t))/5 − (16 sin(5/4 − 50 t))/7 − (23 sin(1/5 − 44 t))/8 − (25 sin(7/6 − 43 t))/7 − (23 sin(27/26 − 39 t))/3 − (9 sin(5/8 − 38 t))/10 − (50 sin(3/2 − 35 t))/11 − (33 sin(2/5 − 33 t))/7 − (505 sin(1/14 − 23 t))/42 − (143 sin(1/13 − 21 t))/6 − (54 sin(3/5 − 20 t))/5 − (35 sin(28/27 − 19 t))/3 − (78 sin(4/5 − 16 t))/5 − (1618 sin(7/5 − 14 t))/49 − (215 sin(10/7 − 9 t))/4 − (530 sin(1/5 − 7 t))/7 − (1604 sin(11/8 − t))/3 + (91 sin(59 t))/18 + (431 sin(8/9 + 2 t))/4 + (1981 sin(10/3 + 3 t))/9 + (1041 sin(9/10 + 4 t))/5 + (1177 sin(15/4 + 5 t))/8 + (1925 sin(15/4 + 6 t))/13 + (101 sin(6/5 + 8 t))/2 + (217 sin(12/7 + 10 t))/6 + (129 sin(5/3 + 11 t))/10 + (505 sin(13/5 + 12 t))/9 + (182 sin(73/18 + 13 t))/11 + (146 sin(17/6 + 15 t))/5 + 20 sin(25/9 + 17 t) + (119 sin(7/4 + 18 t))/20 + (643 sin(19/6 + 22 t))/28 + (57 sin(19/5 + 24 t))/10 + (32 sin(12/7 + 25 t))/3 + (148 sin(16/9 + 26 t))/11 + (56 sin(59/15 + 27 t))/9 + (17 sin(8/3 + 28 t))/5 + (82 sin(9/2 + 29 t))/11 + (22 sin(11/9 + 30 t))/3 + (61 sin(13/3 + 31 t))/7 + 10 sin(22/7 + 32 t) + 5 sin(27/8 + 34 t) + (84 sin(4/5 + 36 t))/13 + (12 sin(40/13 + 37 t))/5 + (19 sin(7/8 + 40 t))/2 + (22 sin(7/3 + 41 t))/7 + (2 sin(11/4 + 42 t))/3 + (5 sin(59/15 + 45 t))/4 + (19 sin(2 + 46 t))/8 + (9 sin(41/10 + 47 t))/4 + (25 sin(10/7 + 48 t))/7 + (3 sin(22/9 + 49 t))/5 + (73 sin(47/12 + 51 t))/36 + (17 sin(2/3 + 52 t))/6 + (27 sin(7/2 + 53 t))/7 + (22 sin(17/10 + 55 t))/9 + (9 sin(5/3 + 56 t))/4 + (7 sin(22/7 + 57 t))/2 + (29 sin(5/7 + 60 t))/9 + (16 sin(21/8 + 61 t))/9 + (11 sin(8/3 + 62 t))/5 + (23 sin(1/8 + 63 t))/8 + (5 sin(13/5 + 65 t))/2 + (13 sin(5/8 + 66 t))/6 + (18 sin(35/12 + 67 t))/17 + (25 sin(33/16 + 68 t))/9 + (24 sin(17/6 + 69 t))/23 + (16 sin(23/8 + 70 t))/7 + (17 sin(18/7 + 72 t))/11 + (26 sin(9/5 + 73 t))/25 + (4 sin(10/3 + 75 t))/5 + (15 sin(13/5 + 76 t))/8 + (16 sin(15/4 + 77 t))/7 + (7 sin(4/7 + 81 t))/6 + (5 sin(19/8 + 82 t))/4 + (7 sin(17/9 + 86 t))/11 + (3 sin(3/8 + 88 t))/2 + (4 sin(18/11 + 89 t))/5 + (8 sin(7/4 + 90 t))/7 + sin(11/6 + 91 t)/5 + (4 sin(3/2 + 92 t))/5 + (51 sin(3/4 + 93 t))/26 + (11 sin(16/11 + 94 t))/9 + (4 sin(16/7 + 95 t))/5 + (9 sin(8/5 + 96 t))/7 + (2 sin(1/3 + 97 t))/7 + (8 sin(139/46 + 98 t))/5 + (3 sin(49/11 + 99 t))/4 + (2 sin(9/4 + 100 t))/5 + (5 sin(11/10 + 101 t))/8 + sin(16/7 + 102 t)/3 + (10 sin(51/13 + 103 t))/11 + (2 sin(15/11 + 106 t))/7 + (8 sin(51/11 + 107 t))/9 + sin(11/3 + 110 t)/2 + (3 sin(38/9 + 111 t))/8 + (7 sin(50/11 + 113 t))/13 + (10 sin(27/14 + 115 t))/11 + (3 sin(16/11 + 118 t))/7 + sin(33/17 + 119 t)/7 + sin(5/6 + 121 t)/3 + (3 sin(19/11 + 122 t))/5 + (7 sin(23/15 + 123 t))/9 + sin(13/4 + 124 t)/4 + (4 sin(39/10 + 125 t))/7 + (5 sin(1/2 + 126 t))/8 + (2 sin(82/27 + 127 t))/9 + (5 sin(26/7 + 128 t))/9 + sin(6/7 + 130 t)/3 + sin(7/3 + 131 t)/4 + (2 sin(25/11 + 134 t))/7 + sin(4/7 + 136 t)/5 + (4 sin(31/30 + 137 t))/9 + (2 sin(15/16 + 138 t))/5 + sin(25/9 + 139 t)/9 && 0 ≤ t ≤ 2 pi

Click to copy the relation ↑ 

Japanese "math" character curve

x = if(sqrt(sgn(sin(t/2))) < 0, 0, 1) (if(7 pi - t < 0, 0, 1) if(-3 pi + t < 0, 0, 1) (-2413/25 - (16 sin(3/2 - 7 t))/9 - (19 sin(7/11 - 2 t))/5 - (801 sin(5/12 - t))/8 + (237 sin(9/7 + 3 t))/14 + (5 sin(37/10 + 4 t))/8 + (38 sin(25/9 + 5 t))/7 + (9 sin(53/12 + 6 t))/14) + if(11 pi - t < 0, 0, 1) if(-7 pi + t < 0, 0, 1) (3395/8 - (3 sin(4/7 - 15 t))/7 - (11 sin(3/4 - 12 t))/14 - (2 sin(5/7 - 9 t))/3 - (4 sin(22/15 - 5 t))/5 + (2259 sin(1/4 + t))/14 + (529 sin(25/7 + 2 t))/13 + (181 sin(5/8 + 3 t))/9 + (13 sin(31/8 + 4 t))/3 + (42 sin(7/5 + 6 t))/11 + (25 sin(33/7 + 7 t))/8 + (30 sin(11/6 + 8 t))/13 + (4 sin(61/14 + 10 t))/9 + (27 sin(17/8 + 11 t))/26 + (7 sin(25/8 + 13 t))/13 + sin(23/10 + 14 t)/7) + if(27 pi - t < 0, 0, 1) if(-23 pi + t < 0, 0, 1) (-7039/11 - (6 sin(10/9 - 11 t))/5 - (146 sin(8/11 - 3 t))/9 + (1117 sin(31/30 + t))/12 + (7 sin(9/4 + 2 t))/2 + (28 sin(104/35 + 4 t))/29 + (23 sin(32/9 + 5 t))/5 + (5 sin(7/10 + 6 t))/12 + (17 sin(19/9 + 7 t))/12 + sin(47/14 + 8 t)/8 + (13 sin(3/4 + 9 t))/8 + (3 sin(29/7 + 10 t))/11 + sin(43/16 + 12 t)/4 + (5 sin(24/7 + 13 t))/11 + sin(16/13 + 14 t)/14 + (5 sin(20/9 + 15 t))/13) + if(23 pi - t < 0, 0, 1) if(-19 pi + t < 0, 0, 1) (-3017/8 - (2 sin(16/15 - 17 t))/5 - (2 sin(7/6 - 13 t))/7 + (1017 sin(2/5 + t))/7 + (103 sin(27/8 + 2 t))/9 + (219 sin(35/11 + 3 t))/19 + (36 sin(1/7 + 4 t))/13 + (22 sin(5/7 + 5 t))/5 + 4 sin(18/5 + 6 t) + (8 sin(47/13 + 7 t))/11 + (13 sin(13/14 + 8 t))/11 + (9 sin(5/6 + 9 t))/17 + (7 sin(35/9 + 10 t))/4 + (2 sin(8/15 + 11 t))/5 + (5 sin(13/8 + 12 t))/8 + (2 sin(117/29 + 14 t))/3 + sin(9/10 + 15 t)/2 + sin(19/9 + 16 t)/3 + (2 sin(50/13 + 18 t))/11) + if(15 pi - t < 0, 0, 1) if(-11 pi + t < 0, 0, 1) (-2129/5 - sin(1 - 27 t)/6 - (18 sin(13/11 - 26 t))/11 - (36 sin(10/9 - 24 t))/13 - (21 sin(4/11 - 23 t))/11 - (24 sin(14/9 - 22 t))/25 - (12 sin(21/16 - 21 t))/5 - (37 sin(13/25 - 17 t))/8 - (379 sin(7/11 - 5 t))/14 + (6169 sin(32/7 + t))/19 + (769 sin(35/23 + 2 t))/7 + (477 sin(6/5 + 3 t))/5 + (1243 sin(28/11 + 4 t))/18 + (1019 sin(31/9 + 6 t))/17 + (238 sin(37/10 + 7 t))/9 + 12 sin(31/11 + 8 t) + (77 sin(37/16 + 9 t))/4 + (14 sin(9/8 + 10 t))/3 + (149 sin(10/7 + 11 t))/14 + (62 sin(42/11 + 12 t))/7 + (41 sin(9/7 + 13 t))/6 + (83 sin(33/7 + 14 t))/15 + (38 sin(14/3 + 15 t))/9 + (17 sin(34/23 + 16 t))/10 + (25 sin(67/15 + 18 t))/8 + (16 sin(15/7 + 19 t))/9 + (10 sin(6/19 + 20 t))/7 + (5 sin(3/5 + 25 t))/6 + (20 sin(22/7 + 28 t))/9 + (3 sin(43/12 + 29 t))/13 + (12 sin(9/5 + 30 t))/13 + sin(7/5 + 31 t)/30 + (29 sin(4/7 + 32 t))/14) + if(3 pi - t < 0, 0, 1) if(pi + t < 0, 0, 1) (-4428/11 - (3 sin(1/8 - 36 t))/8 - (11 sin(1/4 - 32 t))/9 - (11 sin(5/8 - 31 t))/9 - (11 sin(8/7 - 21 t))/3 - (36 sin(67/66 - 20 t))/11 - (19 sin(17/13 - 17 t))/8 - (41 sin(8/7 - 13 t))/10 - (83 sin(3/10 - 10 t))/13 - (86 sin(1/7 - 6 t))/9 + (1583 sin(4/3 + t))/5 + (57 sin(7/4 + 2 t))/5 + (227 sin(7/3 + 3 t))/12 + (830 sin(8/11 + 4 t))/21 + (597 sin(112/37 + 5 t))/7 + (359 sin(19/8 + 7 t))/6 + (251 sin(19/7 + 8 t))/10 + (89 sin(13/9 + 9 t))/8 + (7 sin(7/10 + 11 t))/4 + (119 sin(14/11 + 12 t))/12 + (17 sin(13/3 + 14 t))/8 + (29 