Frohe Weihnachten allen und einen guten Rutsch ins neue Jahr!

Question

Allen Mitgliedern und Lesern ein frohes Weihnachtsfest und einen guten Rutsch ins Neue Jahr!


Ich erlaube mir dazu einen alten Post hervorzuholen. Der wird nie alt:

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Zum Nachzeichnen:

x(t) = ((37/2 sin(t + 39/19) + 8/13 sin(2 t + 13/8) + 3/5 sin(3 t + 37/11) + 4/9 sin(4 t + 19/10) + 2/9 sin(5 t + 1/11) + 2900/7) θ(99 π - t) θ(t - 95 π) + (-10/7 sin(9/11 - 2 t) - 296/11 sin(9/14 - t) + 29/11 sin(3 t + 11/6) + 9/10 sin(4 t + 3/10) + 34/33 sin(5 t + 13/4) + 4797/14) θ(95 π - t) θ(t - 91 π) + (-2 sin(17/13 - 3 t) + 307/8 sin(t + 9/10) + 13/6 sin(2 t + 46/45) + 12/7 sin(4 t + 1/4) + 5/4 sin(5 t + 16/5) + 5903/13) θ(91 π - t) θ(t - 87 π) + (-2/9 sin(6/11 - 4 t) + 89/6 sin(t + 21/22) + 1/3 sin(2 t + 11/8) + 3/7 sin(3 t + 4/7) + 1/5 sin(5 t + 7/11) + 11312/25) θ(87 π - t) θ(t - 83 π) + (378/29 sin(t + 17/13) + 14/15 sin(2 t + 10/7) + 7/13 sin(3 t + 8/9) + 5/8 sin(4 t + 6/7) + 3/11 sin(5 t + 103/26) + 4297/12) θ(83 π - t) θ(t - 79 π) + (862/13 sin(t + 17/13) + 1143/26 sin(2 t + 32/13) + 187/8 sin(3 t + 8/11) + 20/9 sin(4 t + 64/15) + 61/7 sin(5 t + 46/15) + 2887/7) θ(79 π - t) θ(t - 75 π) + (-2/3 sin(4/11 - 2 t) + 133/9 sin(t + 19/6) + 13/10 sin(3 t + 19/18) + 2/7 sin(4 t + 36/13) + 2/13 sin(5 t + 1/11) + 1623/7) θ(75 π - t) θ(t - 71 π) + (327/8 sin(t + 29/7) + 69/7 sin(2 t + 47/11) + 102/7 sin(3 t + 14/3) + 31/7 sin(4 t + 19/9) + 29/6 sin(5 t + 11/3) + 2105/9) θ(71 π - t) θ(t - 67 π) + (-44/19 sin(1/7 - 2 t) - 169/7 sin(2/11 - t) + 23/12 sin(3 t + 53/18) + 6/7 sin(4 t + 16/15) + 5/12 sin(5 t + 41/11) + 13966/35) θ(67 π - t) θ(t - 63 π) + (-9/4 sin(19/13 - 5 t) - 205/9 sin(13/9 - 2 t) - 1051/21 sin(1/3 - t) + 246/11 sin(3 t + 3/4) + 22/5 sin(4 t + 33/8) + 2601/8) θ(63 π - t) θ(t - 59 π) + (-327/8 sin(8/9 - 2 t) + 1260/19 sin(t + 4) + 112/5 sin(3 t + 57/17) + 59/7 sin(4 t + 4/7) + 94/17 sin(5 t + 74/21) + 1771/4) θ(59 π - t) θ(t - 55 π) + (-21/8 sin(1/8 - 5 t) - 1057/13 sin(1/4 - t) + 23/4 sin(2 t + 4/11) + 70/9 sin(3 