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| Esto requiere de cálculos que no entiendo ni de lejos... |
El mundo de la animación hoy en día va de la mano de la informática y de las matemáticas, como vemos en la foto que encabeza esta entrada, los elementos gráficos necesitan de complejos algoritmos capaces de expresar en operaciones matemáticas lo que se intenta dibujar por pantalla.
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| Un Homer Simpson un tanto cutre |
Para dibujar eso por pantalla, mira la operación tan "sencilla" que es necesaria:
x(t) = ((-11/8 sin(17/11-8 t)-3/4 sin(11/7-6 t)-9/10 sin(17/11-5 t)+349/9 sin(t+11/7)+17/12 sin(2 t+8/5)+288/41 sin(3 t+8/5)+69/10 sin(4 t+8/5)+8/5 sin(7 t+13/8)+4/7 sin(9 t+28/17)+4/7 sin(10 t+19/11)+1051/8) theta(39 pi-t) theta(t-35 pi)+(-3/4 sin(11/7-5 t)-54 sin(11/7-t)+237/8 sin(2 t+11/7)+52/11 sin(3 t+33/7)+38/9 sin(4 t+11/7)+249/2) theta(35 pi-t) theta(t-31 pi)+(-16/9 sin(14/9-5 t)-5/2 sin(14/9-3 t)+781/8 sin(t+33/7)+291/11 sin(2 t+11/7)+23/7 sin(4 t+11/7)+18/19 sin(6 t+11/7)+2/5 sin(7 t+61/13)+24/23 sin(8 t+14/9)+1/27 sin(9 t+5/11)+4/11 sin(10 t+11/7)+1/75 sin(11 t+5/8)+1411/7) theta(31 pi-t) theta(t-27 pi)+(-7/11 sin(13/10-13 t)+3003/16 sin(t+33/7)+612/5 sin(2 t+11/7)+542/11 sin(3 t+47/10)+137/7 sin(4 t+51/11)+53/7 sin(5 t+17/11)+23/12 sin(6 t+41/9)+94/11 sin(7 t+51/11)+81/11 sin(8 t+41/9)+53/12 sin(9 t+23/5)+73/21 sin(10 t+13/9)+15/7 sin(11 t+6/5)+37/7 sin(12 t+7/5)+5/9 sin(14 t+27/7)+36/7 sin(15 t+9/2)+68/23 sin(16 t+48/11)+14/9 sin(17 t+32/7)+1999/9) theta(27 pi-t) theta(t-23 pi)+(1692/19 sin(t+29/19)+522/5 sin(2 t+16/11)+767/12 sin(3 t+59/13)+256/11 sin(4 t+31/7)+101/5 sin(5 t+48/11)+163/8 sin(6 t+43/10)+74/11 sin(7 t+49/12)+35/4 sin(8 t+41/10)+22/15 sin(9 t+29/14)+43/10 sin(10 t+4)+16/7 sin(11 t+6/5)+11/21 sin(12 t+55/14)+3/4 sin(13 t+37/10)+13/10 sin(14 t+27/7)+2383/6) theta(23 pi-t) theta(t-19 pi)+(-1/9 sin(7/5-10 t)-2/9 sin(11/9-6 t)+20/11 sin(t+16/15)+7/13 sin(2 t+15/4)+56/13 sin(3 t+25/9)+1/6 sin(4 t+56/15)+5/16 sin(5 t+19/8)+2/5 sin(7 t+5/16)+5/12 sin(8 t+17/5)+1/4 sin(9 t+3)+1181/4) theta(19 pi-t) theta(t-15 pi)+(-1/6 sin(8/11-5 t)+5/8 sin(t+6/5)+13/5 sin(2 t+45/14)+10/3 sin(3 t+7/2)+13/10 sin(4 t+24/25)+1/6 sin(6 t+9/5)+1/4 sin(7 t+37/13)+1/8 sin(8 t+13/4)+1/9 sin(9 t+7/9)+2/9 sin(10 t+63/25)+1/10 sin(11 t+1/9)+4137/8) theta(15 pi-t) theta(t-11 pi)+(-17/13 sin(6/5-12 t)-15/7 sin(25/26-11 t)-13/7 sin(3/14-10 t)-25/7 sin(9/13-6 t)-329/3 sin(8/17-t)+871/8 sin(2 t+2)+513/14 sin(3 t+5/4)+110/9 sin(4 t+3/8)+43/8 sin(5 t+1/5)+43/13 sin(7 t+42/11)+49/16 sin(8 t+11/13)+11/5 sin(9 t+2/7)+5/7 sin(13 t+42/13)+1729/4) theta(11 pi-t) theta(t-7 pi)+(427/5 sin(t+91/45)+3/11 sin(2 t+7/2)+5656/11) theta(7 pi-t) theta(t-3 pi)+(-10/9 sin(7/10-4 t)-7/13 sin(5/6-3 t)-732/7 sin(4/7-t)+63/31 sin(2 t+1/47)+27/16 sin(5 t+11/4)+3700/11) theta(3 pi-t) theta(t+pi)) theta(sqrt(sgn(sin(t/2))))