sin(31/8 + 15 t))/8 + (34 sin(22/13 + 16 t))/11 + (44 sin(53/27 + 18 t))/13 + (49 sin(31/8 + 19 t))/10 + (5 sin(32/9 + 22 t))/6 + (26 sin(16/7 + 23 t))/9 + (41 sin(27/8 + 24 t))/42 + (11 sin(37/10 + 25 t))/16 + (27 sin(25/9 + 26 t))/10 + (43 sin(11/12 + 27 t))/14 + (3 sin(9/7 + 28 t))/5 + (5 sin(1/10 + 29 t))/11 + (5 sin(37/12 + 30 t))/7 + (20 sin(13/8 + 33 t))/19 + (3 sin(8/3 + 34 t))/8 + (5 sin(9/4 + 35 t))/11) + if(19 pi - t < 0, 0, 1) if(-15 pi + t < 0, 0, 1) (5084/13 - sin(13/9 - 35 t)/3 - (19 sin(4/3 - 31 t))/12 - (13 sin(20/19 - 29 t))/4 - (2 sin(19/13 - 27 t))/3 - (45 sin(1/7 - 24 t))/13 - (57 sin(1/32 - 17 t))/17 - (51 sin(30/31 - 14 t))/8 - (654 sin(19/13 - 7 t))/17 - (591 sin(4/5 - 2 t))/11 + (1687 sin(3/10 + t))/5 + (1862 sin(5/7 + 3 t))/13 + (861 sin(9/11 + 4 t))/8 + (305 sin(25/6 + 5 t))/6 + (173 sin(11/3 + 6 t))/9 + (274 sin(21/5 + 8 t))/9 + (451 sin(17/11 + 9 t))/18 + (44 sin(38/9 + 10 t))/9 + (55 sin(1/2 + 11 t))/12 + (73 sin(63/25 + 12 t))/10 + (43 sin(20/9 + 13 t))/5 + (61 sin(19/6 + 15 t))/10 + (56 sin(1/6 + 16 t))/5 + (31 sin(41/10 + 18 t))/11 + (43 sin(23/7 + 19 t))/21 + (4 sin(18/5 + 20 t))/7 + (13 sin(157/39 + 21 t))/7 + (7 sin(21/16 + 22 t))/5 + (13 sin(19/5 + 23 t))/9 + (19 sin(11/4 + 25 t))/8 + (59 sin(7/4 + 26 t))/29 + (7 sin(14/15 + 28 t))/9 + (23 sin(20/13 + 30 t))/15 + (6 sin(28/9 + 32 t))/5 + (5 sin(9/5 + 33 t))/4 + (7 sin(43/14 + 34 t))/11 + (37 sin(34/9 + 36 t))/36)) && y = if(sqrt(sgn(sin(t/2))) < 0, 0, 1) (if(7 pi - t < 0, 0, 1) if(-3 pi + t < 0, 0, 1) (2054/3 - (31 sin(16/17 - 7 t))/11 - (44 sin(13/11 - 5 t))/13 - (83 sin(11/12 - 3 t))/8 - (1511 sin(19/15 - t))/11 + (11 sin(32/13 + 2 t))/4 + (2 sin(10/13 + 4 t))/7 + (5 sin(13/11 + 6 t))/9) + if(11 pi - t < 0, 0, 1) if(-7 pi + t < 0, 0, 1) (731/5 - sin(11/7 - 10 t)/4 - (9 sin(1/13 - 7 t))/5 - (153 sin(1/6 - 6 t))/19 - (441 sin(11/17 - 4 t))/26 - (29 sin(4/5 - 3 t))/3 - (185 sin(10/9 - 2 t))/8 - (589 sin(4/3 - t))/2 + sin(15 t)/7 + (7 sin(34/9 + 5 t))/12 + (13 sin(3/8 + 8 t))/8 + (29 sin(5/9 + 9 t))/9 + (23 sin(1 + 11 t))/10 + (3 sin(9/10 + 12 t))/5 + (5 sin(20/13 + 13 t))/7 + (13 sin(12/7 + 14 t))/10) + if(27 pi - t < 0, 0, 1) if(-23 pi + t < 0, 0, 1) (4175/6 - (5 sin(11/14 - 14 t))/14 - (3 sin(9/7 - 11 t))/7 - (4 sin(5/7 - 10 t))/9 - (5 sin(20/21 - 7 t))/2 - (30 sin(1/3 - 6 t))/29 - (52 sin(1/44 - 3 t))/7 + (517 sin(13/4 + t))/4 + (19 sin(8/9 + 2 t))/11 + (3 sin(21/10 + 4 t))/4 + (39 sin(23/10 + 5 t))/11 + (2 sin(69/34 + 8 t))/7 + (8 sin(23/9 + 9 t))/5 + sin(4/3 + 12 t)/3 + sin(5/3 + 13 t)/2 + (4 sin(53/12 + 15 t))/7) + if(23 pi - t < 0, 0, 1) if(-19 pi + t < 0, 0, 1) (-5016/17 - (39 sin(9/17 - 5 t))/10 - (60 sin(4/3 - 2 t))/7 - (821 sin(13/14 - t))/7 + (77 sin(30/7 + 3 t))/8 + (71 sin(2/5 + 4 t))/12 + (5 sin(3/13 + 6 t))/7 + (2 sin(27/7 + 7 t))/5 + (33 sin(5/7 + 8 t))/14 + (3 sin(1/10 + 9 t))/8 + (3 sin(8/5 + 10 t))/8 + (10 sin(28/13 + 11 t))/19 + (60 sin(50/49 + 12 t))/59 + sin(70/23 + 13 t)/3 + (2 sin(13/5 + 14 t))/9 + (5 sin(7/3 + 15 t))/11 + (3 sin(11/8 + 16 t))/10 + (3 sin(32/9 + 17 t))/8 + sin(24/7 + 18 t)/12) + if(15 pi - t < 0, 0, 1) if(-11 pi + t < 0, 0, 1) (-1844/5 - (7 sin(1/2 - 32 t))/12 - (8 sin(7/6 - 30 t))/11 - (7 sin(31/30 - 27 t))/11 - (5 sin(3/7 - 25 t))/12 - (11 sin(6/5 - 24 t))/7 - (13 sin(5/13 - 23 t))/14 - (9 sin(5/6 - 20 t))/8 - (47 sin(21/20 - 19 t))/16 - (26 sin(12/11 - 13 t))/11 - (749 sin(8/9 - 12 t))/68 - (5 sin(17/11 - 8 t))/3 - (388 sin(1/11 - 3 t))/21 - (3241 sin(4/13 - t))/9 + (143 sin(9/8 + 2 t))/12 + (216 sin(16/9 + 4 t))/7 + (397 sin(47/11 + 5 t))/13 + (133 sin(9/2 + 6 t))/9 + (108 sin(10/9 + 7 t))/7 + (402 sin(74/21 + 9 t))/23 + (178 sin(14/9 + 10 t))/11 + (68 sin(21/10 + 11 t))/9 + (32 sin(5/6 + 14 t))/7 + (38 sin(65/16 + 15 t))/9 + (48 sin(19/12 + 16 t))/11 + (11 sin(39/11 + 17 t))/4 + (17 sin(9/10 + 18 t))/11 + (5 sin(49/11 + 21 t))/6 + 4 sin(13/7 + 22 t) + (27 sin(35/8 + 26 t))/13 + (16 sin(21/10 + 28 t))/11 + (9 sin(23/10 + 29 t))/8 + (6 sin(16/11 + 31 t))/11) + if(19 pi - t < 0, 0, 1) if(-15 pi + t < 0, 0, 1) (-703/10 - (10 sin(5/7 - 36 t))/9 - (3 sin(8/7 - 33 t))/4 - (35 sin(3/8 - 29 t))/17 - (112 sin(4/5 - 26 t))/37 - (11 sin(7/6 - 19 t))/3 - (79 sin(1/5 - 11 t))/9 - (11355 sin(9/7 - t))/16 + (1051 sin(11/4 + 2 t))/14 + (327 sin(11/6 + 3 t))/8 + (867 sin(45/22 + 4 t))/7 + (306 sin(56/13 + 5 t))/7 + (854 sin(19/9 + 6 t))/15 + (93 sin(17/6 + 7 t))/4 + (441 sin(24/7 + 8 t))/17 + (152 sin(12/23 + 9 t))/9 + (99 sin(37/12 + 10 t))/5 + (81 sin(4/5 + 12 t))/10 + (46 sin(23/8 + 13 t))/9 + (118 sin(13/3 + 14 t))/17 + (13 sin(18/19 + 15 t))/3 + (58 sin(33/8 + 16 t))/7 + (26 sin(14/3 + 17 t))/3 + (6 sin(9/13 + 18 t))/11 + (49 sin(30/7 + 20 t))/9 + (19 sin(19/11 + 21 t))/4 + sin(32/9 + 22 t)/2 + (15 sin(35/9 + 23 t))/8 + (16 sin(31/12 + 24 t))/13 + (17 sin(7/12 + 25 t))/11 + (7 sin(1/5 + 27 t))/8 + (31 sin(3/4 + 28 t))/9 + (7 sin(74/17 + 30 t))/9 + (18 sin(25/26 + 31 t))/11 + (19 sin(69/16 + 32 t))/14 + sin(3/4 + 34 t)/2 + sin(26/17 + 35 t)/8) + if(3 pi - t < 0, 0, 1) if(pi + t < 0, 0, 1) (4841/13 - sin(2/9 - 36 t)/2 - (9 sin(50/49 - 31 t))/10 - (8 sin(17/16 - 28 t))/11 - (22 sin(9/17 - 27 t))/7 - (71 sin(7/9 - 22 t))/11 - (17 sin(8/11 - 21 t))/9 - (31 sin(6/7 - 19 t))/15 - (47 sin(23/15 - 16 t))/19 - (85 sin(5/4 - 13 t))/9 - (102 sin(4/5 - 11 t))/11 - (521 sin(1/5 - 4 t))/8 + (1327 sin(35/13 + t))/5 + (766 sin(55/13 + 2 t))/9 + (68 sin(42/11 + 3 t))/5 + (273 sin(17/9 + 5 t))/5 + (314 sin(27/26 + 6 t))/7 + (216 sin(41/9 + 7 t))/5 + (246 sin(33/8 + 8 t))/7 + (79 sin(27/13 + 9 t))/7 + (13 sin(55/13 + 10 t))/14 + (17 sin(41/14 + 12 t))/6 + (29 sin(26/7 + 14 t))/7 + (30 sin(36/35 + 15 t))/31 + (26 sin(21/8 + 17 t))/7 + (36 sin(4 + 18 t))/13 + (43 sin(4/7 + 20 t))/16 + (13 sin(20/7 + 23 t))/8 + (15 sin(2/5 + 24 t))/16 + (14 sin(3/5 + 25 t))/13 + (33 sin(8/7 + 26 t))/34 + (39 sin(47/12 + 29 t))/38 + (18 sin(2/9 + 30 t))/13 + (13 sin(18/5 + 32 t))/11 + (4 sin(6/13 + 33 t))/3 + (17 sin(16/15 + 34 t))/11 + (9 sin(13/8 + 35 t))/8)) && 0 <= t <= 28 pi

Click to copy the relation ↑ 

Yasuna Oribe‐like curve