t + 59/17) + 15/7 sin(4 t + 16/9) + 913/3) θ(55 π - t) θ(t - 51 π) + (-50/9 sin(13/10 - 2 t) + 599/6 sin(t + 14/11) + 29/13 sin(3 t + 5/9) + 28/5 sin(4 t + 55/12) + 6/5 sin(5 t + 43/12) + 5447/12) θ(51 π - t) θ(t - 47 π) + (1729/12 sin(t + 17/9) + 3/8 sin(2 t + 12/5) + 69/5 sin(3 t + 28/11) + 3/5 sin(4 t + 8/3) + 58/13 sin(5 t + 29/9) + 9730/23) θ(47 π - t) θ(t - 43 π) + (-27/5 sin(1/32 - 5 t) + 1859/7 sin(t + 14/11) + 21/8 sin(2 t + 23/11) + 299/14 sin(3 t + 5/8) + 5/2 sin(4 t + 39/20) + 1205/3) θ(43 π - t) θ(t - 39 π) + (-32/3 sin(1/4 - 5 t) + 993/11 sin(t + 51/19) + 657/16 sin(2 t + 53/13) + 106/7 sin(3 t + 31/12) + 61/3 sin(4 t + 25/13) + 4205/7) θ(39 π - t) θ(t - 35 π) + (-55/3 sin(3/8 - 2 t) + 821/11 sin(t + 13/3) + 102/11 sin(3 t + 11/3) + 17/6 sin(4 t + 101/50) + 35/12 sin(5 t + 1/7) + 4550/9) θ(35 π - t) θ(t - 31 π) + (1893/10 sin(t + 21/8) + 934/7 sin(2 t + 39/10) + 133/3 sin(3 t + 33/17) + 47/3 sin(4 t + 27/7) + 108/5 sin(5 t + 17/12) + 11985/16) θ(31 π - t) θ(t - 27 π) + (-7/3 sin(1/26 - 3 t) - 569/10 sin(11/8 - t) + 3/2 sin(2 t + 1/6) + 27/26 sin(4 t + 3/5) + 9/8 sin(5 t + 6/7) + 4980/11) θ(27 π - t) θ(t - 23 π) + (-909/26 sin(3/4 - t) + 18 sin(2 t + 27/16) + 79/9 sin(3 t + 1/7) + 16/7 sin(4 t + 3/7) + 20/11 sin(5 t + 1/8) + 1062/7) θ(23 π - t) θ(t - 19 π) + (-11/9 sin(15/11 - 5 t) - 31/12 sin(1/15 - 2 t) - 316/9 sin(1/7 - t) + 19/9 sin(3 t + 38/9) + 20/9 sin(4 t + 13/9) + 2359/13) θ(19 π - t) θ(t - 15 π) + (-52/5 sin(8/13 - 4 t) + 8905/56 sin(t + 7/9) + 76/7 sin(2 t + 25/24) + 37/3 sin(3 t + 16/5) + 29/7 sin(5 t + 13/8) + 3221/8) θ(15 π - t) θ(t - 11 π) + (-43/6 sin(1/6 - 3 t) - 224/15 sin(1/7 - 2 t) + 834/5 sin(t + 6/7) + 19/5 sin(4 t + 41/12) + 40/9 sin(5 t + 40/9) + 4454/11) θ(11 π - t) θ(t - 7 π) + (886/7 sin(t + 11/7) + 42/11 sin(2 t + 9/5) + 65/6 sin(3 t + 7/5) + 8/15 sin(4 t + 29/11) + 29/7 sin(5 t + 8/7) + 3089/8) θ(7 π - t) θ(t - 3 π) + (-2/9 sin(10/7 - 5 t) - 667/12 sin(13/12 - t) + 29/12 sin(2 t + 6/11) + 10/7 sin(3 t + 75/16) + 27/14 sin(4 t + 13/7) + 5069/28) θ(3 π - t) θ(t + π)) θ(sqrt(sgn(sin(t/2))))