y(t) = ((-4/11 sin(7/5-10 t)-11/16 sin(14/13-7 t)-481/11 sin(17/11-4 t)-78/7 sin(26/17-3 t)+219/11 sin(t+11/7)+15/7 sin(2 t+18/11)+69/11 sin(5 t+11/7)+31/12 sin(6 t+47/10)+5/8 sin(8 t+19/12)+10/9 sin(9 t+17/11)+5365/11) theta(39 pi-t) theta(t-35 pi)+(-75/13 sin(14/9-4 t)-132/5 sin(11/7-2 t)-83 sin(11/7-t)+1/7 sin(3 t+47/10)+1/8 sin(5 t+14/11)+18332/21) theta(35 pi-t) theta(t-31 pi)+(191/3 sin(t+33/7)+364/9 sin(2 t+33/7)+43/22 sin(3 t+14/3)+158/21 sin(4 t+33/7)+1/4 sin(5 t+74/17)+121/30 sin(6 t+47/10)+1/9 sin(7 t+17/6)+25/11 sin(8 t+61/13)+1/6 sin(9 t+40/9)+7/6 sin(10 t+47/10)+1/14 sin(11 t+55/28)+7435/8) theta(31 pi-t) theta(t-27 pi)+(-4/7 sin(14/9-13 t)+2839/8 sin(t+47/10)+893/6 sin(2 t+61/13)+526/11 sin(3 t+8/5)+802/15 sin(4 t+47/10)+181/36 sin(5 t+13/3)+2089/87 sin(6 t+14/3)+29/8 sin(7 t+69/16)+125/12 sin(8 t+47/10)+4/5 sin(9 t+53/12)+93/47 sin(10 t+61/13)+3/10 sin(11 t+9/7)+13/5 sin(12 t+14/3)+41/21 sin(14 t+22/5)+4/5 sin(15 t+22/5)+14/5 sin(16 t+50/11)+17/7 sin(17 t+40/9)+4180/7) theta(27 pi-t) theta(t-23 pi)+(-7/4 sin(8/11-14 t)-37/13 sin(3/2-12 t)+2345/11 sin(t+32/21)+632/23 sin(2 t+14/3)+29/6 sin(3 t+31/21)+245/11 sin(4 t+5/4)+193/16 sin(5 t+7/5)+19/2 sin(6 t+32/7)+19/5 sin(7 t+17/9)+334/23 sin(8 t+35/8)+11/3 sin(9 t+21/11)+106/15 sin(10 t+22/5)+52/15 sin(11 t+19/12)+7/2 sin(13 t+16/13)+12506/41) theta(23 pi-t) theta(t-19 pi)+(-3/7 sin(1/10-9 t)-1/8 sin(5/14-5 t)-9/8 sin(26/17-2 t)+18/7 sin(t+14/11)+249/50 sin(3 t+37/8)+3/13 sin(4 t+19/9)+2/5 sin(6 t+65/16)+9/17 sin(7 t+1/4)+5/16 sin(8 t+44/13)+2/9 sin(10 t+29/10)+6689/12) theta(19 pi-t) theta(t-15 pi)+(-1/27 sin(1-11 t)-1/6 sin(4/11-10 t)-1/5 sin(2/11-9 t)-7/20 sin(1/2-5 t)-51/14 sin(29/28-3 t)+23/7 sin(t+18/5)+25/9 sin(2 t+53/12)+3/2 sin(4 t+41/15)+1/5 sin(6 t+36/11)+1/12 sin(7 t+14/3)+3/10 sin(8 t+19/9)+3845/7) theta(15 pi-t) theta(t-11 pi)+(-8/7 sin(1/3-13 t)-9/13 sin(4/5-11 t)-32/19 sin(17/12-9 t)-11/6 sin(9/13-8 t)-169/15 sin(8/17-3 t)+917/8 sin(t+55/12)+669/10 sin(2 t+4/13)+122/11 sin(4 t+49/24)+31/9 sin(5 t+1/8)+25/9 sin(6 t+6/7)+43/10 sin(7 t+1/21)+18/19 sin(10 t+9/13)+2/9 sin(12 t+31/15)+1309/5) theta(11 pi-t) theta(t-7 pi)+(-267/38 sin(3/10-2 t)+625/8 sin(t+62/17)+8083/14) theta(7 pi-t) theta(t-3 pi)+(1370/13 sin(t+25/6)+41/21 sin(2 t+205/51)+11/16 sin(3 t+8/13)+9/13 sin(4 t+26/9)+6/5 sin(5 t+11/14)+2251/4) theta(3 pi-t) theta(t+pi)) theta(sqrt(sgn(sin(t/2))))
Ahora imagínate tener que calcular tú todo eso, pero no para ese dibujo tan sencillo, pongamos por ejemplo una escena de una película de animación 3D con muchos elementos visuales, muy detallados. Sería un infierno.
Es por ello que las matemáticas tienen un papel tan importante hoy en día en la animación, son imprescindibles para los complejos software de modelado y para los renderizados que se realizan. Sin ellos, no existiría la "magia" de las peliculas de animación.
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