x = if(sqrt(sgn(sin(t/2))) < 0, 0, 1) (if(31 pi − t < 0, 0, 1) if(−27 pi + t < 0, 0, 1) (−5001/37 − (847 sin(47/30 − 3 t))/53 + (194 sin(11/7 + t))/27 + (5 sin(14/9 + 2 t))/6) + if(39 pi − t < 0, 0, 1) if(−35 pi + t < 0, 0, 1) (1751/27 − (103 sin(91/58 − 5 t))/69 − (13 sin(41/27 − 4 t))/17 − (299 sin(36/23 − 3 t))/33 + (118 sin(52/33 + t))/13 + (510 sin(107/68 + 2 t))/73) + if(83 pi − t < 0, 0, 1) if(−79 pi + t < 0, 0, 1) (994/3 − (4117 sin(11/7 − 2 t))/73 + (2006 sin(11/7 + t))/41 + (1979 sin(245/52 + 3 t))/51) + if(35 pi − t < 0, 0, 1) if(−31 pi + t < 0, 0, 1) (−22247/108 − (229 sin(80/51 − 3 t))/24 + (533 sin(11/7 + t))/38 + (85 sin(11/7 + 2 t))/22 + sin(30/29 + 4 t)/146) + if(43 pi − t < 0, 0, 1) if(−39 pi + t < 0, 0, 1) (453/13 + (298 sin(11/7 + t))/35 + (816 sin(11/7 + 2 t))/43 + (73 sin(245/52 + 3 t))/15 + (21 sin(52/33 + 4 t))/29) + if(79 pi − t < 0, 0, 1) if(−75 pi + t < 0, 0, 1) (919/38 − (206 sin(39/25 − 5 t))/35 − (29 sin(41/30 − 4 t))/30 − (1103 sin(25/16 − 3 t))/27 + (1802 sin(41/26 + t))/29 + (2604 sin(41/26 + 2 t))/37 + (62 sin(17/11 + 6 t))/35) + if(107 pi − t < 0, 0, 1) if(−103 pi + t < 0, 0, 1) (−1457/35 − sin(38/25 − 12 t)/18 − (10 sin(61/39 − 6 t))/27 + (1561 sin(107/68 + t))/33 + (237 sin(41/26 + 2 t))/26 + sin(23/15 + 3 t)/4 + (4 sin(46/29 + 4 t))/31 + (52 sin(30/19 + 5 t))/37 + (4 sin(69/43 + 7 t))/19 + (5 sin(23/14 + 8 t))/27 + (3 sin(48/31 + 9 t))/32 + sin(7/20 + 10 t)/148 + (5 sin(11/7 + 11 t))/23) + if(63 pi − t < 0, 0, 1) if(−59 pi + t < 0, 0, 1) (−5558/31 − (41 sin(17/11 − 8 t))/17 − (199 sin(39/25 − 7 t))/25 − (57 sin(54/35 − 6 t))/40 − (487 sin(36/23 − 3 t))/23 + (1967 sin(96/61 + t))/66 + (19 sin(50/33 + 2 t))/35 + (2131 sin(30/19 + 4 t))/87 + (41 sin(80/17 + 5 t))/12 + (19 sin(221/47 + 9 t))/14 + (13 sin(14/9 + 10 t))/22 + (15 sin(53/33 + 11 t))/11 + (53 sin(35/22 + 12 t))/23) + if(75 pi − t < 0, 0, 1) if(−71 pi + t < 0, 0, 1) (3886/27 − (4319 sin(47/30 − 3 t))/216 + (2632 sin(49/31 + t))/87 + (4858 sin(30/19 + 2 t))/55 + (37 sin(67/46 + 4 t))/21 + (16 sin(59/13 + 5 t))/21 + (51 sin(69/44 + 6 t))/13 + (49 sin(136/29 + 7 t))/26 + (52 sin(68/43 + 8 t))/17 + (12 sin(121/26 + 9 t))/19 + (141 sin(107/67 + 10 t))/65 + (7 sin(221/48 + 11 t))/50 + (4 sin(85/53 + 12 t))/9) + if(67 pi − t < 0, 0, 1) if(−63 pi + t < 0, 0, 1) (200/21 + (509 sin(146/31 + t))/51 + (3728 sin(74/47 + 2 t))/49 + (301 sin(68/43 + 3 t))/62 + (19 sin(52/33 + 4 t))/6 + (7 sin(108/23 + 5 t))/10 + (41 sin(30/19 + 6 t))/9 + (49 sin(49/31 + 7 t))/31 + (22 sin(46/29 + 8 t))/23 + (9 sin(41/25 + 9 t))/25 + (26 sin(27/17 + 10 t))/19 + (10 sin(53/33 + 11 t))/17 + (13 sin(71/44 + 12 t))/34) + if(111 pi − t < 0, 0, 1) if(−107 pi + t < 0, 0, 1) (21459/56 + (529 sin(11/7 + t))/24 + (611 sin(49/31 + 2 t))/204 + (91 sin(49/31 + 3 t))/29 + (11 sin(49/30 + 4 t))/19 + (152 sin(46/29 + 5 t))/65 + (3 sin(76/43 + 6 t))/29 + (19 sin(89/19 + 7 t))/44 + (8 sin(155/97 + 8 t))/17 + (120 sin(35/22 + 9 t))/239 + (19 sin(62/39 + 10 t))/67 + (41 sin(62/39 + 11 t))/81 + (5 sin(57/34 + 12 t))/42) + if(71 pi − t < 0, 0, 1) if(−67 pi + t < 0, 0, 1) (7201/21 − (43 sin(39/25 − 10 t))/38 − (6 sin(143/95 − 9 t))/29 − (64 sin(17/11 − 8 t))/51 − (85 sin(53/34 − 6 t))/24 − (37 sin(142/95 − 5 t))/53 − (1380 sin(36/23 − 2 t))/29 − (212 sin(39/25 − t))/25 + (41 sin(47/31 + 3 t))/28 + (207 sin(174/37 + 4 t))/62 + (3 sin(41/26 + 7 t))/23 + (3 sin(37/26 + 11 t))/25 + (16 sin(146/31 + 12 t))/23) + if(103 pi − t < 0, 0, 1) if(−99 pi + t < 0, 0, 1) (−3569/8 − (9 sin(37/24 − 12 t))/40 − (11 sin(57/37 − 11 t))/43 − (24 sin(14/9 − 10 t))/47 − (9 sin(53/34 − 6 t))/7 + (1217 sin(11/7 + t))/32 + (762 sin(41/26 + 2 t))/103 + (292 sin(52/33 + 3 t))/33 + (34 sin(49/31 + 4 t))/19 + (5 sin(25/16 + 5 t))/13 + (13 sin(61/39 + 7 t))/23 + (14 sin(11/7 + 8 t))/27 + (3 sin(67/43 + 9 t))/7 + (5 sin(68/43 + 13 t))/22) + if(51 pi − t < 0, 0, 1) if(−47 pi + t < 0, 0, 1) (−28410/31 − (68 sin(26/17 − 6 t))/19 − (67 sin(32/21 − 4 t))/19 − (1177 sin(80/51 − t))/24 + (5591 sin(91/58 + 2 t))/51 + (229 sin(31/20 + 3 t))/28 + (927 sin(36/23 + 5 t))/59 + (148 sin(20/13 + 7 t))/19 + (430 sin(87/56 + 8 t))/29 + (586 sin(25/16 + 9 t))/35 + (31 sin(52/33 + 10 t))/7 + (769 sin(136/29 + 11 t))/62 + (1630 sin(127/27 + 12 t))/59 + (231 sin(44/27 + 13 t))/47 + (17 sin(47/27 + 14 t))/19 + (209 sin(146/31 + 15 t))/21 + (107 sin(80/17 + 16 t))/42 + (159 sin(11/7 + 17 t))/28 + (184 sin(37/24 + 18 t))/47 + (18 sin(35/27 + 19 t))/53) + if(27 pi − t < 0, 0, 1) if(−23 pi + t < 0, 0, 1) (940/21 − (82 sin(212/141 − 16 t))/31 − (839 sin(32/21 − 14 t))/140 − (138 sin(63/41 − 13 t))/19 − (98 sin(56/37 − 12 t))/29 − (272 sin(71/46 − 11 t))/23 − (126 sin(17/11 − 9 t))/25 − (103 sin(47/30 − 6 t))/20 + (2768 sin(11/7 + t))/17 + (40 sin(28/19 + 2 t))/27 + (478 sin(245/52 + 3 t))/21 + (521 sin(113/24 + 4 t))/32 + (254 sin(46/29 + 5 t))/25 + (290 sin(30/19 + 7 t))/31 + (148 sin(47/30 + 8 t))/45 + (148 sin(69/44 + 10 t))/23 + (7 sin(17/29 + 15 t))/34 + (124 sin(49/31 + 17 t))/71 + (26 sin(45/28 + 18 t))/23 + (46 sin(28/17 + 19 t))/35) + if(47 pi − t < 0, 0, 1) if(−43 pi + t < 0, 0, 1) (9157/22 − (124 sin(70/47 − 16 t))/41 − (85 sin(17/11 − 8 t))/19 − (133 sin(65/42 − 6 t))/40 − (431 sin(47/30 − 4 t))/26 − (803 sin(80/51 − 2 t))/12 + (1477 sin(212/45 + t))/27 + (446 sin(41/26 + 3 t))/35 + (273 sin(49/31 + 5 t))/20 + (287 sin(46/29 + 7 t))/30 + (1615 sin(36/23 + 9 t))/269 + (467 sin(80/17 + 10 t))/34 + (172 sin(155/33 + 11 t))/69 + (684 sin(11/7 + 12 t))/25 + (323 sin(25/16 + 13 t))/39 + (199 sin(249/53 + 14 t))/29 + (221 sin(49/31 + 15 t))/21 + (121 sin(55/34 + 17 t))/23 + (7 sin(49/33 + 18 t))/9 + (59 sin(25/16 + 19 t))/32 + (62 sin(44/25 + 20 t))/103) + if(91 pi − t < 0, 0, 1) if(−87 pi + t < 0, 0, 1) (5174/19 − (149 sin(42/29 − 26 t))/224 − (4 sin(37/26 − 25 t))/13 − (3 sin(67/46 − 24 t))/20 − (2 sin(4/25 − 23 t))/23 − (18 sin(53/35 − 22 t))/19 − sin(16/11 − 20 t)/22 − (52 sin(299/199 − 16 t))/29 − (31 sin(19/13 − 15 t))/21 − (170 sin(32/21 − 14 t))/37 − (18 sin(40/27 − 13 t))/7 − (94 sin(146/97 − 12 t))/35 − (67 sin(157/105 − 11 t))/29 − (107 sin(65/42 − 10 t))/14 − (34 sin(10/7 − 9 t))/21 − (11 sin(43/36 − 7 t))/36 − (337 sin(31/20 − 6 t))/20 − (166 sin(37/24 − 5 t))/35 − (396 sin(31/20 − 4 t))/41 − (2259 