y(t) = ((162/17 sin(t + 3/7) + 16/13 sin(2 t + 5/8) + 5/3 sin(3 t + 19/9) + 1/2 sin(4 t + 9/13) + 9/19 sin(5 t + 38/11) + 11270/13) θ(99 π - t) θ(t - 95 π) + (-5/4 sin(25/17 - 5 t) + (215 sin(t))/11 + 49/16 sin(2 t) + 29/9 sin(3 t + 30/11) + 9/14 sin(4 t + 13/8) + 10728/11) θ(95 π - t) θ(t - 91 π) + (-421/30 sin(7/6 - t) + 24/7 sin(2 t + 22/7) + 47/11 sin(3 t + 49/13) + 7/12 sin(4 t + 91/46) + 5/3 sin(5 t + 63/25) + 3981/4) θ(91 π - t) θ(t - 87 π) + (-2/9 sin(1/57 - 5 t) - 10/11 sin(13/9 - 3 t) - 62/5 sin(11/14 - t) + 9/14 sin(2 t + 23/9) + 1/7 sin(4 t + 35/9) + 43019/45) θ(87 π - t) θ(t - 83 π) + (-2/13 sin(3/5 - 5 t) - 6/17 sin(20/13 - 4 t) - 7/8 sin(4/13 - 3 t) - 57/7 sin(5/8 - t) + 8/13 sin(2 t + 37/14) + 8515/9) θ(83 π - t) θ(t - 79 π) + (-57/5 sin(11/14 - 3 t) - 958/25 sin(1/29 - t) + 88/7 sin(2 t + 47/14) + 116/7 sin(4 t + 2/7) + 27/5 sin(5 t + 41/10) + 6243/7) θ(79 π - t) θ(t - 75 π) + (97/5 sin(t + 85/19) + 4/7 sin(2 t + 40/9) + 42/41 sin(3 t + 4) + 4/9 sin(4 t + 21/5) + 1/2 sin(5 t + 31/7) + 2786/5) θ(75 π - t) θ(t - 71 π) + (-5/2 sin(1/3 - 5 t) - 243/22 sin(12/13 - 3 t) - 1253/11 sin(4/3 - t) + 43/11 sin(2 t + 34/13) + 9/10 sin(4 t + 9/2) + 2961/5) θ(71 π - t) θ(t - 67 π) + (135/8 sin(t + 22/5) + 43/21 sin(2 t + 7/9) + 18/19 sin(3 t + 1) + 8/7 sin(4 t + 5/8) + 8/7 sin(5 t + 13/3) + 4558/7) θ(67 π - t) θ(t - 63 π) + (479/9 sin(t + 17/4) + 13/4 sin(2 t + 33/10) + 35/4 sin(3 t + 26/7) + 99/10 sin(4 t + 3/5) + 45/13 sin(5 t + 14/5) + 5380/33) θ(63 π - t) θ(t - 59 π) + (-45/11 sin(1 - 5 t) - 160/11 sin(23/17 - 3 t) - 524/9 sin(12/13 - t) + 333/14 sin(2 t + 1) + 3/7 sin(4 t + 7/6) + 1861/12) θ(59 π - t) θ(t - 55 π) + (-91/17 sin(1/19 - 3 t) + 471/8 sin(t + 31/8) + 25/8 sin(2 t + 20/11) + 38/13 sin(4 t + 6/5) + 18/7 sin(5 t + 31/7) + 3043/10) θ(55 π - t) θ(t - 51 π) + (-3/4 sin(11/12 - 5 t) - 73/9 sin(10/11 - 3 t) - 287/5 sin(2/5 - t) + 83/7 sin(2 t + 2/3) + 13/5 sin(4 t + 2/7) + 2732/9) θ(51 π - t) θ(t - 47 π) + (184/7 sin(t + 23/7) + 279/28 sin(2 t + 19/11) + 102/13 sin(3 t + 119/30) + 21/11 sin(4 t + 143/48) + 57/29 sin(5 t + 61/13) + 6782/13) θ(47 π - t) θ(t - 43 π) + (-71/7 sin(17/12 - 5 t) - 1609/70 sin(5/6 - 3 t) - 425/8 sin(9/19 - t) + 263/8 sin(2 t + 9/10) + 101/13 sin(4 t + 1/5) + 407) θ(43 π - t) θ(t - 39 π) + (763/6 sin(t + 13/11) + 279/10 sin(2 t + 20/11) + 37/5 sin(3 t + 86/29) + 246/35 sin(4 t + 1/10) + 32/5 sin(5 t + 18/7) + 7257/11) θ(39 π - t) θ(t - 35 π) + (573/8 sin(t + 27/8) + 193/10 sin(2 t + 10/3) + 13 sin(3 t + 40/41) + 45/17 sin(4 t + 135/34) + 23/8 sin(5 t + 1/5) + 8474/13) θ(35 π - t) θ(t - 31 π) + (-45 sin(5/4 - 2 t) + 2833/8 sin(t + 104/23) + 37/3 sin(3 t + 5/16) + 220/9 sin(4 t + 9/2) + 188/13 sin(5 t + 19/12) + 4790/9) θ(31 π - t) θ(t - 27 π) + (502/11 sin(t + 88/25) + 56/9 sin(2 t + 36/11) + 19/13 sin(3 t + 17/9) + 48/49 sin(4 t + 13/5) + sin(5 t + 1/2) + 11505/16) θ(27 π - t) θ(t - 23 π) + (-9/4 sin(81/80 - 5 t) - 92/11 sin(10/11 - 2 t) + 1089/16 sin(t + 51/11) + 96/17 sin(3 t + 37/9) + 11/6 sin(4 t + 17/13) + 2453/4) θ(23 π - t) θ(t - 19 π) + (-16/11 sin(6/7 - 2 t) + 473/10 sin(t + 9/2) + 19/8 sin(3 t + 41/11) + 4/7 sin(4 t + 25/7) + 2/5 sin(5 t + 79/17) + 12473/21) θ(19 π - t) θ(t - 15 π) + (-643/6 sin(3/10 - t) + 263/7 sin(2 t + 1/6) + 143/6 sin(3 t + 49/11) + 73/8 sin(4 t + 30/13) + 33/10 sin(5 t + 31/8) + 12604/15) θ(15 π - t) θ(t - 11 π) + (-619/9 sin(1/4 - t) + 499/17 sin(2 t + 13/4) + 65/3 sin(3 t + 41/10) + 53/27 sin(4 t + 1/5) + 96/11 sin(5 t + 19/8) + 13608/13) θ(11 π - t) θ(t - 7 π) + (-13/9 sin(1/8 - 4 t) - 103/6 sin(9/8 - 2 t) + 43 sin(t + 14/5) + 72/7 sin(3 t + 43/13) + 13/3 sin(5 t + 37/10) + 54911/48) θ(7 π - t) θ(t - 3 π) + (655/13 sin(t + 15/4) + 13/4 sin(2 t + 25/9) + 11/9 sin(3 t + 61/13) + 2/9 sin(4 t + 13/5) + 4/7 sin(5 t + 82/19) + 20652/19) θ(3 π - t) θ(t + π)) θ(sqrt(sgn(sin(t/2))))

