Translation, Rotation and Inversion of a Parabola

http://mypeoplepc.com/members/jon8338/math/id41.html

Red Curve: Translating and Rotating Parabola

r_x
(5*abs(sin(t))+5*abs(sin(t))*cos(2*t+acos(-1))-(u^2)*cos(2*t+acos(-1))+u*sin(2*t+acos(-1)))
r_y
(5*abs(sin(t))*sin(2*t+acos(-1))-(u^2)*sin(2*t+acos(-1))-u*cos(2*t+acos(-1)))


Blue Curve: Inverted Translating and Rotating Parabola:

B_x=10*(5*abs(sin(t))+5*abs(sin(t))*cos(2*t+acos(-1))-(u^2)*cos(2*t+acos(-1))+u*sin(2*t+acos(-1)))/(((5*abs(sin(t))+5*abs(sin(t))*cos(2*t+acos(-1))-(u^2)*cos(2*t+acos(-1))+u*sin(2*t+acos(-1)))^2+(5*abs(sin(t))*sin(2*t+acos(-1))-(u^2)*sin(2*t+acos(-1))-u*cos(2*t+acos(-1)))^2)^.5) 
 - 
(5*abs(sin(t))+5*abs(sin(t))*cos(2*t+acos(-1))-(u^2)*cos(2*t+acos(-1))+u*sin(2*t+acos(-1)))

B_y=10*(5*abs(sin(t))*sin(2*t+acos(-1))-(u^2)*sin(2*t+acos(-1))-u*cos(2*t+acos(-1)))/(((5*abs(sin(t))+5*abs(sin(t))*cos(2*t+acos(-1))-(u^2)*cos(2*t+acos(-1))+u*sin(2*t+acos(-1)))^2+(5*abs(sin(t))*sin(2*t+acos(-1))-(u^2)*sin(2*t+acos(-1))-u*cos(2*t+acos(-1)))^2)^.5) 
 - 
(5*abs(sin(t))*sin(2*t+acos(-1))-(u^2)*sin(2*t+acos(-1))-u*cos(2*t+acos(-1)))

(x,f(x))=(u^2,u)
t=time

I always wanted to solve this.  It gives the incremental steps in the 
process of turning a T-shirt inside-out, only everything in the room gets 
turned inside-out as well.

The animated gif is made of 25 frames and the file is 250 kilobytes.