sin(47/30 − 2 t))/14 + (2567 sin(11/7 + t))/16 + (370 sin(77/50 + 3 t))/33 + (11 sin(60/37 + 8 t))/30 + (5 sin(56/41 + 17 t))/23 + (4 sin(75/16 + 18 t))/7 + (19 sin(45/28 + 19 t))/23 + sin(245/53 + 21 t)/14) + if(3 pi − t < 0, 0, 1) if(pi + t < 0, 0, 1) (−12713/48 − (92 sin(47/30 − 21 t))/29 − (131 sin(59/38 − 19 t))/21 − (177 sin(53/34 − 17 t))/23 − (1580 sin(87/56 − 9 t))/69 − (1348 sin(53/34 − 8 t))/23 − (524 sin(69/44 − 5 t))/15 − (4208 sin(47/30 − 2 t))/35 + (767 sin(107/68 + t))/21 + (1503 sin(11/7 + 3 t))/38 + (571 sin(212/45 + 4 t))/33 + (947 sin(46/29 + 6 t))/26 + (101 sin(523/112 + 7 t))/33 + (7 sin(75/16 + 10 t))/2 + (331 sin(8/5 + 11 t))/25 + (35 sin(329/72 + 12 t))/32 + (195 sin(39/25 + 13 t))/34 + (89 sin(81/52 + 14 t))/16 + (43 sin(21/13 + 15 t))/23 + (169 sin(27/17 + 16 t))/19 + (12 sin(26/17 + 18 t))/19 + (47 sin(68/43 + 20 t))/20 + (27 sin(46/27 + 22 t))/29) + if(7 pi − t < 0, 0, 1) if(−3 pi + t < 0, 0, 1) (8021/38 − (433 sin(71/46 − 20 t))/63 − (509 sin(39/25 − 15 t))/40 − (109 sin(17/11 − 13 t))/15 − (443 sin(58/37 − 6 t))/29 − (2283 sin(58/37 − 5 t))/47 − (1091 sin(36/23 − 2 t))/11 + (8067 sin(69/44 + t))/109 + (18461 sin(63/40 + 3 t))/142 + (3241 sin(41/26 + 4 t))/46 + (1471 sin(65/41 + 7 t))/64 + (19 sin(91/57 + 8 t))/9 + (754 sin(49/31 + 9 t))/33 + (562 sin(85/54 + 10 t))/25 + (643 sin(52/33 + 11 t))/29 + (237 sin(30/19 + 12 t))/26 + (180 sin(43/27 + 14 t))/17 + (145 sin(53/32 + 16 t))/38 + (86 sin(207/44 + 17 t))/25 + (11 sin(9/2 + 18 t))/36 + (70 sin(113/24 + 19 t))/31 + (429 sin(101/63 + 21 t))/86 + (7 sin(48/31 + 22 t))/4 + (51 sin(91/57 + 23 t))/8 + (176 sin(43/27 + 24 t))/37) + if(11 pi − t < 0, 0, 1) if(−7 pi + t < 0, 0, 1) (−5339/12 − (13 sin(317/211 − 23 t))/11 − (151 sin(17/11 − 20 t))/46 − (70 sin(32/21 − 17 t))/39 − (12 sin(43/31 − 16 t))/25 − (311 sin(45/29 − 11 t))/32 − (127 sin(31/20 − 9 t))/21 − (1813 sin(25/16 − 6 t))/47 − (1729 sin(61/39 − 4 t))/30 + (100 sin(67/43 + t))/31 + (4206 sin(74/47 + 2 t))/35 + (1352 sin(63/40 + 3 t))/25 + (232 sin(30/19 + 5 t))/15 + (223 sin(49/31 + 7 t))/11 + (500 sin(68/43 + 8 t))/19 + (7 sin(102/65 + 10 t))/2 + (141 sin(113/24 + 12 t))/37 + (406 sin(67/42 + 13 t))/81 + (274 sin(43/27 + 14 t))/61 + (31 sin(46/29 + 15 t))/21 + (67 sin(80/17 + 18 t))/33 + (77 sin(45/28 + 19 t))/20 + (56 sin(43/27 + 21 t))/33 + (32 sin(11/7 + 22 t))/19 + (236 sin(29/18 + 24 t))/79 + (21 sin(8/5 + 25 t))/26) + if(15 pi − t < 0, 0, 1) if(−11 pi + t < 0, 0, 1) (−438/17 − (101 sin(18/13 − 24 t))/50 − (25 sin(41/32 − 23 t))/27 − (403 sin(23/16 − 19 t))/48 − (267 sin(55/38 − 18 t))/44 − (722 sin(16/11 − 15 t))/73 − (452 sin(63/44 − 14 t))/35 − (133 sin(60/43 − 13 t))/26 − (1052 sin(25/17 − 10 t))/59 − (1128 sin(3/2 − 9 t))/31 − (713 sin(80/53 − 8 t))/48 − (779 sin(26/17 − 6 t))/44 − (391 sin(26/17 − 5 t))/10 − (89 sin(29/19 − 4 t))/5 − (1109 sin(25/16 − 2 t))/10 + (1573 sin(61/39 + t))/24 + (223 sin(229/153 + 3 t))/34 + (809 sin(35/22 + 7 t))/35 + (164 sin(113/72 + 11 t))/23 + (17 sin(23/5 + 12 t))/10 + (171 sin(43/24 + 16 t))/86 + (48 sin(51/31 + 17 t))/5 + (62 sin(39/25 + 20 t))/39 + (37 sin(75/43 + 21 t))/12 + (25 sin(47/26 + 22 t))/29 + (7 sin(43/31 + 25 t))/13 + (9 sin(202/43 + 26 t))/8) + if(95 pi − t < 0, 0, 1) if(−91 pi + t < 0, 0, 1) (−13441/56 − sin(36/23 − 22 t)/8 + (1201 sin(11/7 + t))/13 + (145 sin(36/23 + 2 t))/34 + (350 sin(11/7 + 3 t))/29 + (83 sin(74/47 + 4 t))/26 + (137 sin(11/7 + 5 t))/18 + (19 sin(74/47 + 6 t))/9 + (23 sin(11/7 + 7 t))/9 + (33 sin(27/17 + 8 t))/43 + (11 sin(91/58 + 9 t))/12 + (49 sin(74/47 + 10 t))/37 + (55 sin(41/26 + 11 t))/63 + (4 sin(57/37 + 12 t))/25 + (43 sin(19/12 + 13 t))/27 + sin(113/24 + 14 t)/15 + sin(67/43 + 15 t)/5 + (2 sin(59/37 + 16 t))/5 + sin(30/17 + 17 t)/98 + sin(31/7 + 18 t)/82 + (15 sin(113/72 + 19 t))/22 + (43 sin(63/40 + 20 t))/85 + (17 sin(125/78 + 21 t))/52 + (5 sin(11/7 + 23 t))/22 + (4 sin(36/23 + 24 t))/37 + (15 sin(59/38 + 25 t))/59 + (4 sin(25/16 + 26 t))/17 + (3 sin(20/13 + 27 t))/13 + (11 sin(58/37 + 28 t))/31) + if(55 pi − t < 0, 0, 1) if(−51 pi + t < 0, 0, 1) (989/18 − (27 sin(49/33 − 38 t))/35 − (13 sin(71/47 − 36 t))/15 − (41 sin(22/15 − 33 t))/31 − (26 sin(238/159 − 29 t))/17 − (93 sin(32/21 − 28 t))/35 − (87 sin(86/57 − 24 t))/40 − (73 sin(43/29 − 22 t))/85 − (44 sin(20/13 − 19 t))/17 − (179 sin(31/20 − 18 t))/52 − (1766 sin(23/15 − 17 t))/321 − (6 sin(35/33 − 13 t))/31 − (269 sin(53/34 − 10 t))/29 − (613 sin(67/43 − 8 t))/30 − (578 sin(61/39 − 6 t))/67 − (1059 sin(25/16 − 4 t))/37 − (1315 sin(58/37 − 2 t))/39 − (236 sin(80/51 − t))/7 + (431 sin(52/33 + 3 t))/76 + (467 sin(49/31 + 5 t))/21 + (41 sin(102/65 + 7 t))/45 + (17 sin(30/19 + 9 t))/3 + (97 sin(49/31 + 11 t))/17 + (13 sin(271/58 + 12 t))/19 + (41 sin(45/28 + 14 t))/7 + (252 sin(19/12 + 15 t))/65 + (15 sin(257/55 + 16 t))/26 + (31 sin(77/48 + 20 t))/21 + (227 sin(47/29 + 21 t))/81 + sin(135/32 + 23 t)/26 + (48 sin(31/19 + 25 t))/19 + (5 sin(43/26 + 26 t))/18 + (2 sin(47/10 + 27 t))/13 + (26 sin(147/88 + 30 t))/17 + (10 sin(33/25 + 31 t))/51 + (51 sin(68/41 + 32 t))/41 + (26 sin(569/122 + 34 t))/47 + (13 sin(36/23 + 35 t))/43 + (23 sin(44/27 + 37 t))/29 + (35 sin(77/46 + 39 t))/39) + if(87 pi − t < 0, 0, 1) if(−83 pi + t < 0, 0, 1) (768/35 − (26 sin(65/42 − 3 t))/29 + (97 sin(39/25 + t))/38 + (149 sin(61/13 + 2 t))/34 + (35 sin(209/45 + 4 t))/16 + (293 sin(49/32 + 5 t))/26 + (407 sin(14/3 + 6 t))/42 + (269 sin(86/57 + 7 t))/35 + (133 sin(50/31 + 8 t))/53 + (201 sin(43/29 + 9 t))/26 + (805 sin(167/36 + 10 t))/62 + (205 sin(54/37 + 11 t))/31 + (321 sin(83/18 + 12 t))/38 + (41 sin(59/40 + 13 t))/4 + (11 sin(37/24 + 14 t))/5 + (96 sin(60/43 + 15 t))/55 + (231 sin(46/31 + 16 t))/46 + (175 sin(129/28 + 17 t))/44 + (499 sin(25/17 + 18 t))/73 + (133 sin(142/31 + 19 t))/20 + (53 sin(23/5 + 20 t))/20 + (613 sin(197/43 + 21 t))/28 + (23 sin(212/141 + 22 t))/32 + (47 sin(79/53 + 23 t))/30 + (205 sin(41/28 + 24 t))/57 + (40 sin(121/26 + 25 t))/11 + (43 sin(230/51 + 26 t))/16 + (422 sin(25/18 + 27 t))/29 + (559 sin(10/7 + 28 t))/61 + (31 sin(28/23 + 29 t))/23 + (117 sin(31/22 + 30 t))/34 + (332 sin(73/16 + 31 t))/41 + (133 sin(116/83 + 32 t))/30 + (49 sin(159/35 + 33 t))/26 + (41 sin(383/87 + 34 t))/14 + (74 sin(48/37 + 35 t))/23 + (75 sin(71/16 + 36 t))/23 + (121 sin(141/31 + 37 t))/42 + (50 sin(152/35 + 38 t))/51 + (76 sin(518/115 + 39 t))/35 + (72 sin(56/39 + 40 t))/23 + (95 sin(77/17 + 41 t))/71 + (182 sin(151/34 + 42 t))/31) + if(99 pi − t < 0, 0, 1) if(−95 pi + t < 0, 0, 1) (17527/56 − (160 sin(31/21 − 34 t))/33 − (117 sin(58/37 − 31 t))/20 − (31 sin(23/19 − 29 t))/34 − (179 sin(112/75 − 22 t))/57 − (51 sin(45/32 − 18 t))/28 − (291 sin(32/21 − 14 t))/91 − (75 sin(58/37 − 6 t))/29 − (104 sin(47/30 − 3 t))/29 − (113 sin(91/58 − 2 t))/20 − (57 sin(45/29 − t))/34 + (81 sin(74/47 + 4 t))/17 + (10 sin(46/29 + 5 t))/7 + (14 sin(12/7 + 7 t))/37 + (97 sin(80/17 + 8 t))/18 + (164 sin(35/22 + 9 t))/57 + (66 sin(58/37 + 10 t))/19 + (53 sin(41/26 + 11 t))/6 + (32 sin(143/31 + 12 t))/37 + (143 sin(52/33 + 13 t))/21 + (53 sin(58/35 + 15 t))/30 + (373 sin(127/27 + 16 t))/30 + (391 sin(14/9 + 17 t))/43 + (75 sin(56/33 + 19 t))/41 + (231 sin(146/31 + 20 t))/19 + (239 sin(36/23 + 21 t))/38 + (155 sin(71/16 + 23 t))/156 + (33 sin(158/35 + 24 t))/19 + (120 sin(20/13 + 25 t))/29 + (308 sin(14/9 + 26 t))/27 + (95 sin(215/46 + 27 t))/29 + (45 sin(128/71 + 28 t))/28 + (916 sin(39/25 + 30 t))/131 + (79 sin(719/154 + 32 t))/25 + (6 sin(108/23 + 33 t))/19 + (69 sin(43/26 + 35 t))/20 + (173 sin(169/36 + 36 t))/35 + (97 sin(31/20 + 37 t))/21 + (172 sin(63/40 + 38 t))/19 + (72 sin(108/23 + 39 t))/25 + (158 sin(51/31 + 40 t))/27 + (51 sin(33/19 + 41 t))/47 + (49 sin(71/41 + 42 t))/36 + (178 sin(41/26 + 43 t))/23 + (165 sin(71/46 + 44 t))/43) + if(23 pi − t < 0, 0, 1) if(−19 pi + t < 0, 0, 1) (−9397/55 − (94 sin(44/29 − 27 t))/33 − (93 sin(35/23 − 24 t))/32 − (669 sin(47/30 − 23 t))/55 − (38 sin(47/30 − 13 t))/3 − (777 sin(31/20 − 4 t))/26 + (7013 sin(80/51 + t))/20 + (1121 sin(36/23 + 2 t))/20 + (8619 sin(113/24 + 3 t))/44 + (3055 sin(80/17 + 5 t))/32 + (1212 sin(25/16 + 6 t))/17 + (630 sin(39/25 + 7 t))/31 + (1813 sin(197/42 + 8 t))/24 + (1681 sin(48/31 + 9 t))/35 + (435 sin(68/43 + 10 t))/28 + (1001 sin(221/47 + 11 t))/37 + (103 sin(117/25 + 12 t))/38 + (746 sin(17/11 + 14 t))/41 + (529 sin(80/17 + 15 t))/29 + (139 sin(116/25 + 16 t))/21 + (47 sin(13/11 + 17 t))/33 + (131 sin(97/21 + 18 t))/30 + (189 sin(117/25 + 19 t))/32 + (583 sin(39/25 + 20 t))/19 + (45 sin(373/80 + 21 t))/7 + (115 sin(107/68 + 22 t))/18 + (767 sin(155/33 + 25 t))/43 + (511 sin(23/15 + 26 t))/93 + (29 sin(265/59 + 28 t))/16 + (106 sin(67/46 + 29 t))/39 + (67 sin(31/19 + 30 t))/21 + (94 sin(61/13 + 31 t))/37 + (32 sin(63/37 + 32 t))/33 + (90 sin(17/12 + 33 t))/29 + (266 sin(51/11 + 34 t))/33 + (691 sin(3/2 + 35 t))/148 + (225 sin(53/35 + 36 t))/44 + (125 sin(134/29 + 37 t))/21 + (51 sin(25/18 + 38 t))/29 + (50 sin(17/11 + 39 t))/37 + (59 sin(155/33 + 40 t))/33 + (132 sin(78/17 + 41 t))/61 + (72 sin(43/29 + 42 t))/25 + (46 sin(134/29 + 43 t))/29 + (112 sin(173/37 + 44 t))/39 + (44 sin(45/32 + 45 t))/39) + if(19 pi − t < 0, 0, 1) if(−15 pi + t < 0, 0, 1) (−8528/25 − (152 sin(178/119 − 47 t))/51 − (83 sin(20/13 − 37 t))/17 − (107 sin(28/19 − 35 t))/21 − (159 sin(42/29 − 34 t))/38 − (145 sin(38/25 − 30 t))/38 − (124 sin(47/32 − 29 t))/23 − (113 sin(51/35 − 25 t))/14 − (309 sin(163/109 − 24 t))/25 − (633 sin(45/29 − 21 t))/32 − (421 sin(65/42 − 11 t))/23 − (85 sin(24/17 − 10 t))/21 − (5200 sin(59/38 − 3 t))/107 − (6214 sin(36/23 − 2 t))/31 + (3868 sin(11/7 + t))/19 + (2002 sin(46/29 + 4 t))/37 + (1720 sin(43/27 + 5 t))/19 + (578 sin(59/37 + 6 t))/5 + (247 sin(45/28 + 7 t))/4 + (2990 sin(51/32 + 8 t))/67 + (11 sin(75/16 + 9 t))/3 + (151 sin(36/23 + 12 t))/14 + (52 sin(58/13 + 13 t))/37 + (306 sin(50/31 + 14 t))/19 + (18 sin(79/21 + 15 t))/37 + (247 sin(65/41 + 16 t))/31 + (28 sin(117/59 + 17 t))/29 + (119 sin(41/27 + 18 t))/25 + (233 sin(136/29 + 19 t))/24 + (653 sin(46/29 + 20 t))/27 + (47 sin(68/47 + 22 t))/20 + (76 sin(63/41 + 23 t))/29 + (63 sin(59/32 + 26 t))/37 + (27 sin(18/11 + 27 t))/2 + (3841 sin(7/4 + 28 t))/960 + (177 sin(59/36 + 31 t))/32 + (58 sin(55/32 + 32 t))/11 + (94 sin(37/22 + 33 t))/43 + (127 sin(64/41 + 36 t))/42 + (121 sin(43/26 + 38 t))/31 + (192 sin(29/17 + 39 t))/47 + (47 sin(136/29 + 40 t))/35 + (9 sin(73/43 + 41 t))/14 + (191 sin(53/31 + 42 t))/49 + (95 sin(79/45 + 43 t))/61 + (69 sin(49/26 + 44 t))/55 + (56 sin(49/29 + 45 t))/23 + (17 sin(43/27 + 46 t))/15 + (13 sin(22/21 + 48 t))/42 + (14 sin(92/21 + 49 t))/33) + if(59 pi − t < 0, 0, 1) if(−55 pi + t < 0, 0, 1) (3469/27 − (85 sin(17/11 − 54 t))/37 − (4 sin(37/25 − 51 t))/27 − (22 sin(133/89 − 48 t))/31 − (44 sin(34/23 − 37 t))/27 − (133 sin(31/21 − 26 t))/61 − (2 sin(45/29 − 23 t))/5 − (3827 sin(69/44 − 4 t))/26 + 179 sin(113/24 + t) + (79162 sin(212/45 + 2 t))/263 + (3350 sin(41/26 + 3 t))/19 + (3820 sin(49/31 + 5 t))/57 + (1830 sin(245/52 + 6 t))/41 + (307 sin(245/52 + 7 t))/31 + (317 sin(51/31 + 8 t))/37 + (2066 sin(113/24 + 9 t))/81 + (86 sin(102/23 + 10 t))/35 + (502 sin(197/42 + 11 t))/37 + (121 sin(45/28 + 12 t))/91 + (61 sin(191/41 + 13 t))/20 + (99 sin(67/43 + 14 t))/19 + (3 sin(43/34 + 15 t))/8 + (25 sin(64/41 + 16 t))/11 + (71 sin(58/37 + 17 t))/18 + (616 sin(383/82 + 18 t))/137 + (101 sin(139/30 + 19 t))/21 + (291 sin(139/30 + 20 t))/53 + (43 sin(117/25 + 21 t))/13 + (5 sin(45/23 + 22 t))/6 + (533 sin(207/44 + 24 t))/178 + (96 sin(60/37 + 25 t))/23 + (31 sin(63/34 + 27 t))/47 + (7 sin(779/167 + 28 t))/50 + (13 sin(41/33 + 29 t))/27 + (182 sin(59/37 + 30 t))/81 + (15 sin(177/76 + 31 t))/46 + (311 sin(145/31 + 32 t))/44 + (71 sin(143/32 + 33 t))/34 + (31 sin(188/41 + 34 t))/28 + (32 sin(46/29 + 35 t))/21 + (17 sin(95/21 + 36 t))/14 + (83 sin(49/31 + 38 t))/40 + (26 sin(39/22 + 39 t))/31 + (169 sin(174/37 + 40 t))/38 + (46 sin(88/49 + 41 t))/35 + (18 sin(83/19 + 42 t))/31 + (209 sin(593/127 + 43 t))/104 + (52 sin(157/35 + 44 t))/33 + (39 sin(141/31 + 45 t))/35 + (41 sin(181/39 + 46 t))/28 + (44 sin(51/31 + 47 t))/29 + (25 sin(40/27 + 49 t))/36 + (5 sin(100/23 + 50 t))/22 + (19 sin(308/67 + 52 t))/58 + (18 sin(52/29 + 53 t))/19)) && y = if(sqrt(sgn(sin(t/2))) < 0, 0, 1) (if(83 pi − t < 0, 0, 1) if(−79 pi + t < 0, 0, 