Quelle: Wolfram Alpha

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Grüße

Comments

Ob eine Formel das hier auch bilden kann?

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Klar! Wenn Du auf ein paar Sachen verzichten kannst :D.

max(min(max(min((x/a - 47/48)^2 + (y/a + 19/29)^2 - 1, -(x/a - 31/77)^2 - (y/a + 23/22)^2 + 25/22, x/a), min((x/a + 47/48)^2 + (y/a + 19/29)^2 - 1, -(x/a + 27/67)^2 - (y/a + 23/22)^2 + 25/22, -x/a)), -y/a - 1/2), min(max(min((x/a - 16/19)^2 + (y/a + 56/67)^2 - 49/25, -(x/a - 8/19)^2 - (y/a + 27/20)^2 + 31/16, x/a), min((x/a + 16/19)^2 + (y/a + 56/67)^2 - 49/25, -(x/a + 8/19)^2 - (y/a + 27/20)^2 + 31/16, -x/a)), -y/a - 1/2), min(-(x/a + 17/37)^2 - (y/a + 3/5)^2 + 13/28, y^2/a^2 + (x/a + 1)^2 - 1, -x/a), min(-(x/a - 17/37)^2 - (y/a + 3/5)^2 + 13/28, y^2/a^2 + (x/a - 1)^2 - 1, x/a, -y/a), min(1/6 - x/a, x/a + 1/6, 1/3 (-y/a - 5/2), 1/3 (y/a + 7/2)))>=0

(https://www.wolframalpha.com/input?i=christmas+tree+curve)