1) (15991/69 − (911 sin(80/51 − 3 t))/27 + (793 sin(113/72 + t))/16 + (1600 sin(11/7 + 2 t))/23) + if(35 pi − t < 0, 0, 1) if(−31 pi + t < 0, 0, 1) (−11681/15 − (47 sin(39/25 − 4 t))/39 + (14 sin(69/44 + t))/43 + (444 sin(11/7 + 2 t))/19 + (19 sin(11/7 + 3 t))/21) + if(31 pi − t < 0, 0, 1) if(−27 pi + t < 0, 0, 1) (−10395/17 + (5 sin(117/25 + t))/14 + (715 sin(85/54 + 2 t))/38 + (8 sin(145/31 + 3 t))/37) + if(43 pi − t < 0, 0, 1) if(−39 pi + t < 0, 0, 1) (−29349/38 + (389 sin(212/45 + t))/32 + (674 sin(11/7 + 2 t))/55 + (279 sin(11/7 + 3 t))/29 + (41 sin(245/52 + 4 t))/30) + if(39 pi − t < 0, 0, 1) if(−35 pi + t < 0, 0, 1) (−21578/35 + (33 sin(245/52 + t))/5 + (379 sin(52/33 + 2 t))/22 + (115 sin(27/17 + 3 t))/32 + sin(29/19 + 4 t)/7 + (8 sin(35/22 + 5 t))/25) + if(79 pi − t < 0, 0, 1) if(−75 pi + t < 0, 0, 1) (8477/37 − (974 sin(80/51 − t))/19 + (3857 sin(30/19 + 2 t))/46 + (426 sin(27/17 + 3 t))/13 + (82 sin(5/3 + 4 t))/39 + (68 sin(61/38 + 5 t))/9 + (27 sin(57/32 + 6 t))/37) + if(71 pi − t < 0, 0, 1) if(−67 pi + t < 0, 0, 1) (59329/144 − (17 sin(43/28 − 12 t))/37 − (52 sin(43/28 − 11 t))/67 − (13 sin(45/29 − 8 t))/10 − (31 sin(37/24 − 7 t))/18 − (306 sin(39/25 − 4 t))/31 − (43 sin(48/31 − 3 t))/28 + (91 sin(74/47 + t))/10 + (454 sin(30/19 + 2 t))/43 + (69 sin(49/31 + 5 t))/19 + (91 sin(61/38 + 6 t))/73 + (39 sin(8/5 + 9 t))/37 + (13 sin(133/83 + 10 t))/41) + if(67 pi − t < 0, 0, 1) if(−63 pi + t < 0, 0, 1) (3599/9 − (30 sin(61/39 − 12 t))/17 − (15 sin(43/28 − 9 t))/29 − (239 sin(25/16 − 8 t))/50 − (595 sin(36/23 − 4 t))/31 + (49 sin(47/10 + t))/99 + (523 sin(63/40 + 2 t))/49 + (93 sin(36/23 + 3 t))/46 + (31 sin(58/37 + 5 t))/23 + (13 sin(27/17 + 6 t))/11 + (33 sin(102/65 + 7 t))/17 + (2 sin(117/73 + 10 t))/9 + (35 sin(11/7 + 11 t))/27) + if(107 pi − t < 0, 0, 1) if(−103 pi + t < 0, 0, 1) (−20442/13 − (1383 sin(11/7 − t))/79 + (114 sin(107/68 + 2 t))/5 + (15 sin(14/3 + 3 t))/19 + (44 sin(107/68 + 4 t))/13 + (3 sin(46/29 + 5 t))/5 + (70 sin(65/41 + 6 t))/33 + sin(23/12 + 7 t)/32 + (31 sin(52/33 + 8 t))/29 + sin(169/37 + 9 t)/11 + (14 sin(30/19 + 10 t))/23 + sin(109/73 + 11 t)/53 + (3 sin(35/22 + 12 t))/7) + if(75 pi − t < 0, 0, 1) if(−71 pi + t < 0, 0, 1) (−81/16 − (3 sin(23/15 − 11 t))/25 − (47 sin(32/21 − 8 t))/43 − (851 sin(36/23 − t))/21 + (781 sin(49/31 + 2 t))/26 + (775 sin(46/29 + 3 t))/22 + (23 sin(27/17 + 4 t))/4 + (10 sin(61/39 + 5 t))/13 + (607 sin(123/77 + 6 t))/91 + (47 sin(53/33 + 7 t))/38 + (110 sin(66/41 + 9 t))/47 + (41 sin(70/43 + 10 t))/38 + (14 sin(21/13 + 12 t))/11) + if(63 pi − t < 0, 0, 1) if(−59 pi + t < 0, 0, 1) (4273/38 − (437 sin(25/16 − 10 t))/131 − (269 sin(59/38 − 8 t))/43 − (151 sin(45/29 − 4 t))/49 − (451 sin(39/25 − 3 t))/38 − (509 sin(11/7 − t))/30 + (173 sin(52/33 + 2 t))/3 + (1214 sin(30/19 + 5 t))/47 + (397 sin(65/41 + 6 t))/30 + (71 sin(49/31 + 7 t))/9 + (8 sin(69/47 + 9 t))/29 + (39 sin(49/31 + 11 t))/43 + (7 sin(93/56 + 12 t))/23) + if(111 pi − t < 0, 0, 1) if(−107 pi + t < 0, 0, 1) (2053/20 − (83 sin(61/39 − 5 t))/13 − (253 sin(36/23 − 3 t))/59 + (938 sin(11/7 + t))/75 + (17 sin(31/20 + 2 t))/16 + sin(23/28 + 4 t)/23 + (47 sin(11/7 + 6 t))/20 + (22 sin(46/29 + 7 t))/15 + sin(278/61 + 8 t)/24 + sin(44/27 + 9 t)/4 + (17 sin(77/48 + 10 t))/18 + (12 sin(55/34 + 11 t))/23 + sin(152/33 + 12 t)/9) + if(103 pi − t < 0, 0, 1) if(−99 pi + t < 0, 0, 1) (−57768/37 − (2799 sin(113/72 − t))/55 + (409 sin(11/7 + 2 t))/28 + (22 sin(65/41 + 3 t))/29 + (27 sin(11/7 + 4 t))/7 + (21 sin(179/38 + 5 t))/20 + (91 sin(49/31 + 6 t))/53 + (21 sin(41/26 + 7 t))/26 + (543 sin(96/61 + 8 t))/272 + (4 sin(51/32 + 9 t))/13 + (40 sin(69/44 + 10 t))/67 + sin(41/24 + 11 t)/105 + (30 sin(65/41 + 12 t))/37 + (31 sin(49/31 + 13 t))/72) + if(27 pi − t < 0, 0, 1) if(−23 pi + t < 0, 0, 1) (−4289/14 − (233 sin(113/72 − 9 t))/51 − (563 sin(36/23 − t))/18 + (2883 sin(107/68 + 2 t))/16 + (321 sin(46/29 + 3 t))/20 + (154 sin(14/3 + 4 t))/17 + (53 sin(114/25 + 5 t))/18 + (593 sin(46/29 + 6 t))/30 + (46 sin(47/29 + 7 t))/17 + (94 sin(19/12 + 8 t))/15 + (193 sin(85/54 + 10 t))/19 + (45 sin(257/55 + 11 t))/44 + (23 sin(53/33 + 12 t))/9 + (49 sin(89/19 + 13 t))/19 + (79 sin(101/63 + 14 t))/21 + (65 sin(50/29 + 15 t))/54 + (75 sin(41/25 + 16 t))/113 + (26 sin(19/11 + 17 t))/51 + (70 sin(8/5 + 18 t))/47 + (25 sin(57/35 + 19 t))/14) + if(51 pi − t < 0, 0, 1) if(−47 pi + t < 0, 0, 1) (−46465/88 − (69 sin(73/47 − 14 t))/28 − (103 sin(116/83 − 13 t))/90 − (427 sin(39/25 − 9 t))/37 − (125 sin(47/30 − 7 t))/12 − (56 sin(374/249 − 5 t))/41 + (313 sin(146/31 + t))/19 + (1543 sin(179/38 + 2 t))/23 + (289 sin(11/7 + 3 t))/15 + (52 sin(41/26 + 4 t))/7 + (495 sin(91/58 + 6 t))/26 + (491 sin(80/51 + 8 t))/29 + (853 sin(61/39 + 10 t))/46 + (371 sin(83/55 + 11 t))/74 + (1137 sin(36/23 + 12 t))/62 + (202 sin(47/30 + 15 t))/27 + (42 sin(57/37 + 16 t))/13 + (26 sin(8/5 + 17 t))/53 + (56 sin(133/89 + 18 t))/55 + (9 sin(164/37 + 19 t))/32) + if(47 pi − t < 0, 0, 1) if(−43 pi + t < 0, 0, 1) (−23041/45 − (38 sin(59/38 − 18 t))/15 − (208 sin(59/38 − 16 t))/29 − (73 sin(64/41 − 14 t))/39 − (13 sin(37/30 − 8 t))/59 − (297 sin(47/30 − 6 t))/32 + (2519 sin(245/52 + t))/28 + (83 sin(179/38 + 2 t))/15 + (603 sin(69/44 + 3 t))/31 + (128 sin(52/33 + 4 t))/27 + (41 sin(61/13 + 5 t))/21 + (53 sin(53/33 + 7 t))/44 + (215 sin(63/40 + 9 t))/29 + (37 sin(37/23 + 10 t))/26 + (419 sin(41/26 + 11 t))/37 + (489 sin(74/47 + 12 t))/31 + (177 sin(85/54 + 13 t))/23 + (43 sin(35/22 + 15 t))/18 + (14 sin(37/22 + 17 t))/17 + (16 sin(34/21 + 19 t))/25 + (35 sin(37/23 + 20 t))/34) + if(3 pi − t < 0, 0, 1) if(pi + t < 0, 0, 1) (−48856/21 − (155 sin(45/29 − 21 t))/43 − (139 sin(102/65 − 19 t))/36 − (112 sin(71/46 − 16 t))/17 − (267 sin(45/29 − 12 t))/22 − (1556 sin(14/9 − 11 t))/63 − (872 sin(69/44 − 9 t))/39 − (143 sin(25/16 − 5 t))/12 − (908 sin(47/30 − 3 t))/27 + (661 sin(96/61 + t))/7 + (327 sin(74/47 + 2 t))/17 + (1106 sin(96/61 + 4 t))/37 + (58 sin(52/33 + 6 t))/15 + (41 sin(139/30 + 7 t))/35 + (487 sin(91/57 + 8 t))/73 + (5 sin(12/7 + 10 t))/26 + (143 sin(127/27 + 13 t))/25 + (255 sin(29/18 + 14 t))/29 + (444 sin(45/28 + 15 t))/71 + (27 sin(3/2 + 17 t))/25 + (113 sin(30/19 + 18 t))/42 + (275 sin(67/42 + 20 t))/42 + (79 sin(48/31 + 22 t))/38) + if(91 pi − t < 0, 0, 1) if(−87 pi + t < 0, 0, 1) (−2798/49 − (124 sin(23/16 − 26 t))/29 − (131 sin(37/25 − 25 t))/29 − (76 sin(69/44 − 15 t))/35 − (73 sin(26/17 − 14 t))/11 − (106 sin(77/51 − 13 t))/31 − (29 sin(48/31 − 11 t))/19 − (50 sin(29/19 − 10 t))/11 − (308 sin(95/61 − 9 t))/31 − sin(25/24 − 6 t)/23 − (1017 sin(36/23 − 5 t))/46 − (337 sin(61/39 − 3 t))/18 − (257 sin(25/16 − 2 t))/15 − (522 sin(47/30 − t))/31 + (484 sin(85/54 + 4 t))/19 + (120 sin(8/5 + 7 t))/19 + (483 sin(65/41 + 8 t))/40 + (79 sin(36/23 + 12 t))/14 + (427 sin(34/21 + 16 t))/67 + (207 sin(43/26 + 17 t))/47 + (39 sin(62/37 + 18 t))/19 + (22 sin(88/19 + 19 t))/35 + (2 sin(64/33 + 20 t))/33 + (23 sin(59/33 + 21 t))/30 + (167 sin(48/29 + 22 t))/38 + (81 sin(227/136 + 23 t))/22 + (25 sin(71/44 + 24 t))/24) + if(11 pi − t < 0, 0, 1) if(−7 pi + t < 0, 0, 1) (−64516/39 − (103 sin(71/46 − 25 t))/23 − (127 sin(54/35 − 20 t))/19 − (79 sin(72/47 − 19 t))/28 − (79 sin(38/25 − 18 t))/27 − (158 sin(43/28 − 15 t))/35 − (236 sin(71/46 − 14 t))/37 − (229 sin(66/43 − 12 t))/33 − (1322 sin(14/9 − 9 t))/33 − (263 sin(61/39 − 7 t))/7 − (447 sin(58/37 − 5 t))/25 − (8509 sin(47/30 − 3 t))/39 − (11816 sin(58/37 − 2 t))/41 + (13897 sin(85/54 + t))/38 + (399 sin(179/38 + 4 t))/11 + (737 sin(30/19 + 6 t))/36 + (1248 sin(46/29 + 8 t))/79 + (205 sin(59/37 + 10 t))/12 + (273 sin(212/45 + 11 t))/38 + (269 sin(146/31 + 13 t))/55 + (143 sin(83/52 + 16 t))/18 + (87 sin(193/41 + 17 t))/23 + (95 sin(61/37 + 21 t))/46 + (158 sin(37/24 + 22 t))/105 + (81 sin(108/23 + 23 t))/43 + (25 sin(74/45 + 24 t))/41) + if(7 pi − t < 0, 0, 1) if(−3 pi + t < 0, 0, 1) (−39578/17 − (71 sin(54/35 − 23 t))/21 − (55 sin(38/25 − 18 t))/21 − (251 sin(36/23 − 17 t))/42 − (71 sin(39/25 − 16 t))/22 − (120 sin(48/31 − 13 t))/23 − (67 sin(3/2 − 11 t))/23 − (354 sin(67/43 − 9 t))/41 − (497 sin(39/25 − 7 t))/19 − (5852 sin(58/37 − 3 t))/97 − (593 sin(69/44 − 2 t))/29 + (3680 sin(11/7 + t))/49 + (155 sin(30/19 + 4 t))/8 + (181 sin(46/29 + 5 t))/32 + (229 sin(179/38 + 6 t))/21 + (1101 sin(49/31 + 8 t))/55 + (398 sin(46/29 + 10 t))/19 + (121 sin(39/25 + 12 t))/23 + (783 sin(123/77 + 14 t))/94 + (74 sin(49/29 + 15 t))/47 + (266 sin(93/58 + 19 t))/43 + (164 sin(19/12 + 20 t))/33 + (56 sin(141/88 + 21 t))/25 + (57 sin(14/9 + 22 t))/25 + sin(26/11 + 24 t)/23) + if(15 pi − t < 0, 0, 1) if(−11 pi + t < 0, 0, 1) (−67025/39 − (7 sin(42/29 − 23 t))/4 − (7 sin(57/49 − 22 t))/10 − (188 sin(55/37 − 17 t))/39 − (59 sin(31/23 − 16 t))/25 − (52 sin(39/28 − 15 t))/21 − (543 sin(49/32 − 13 t))/52 − (243 sin(19/13 − 11 t))/20 − (1019 sin(142/95 − 10 t))/58 − (1465 sin(67/43 − 9 t))/157 − (1276 sin(23/15 − 7 t))/39 − (1517 sin(49/32 − 6 t))/40 + (5219 sin(35/22 + t))/33 + (15493 sin(49/31 + 2 t))/36 + (1583 sin(103/22 + 3 t))/21 + (656 sin(46/29 + 4 t))/7 + (524 sin(83/51 + 5 t))/105 + (2064 sin(65/41 + 8 t))/59 + (39 sin(28/65 + 12 t))/46 + (54 sin(44/29 + 14 t))/23 + sin(40/27 + 18 t) + (9 sin(137/31 + 19 t))/22 + (269 sin(47/28 + 20 t))/55 + (33 sin(146/43 + 21 t))/83 + (103 sin(68/39 + 24 t))/24 + (31 sin(100/53 + 25 t))/13 + sin(4/29 + 26 t)/18) + if(95 pi − t < 0, 0, 1) if(−91 pi + t < 0, 0, 1) (52/7 − (5 sin(63/41 − 26 t))/9 − (4 sin(48/31 − 25 t))/31 − (8 sin(77/53 − 23 t))/41 − sin(20/13 − 15 t)/4 − (133 sin(47/30 − 12 t))/23 − (605 sin(64/41 − 11 t))/56 − (97 sin(48/31 − 8 t))/31 − (423 sin(36/23 − 7 t))/31 − (763 sin(58/37 − 5 t))/41 − (1177 sin(11/7 − t))/43 + (31 sin(67/43 + 2 t))/28 + (287 sin(113/24 + 3 t))/32 + (915 sin(11/7 + 4 t))/52 + (3231 sin(52/33 + 6 t))/202 + (647 sin(49/31 + 9 t))/41 + (123 sin(74/47 + 10 t))/52 + (73 sin(212/45 + 13 t))/19 + (28 sin(19/12 + 14 t))/19 + (89 sin(19/12 + 16 t))/21 + (193 sin(41/26 + 17 t))/58 + (83 sin(11/7 + 18 t))/25 + (87 sin(19/12 + 19 t))/41 + (3 sin(17/12 + 20 t))/19 + (44 sin(43/27 + 21 t))/31 + (22 sin(46/29 + 22 t))/9 + (21 sin(19/12 + 24 t))/13 + (17 sin(51/32 + 27 t))/44 + (18 sin(27/17 + 28 t))/17) + if(55 pi − t < 0, 0, 1) if(−51 pi + t < 0, 0, 1) (−7753/33 − (25 sin(26/17 − 39 t))/18 − (5 sin(40/29 − 38 t))/26 − (4 sin(61/43 − 36 t))/23 − (54 sin(33/23 − 31 t))/163 − sin(19/24 − 27 t)/66 − (16 sin(83/55 − 26 t))/11 − (100 sin(55/36 − 25 t))/27 − (97 sin(181/121 − 24 t))/49 − (54 sin(340/227 − 20 t))/29 − (13 sin(43/28 − 19 t))/17 − (680 sin(31/20 − 13 t))/47 − (329 sin(14/9 − 11 t))/66 − (3254 sin(36/23 − 3 t))/35 + (106 sin(46/29 + t))/17 + (1372 sin(63/40 + 2 t))/13 + (645 sin(41/26 + 4 t))/52 + (2806 sin(49/31 + 5 t))/37 + (1066 sin(52/33 + 6 t))/73 + (109 sin(41/26 + 7 t))/9 + (1043 sin(19/12 + 8 t))/48 + (252 sin(101/63 + 9 t))/31 + (67 sin(41/26 + 10 t))/23 + (103 sin(21/13 + 12 t))/33 + (111 sin(59/37 + 14 t))/32 + (72 sin(43/27 + 15 t))/23 + (217 sin(51/32 + 16 t))/34 + (35 sin(49/30 + 17 t))/24 + (45 sin(19/12 + 18 t))/17 + (1589 sin(47/29 + 21 t))/318 + (391 sin(37/23 + 22 t))/78 + (7 sin(108/65 + 23 t))/30 + (59 sin(21/13 + 28 t))/12 + (9 sin(60/37 + 29 t))/20 + sin(47/27 + 30 t)/12 + (23 sin(95/61 + 32 t))/32 + (5 sin(71/39 + 33 t))/36 + (49 sin(37/23 + 34 t))/50 + (43 sin(178/107 + 35 t))/36 + (4 sin(205/44 + 37 t))/45) + if(87 pi − t < 0, 0, 1) if(−83 pi + t < 0, 0, 1) (14846/61 − (9 sin(5/12 − 35 t))/46 + (433 sin(81/52 + t))/63 + (43 sin(218/47 + 2 t))/16 + (40 sin(58/39 + 3 t))/9 + (158 sin(172/37 + 4 t))/27 + (431 sin(35/23 + 5 t))/37 + (91 sin(377/82 + 6 t))/27 + (100 sin(45/31 + 7 t))/27 + (197 sin(64/41 + 8 t))/34 + (39 sin(47/32 + 9 t))/14 + (92 sin(43/28 + 10 t))/17 + (233 sin(135/29 + 11 t))/43 + (194 sin(55/37 + 12 t))/33 + (409 sin(125/27 + 13 t))/26 + (346 sin(49/33 + 14 t))/23 + (253 sin(97/21 + 15 t))/27 + (211 sin(22/15 + 16 t))/17 + (358 sin(134/29 + 17 t))/35 + (469 sin(25/17 + 18 t))/46 + (92 sin(24/17 + 19 t))/39 + (147 sin(47/32 + 20 t))/13 + (259 sin(299/64 + 21 t))/72 + (381 sin(214/47 + 22 t))/29 + (152 sin(173/37 + 23 t))/45 + (103 sin(361/82 + 24 t))/30 + (15 sin(27/32 + 25 t))/28 + (335 sin(86/19 + 26 t))/32 + (321 sin(55/12 + 27 t))/37 + (118 sin(10/7 + 28 t))/15 + (77 sin(39/29 + 29 t))/29 + (57 sin(47/33 + 30 t))/8 + (29 sin(192/41 + 31 t))/13 + (207 sin(112/25 + 32 t))/59 + (513 sin(29/22 + 33 t))/79 + (89 sin(71/16 + 34 t))/23 + (145 sin(38/27 + 36 t))/36 + (122 sin(41/9 + 37 t))/47 + sin(93/23 + 38 t)/4 + (139 sin(279/61 + 39 t))/50 + (35 sin(95/23 + 40 t))/52 + (116 sin(25/19 + 41 t))/25 + (151 sin(135/31 + 42 t))/76) + if(99 pi − t < 0, 0, 1) if(−95 pi + t < 0, 0, 1) (5111/21 − (29 sin(54/37 − 40 t))/27 − (23 sin(21/20 − 39 t))/30 − (503 sin(25/16 − 37 t))/42 − (49 sin(71/53 − 35 t))/25 − (115 sin(92/61 − 34 t))/22 − (225 sin(25/16 − 32 t))/38 − (188 sin(29/19 − 23 t))/23 − (456 sin(36/23 − 21 t))/37 − (205 sin(47/30 − 10 t))/32 − (32 sin(64/41 − 8 t))/5 − (107 sin(53/34 − 6 t))/32 − (63 sin(57/37 − 2 t))/43 + (223 sin(25/16 + t))/28 + (273 sin(63/40 + 3 t))/38 + (616 sin(108/23 + 4 t))/137 + (64 sin(35/22 + 5 t))/11 + (487 sin(47/30 + 7 t))/55 + (386 sin(52/33 + 9 t))/73 + (44 sin(67/42 + 11 t))/15 + (74 sin(207/44 + 12 t))/19 + (179 sin(43/27 + 13 t))/52 + (110 sin(49/32 + 14 t))/47 + (394 sin(65/42 + 15 t))/51 + (74 sin(145/31 + 16 t))/21 + (247 sin(173/37 + 17 t))/35 + (125 sin(43/28 + 18 t))/27 + (9 sin(11/67 + 19 t))/38 + (49 sin(21/13 + 20 t))/19 + (90 sin(25/16 + 22 t))/13 + (71 sin(119/27 + 24 t))/57 + (133 sin(136/29 + 25 t))/11 + (81 sin(45/29 + 26 t))/8 + (63 sin(18/13 + 27 t))/31 + (54 sin(79/42 + 28 t))/31 + (97 sin(144/31 + 29 t))/34 + (379 sin(65/42 + 30 t))/52 + (2099 sin(25/16 + 31 t))/350 + (13 sin(33/16 + 33 t))/17 + (49 sin(163/36 + 36 t))/30 + (359 sin(95/61 + 38 t))/45 + (227 sin(23/14 + 41 t))/81 + (163 sin(135/29 + 42 t))/28 + (14 sin(100/47 + 43 t))/17 + (568 sin(20/13 + 44 t))/53) + if(23 pi − t < 0, 0, 1) if(−19 pi + t < 0, 0, 1) (−3585/8 − (24 sin(46/35 − 34 t))/31 − (163 sin(47/30 − 26 t))/17 − (123 sin(57/37 − 21 t))/44 − (101 sin(14/9 − 19 t))/12 − (8 sin(23/15 − 17 t))/21 − (779 sin(36/23 − 4 t))/25 + (689 sin(145/31 + t))/38 + (2649 sin(80/51 + 2 t))/10 + (113 sin(69/44 + 3 t))/6 + (1707 sin(113/24 + 5 t))/13 + (281 sin(25/16 + 6 t))/16 + (1817 sin(45/29 + 7 t))/34 + (453 sin(65/14 + 8 t))/52 + (55 sin(41/27 + 9 t))/13 + (1927 sin(25/16 + 10 t))/29 + (1073 sin(69/44 + 11 t))/31 + (2221 sin(36/23 + 12 t))/33 + (287 sin(53/33 + 13 t))/34 + (9639 sin(61/39 + 14 t))/482 + (99 sin(86/57 + 15 t))/13 + (41 sin(40/23 + 16 t))/40 + (222 sin(63/41 + 18 t))/25 + (434 sin(108/23 + 20 t))/27 + (17 sin(149/42 + 22 t))/32 + (791 sin(65/42 + 23 t))/34 + (19 sin(143/31 + 24 t))/4 + (63 sin(45/31 + 25 t))/41 + (185 sin(131/28 + 27 t))/27 + (46 sin(76/59 + 28 t))/33 + (149 sin(46/29 + 29 t))/34 + (208 sin(353/235 + 30 t))/43 + (76 sin(32/19 + 31 t))/33 + (87 sin(40/27 + 32 t))/17 + (73 sin(203/45 + 33 t))/49 + (77 sin(84/19 + 35 t))/47 + (283 sin(61/40 + 36 t))/29 + (88 sin(53/33 + 37 t))/19 + (71 sin(20/13 + 38 t))/28 + (35 sin(10/7 + 39 t))/18 + (54 sin(181/39 + 40 t))/13 + (24 sin(34/23 + 41 t))/13 + (39 sin(117/70 + 42 t))/25 + (23 sin(32/25 + 43 t))/26 + (212 sin(125/27 + 44 t))/37 + (21 sin(37/29 + 45 t))/20) + if(19 pi − t < 0, 0, 1) if(−15 pi + t < 0, 0, 1) (−23029/24 − (71 sin(14/9 − 48 t))/85 − (17 sin(10/7 − 44 t))/29 − (150 sin(19/13 − 43 t))/37 − (51 sin(43/28 − 39 t))/8 − (296 sin(76/51 − 37 t))/31 − (147 sin(33/23 − 36 t))/32 − (8 sin(12/31 − 33 t))/33 − (127 sin(53/37 − 32 t))/20 − (573 sin(47/32 − 31 t))/38 − (25 sin(35/26 − 30 t))/36 − (774 sin(26/17 − 26 t))/31 − (52 sin(13/10 − 23 t))/17 − (811 sin(41/27 − 22 t))/26 − (3257 sin(45/29 − 19 t))/71 − (921 sin(65/42 − 9 t))/47 − (522 sin(26/17 − 8 t))/31 − (861 sin(17/11 − 7 t))/22 − (897 sin(66/43 − 6 t))/35 − (677 sin(53/34 − 5 t))/15 − (33 sin(37/34 − 4 t))/40 + (433 sin(51/32 + t))/18 + (8978 sin(52/33 + 2 t))/57 + (839 sin(146/31 + 3 t))/18 + (190 sin(81/52 + 10 t))/23 + (17 sin(59/13 + 11 t))/12 + (401 sin(50/31 + 12 t))/20 + (461 sin(59/36 + 13 t))/31 + (266 sin(34/21 + 14 t))/11 + (222 sin(31/19 + 15 t))/11 + (183 sin(58/37 + 16 t))/46 + (241 sin(103/22 + 17 t))/22 + (865 sin(25/16 + 18 t))/32 + (699 sin(49/31 + 20 t))/32 + (306 sin(49/30 + 21 t))/41 + (255 sin(63/37 + 24 t))/31 + (227 sin(31/21 + 25 t))/38 + (60 sin(24/19 + 27 t))/31 + (392 sin(77/45 + 28 t))/45 + (390 sin(107/64 + 29 t))/31 + (28 sin(53/27 + 34 t))/25 + (513 sin(51/31 + 35 t))/110 + (18 sin(34/25 + 38 t))/7 + (127 sin(67/41 + 40 t))/25 + (31 sin(76/41 + 41 t))/9 + (61 sin(53/33 + 42 t))/28 + (52 sin(33/19 + 45 t))/31 + (5 sin(134/73 + 46 t))/16 + (33 sin(39/29 + 47 t))/83 + (19 sin(55/36 + 49 t))/27) + if(59 pi − t < 0, 0, 1) if(−55 pi + t < 0, 0, 1) (11225/33 − (21 sin(44/45 − 36 t))/29 − (433 sin(53/34 − 30 t))/21 − (587 sin(47/31 − 8 t))/36 − (3175 sin(25/16 − 6 t))/26 − (2589 sin(11/7 − t))/32 + (34 sin(125/38 + 2 t))/31 + (3176 sin(179/38 + 3 t))/19 + (223 sin(77/46 + 4 t))/52 + (1655 sin(11/7 + 5 t))/16 + (9074 sin(63/40 + 7 t))/75 + (158 sin(63/40 + 9 t))/11 + (874 sin(155/33 + 10 t))/27 + (265 sin(93/20 + 11 t))/28 + (756 sin(289/62 + 12 t))/25 + (474 sin(65/14 + 13 t))/31 + (744 sin(229/49 + 14 t))/41 + (74 sin(133/29 + 15 t))/13 + (1576 sin(113/24 + 16 t))/59 + (377 sin(46/29 + 17 t))/41 + (206 sin(52/33 + 18 t))/15 + (311 sin(26/17 + 19 t))/29 + (53 sin(13/28 + 20 t))/88 + (491 sin(10/7 + 21 t))/70 + (464 sin(49/33 + 22 t))/33 + (872 sin(45/29 + 23 t))/39 + (20 sin(49/23 + 24 t))/27 + (765 sin(129/28 + 25 t))/52 + (1493 sin(135/29 + 26 t))/39 + (817 sin(261/56 + 27 t))/33 + (803 sin(19/12 + 28 t))/42 + (725 sin(102/65 + 29 t))/41 + (31 sin(302/67 + 31 t))/10 + (37 sin(67/33 + 32 t))/18 + (1312 sin(51/11 + 33 t))/99 + (230 sin(68/15 + 34 t))/31 + (13 sin(43/15 + 35 t))/25 + (479 sin(69/44 + 37 t))/49 + (181 sin(75/16 + 38 t))/37 + (520 sin(131/28 + 39 t))/57 + (302 sin(26/15 + 40 t))/55 + (39 sin(539/135 + 41 t))/47 + (1232 sin(191/41 + 42 t))/93 + (33 sin(40/11 + 43 t))/35 + (22 sin(35/8 + 44 t))/17 + (377 sin(152/33 + 45 t))/60 + (69 sin(179/40 + 46 t))/22 + (67 sin(30/19 + 47 t))/42 + (7 sin(77/29 + 48 t))/31 + (33 sin(93/20 + 49 t))/31 + (41 sin(174/37 + 50 t))/31 + (21 sin(317/88 + 51 t))/29 + (868 sin(129/28 + 52 t))/137 + (71 sin(159/35 + 53 t))/19 + (13 sin(70/27 + 54 t))/20)) && 0 ≤ t ≤ 112 pi

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