Assuming I have two path functions $$f, g : R^+\to R^2$$ for example a sin curve: $$f(t) = (t, \sin(t)) t:[0, 1]$$ or a circle: $$g(t) = (\sin(t), \cos(t)) t:[0, 1]$$ What I need is a way to calculate $$h = f * g$$
so that the the result will look like it's a sin going in a circle, assume you take the X axis and bent it into a circle while the sin on it, same way bending sin over another sin and etc.
So this operation basically takes the first function and shape it over the second.
Anyone know how it's called and what is the operation? There must be something like this in topology.
applied on this:
will result in something like this (using coffeemath method):
the blue line is the sin going around the circle.
but this only works for functions like: $$f(t)=(t, v(t))$$
here is sin around sin around sin using same method:
This is good already but maybe there is a function for the general case?
Solution: (by coffeemath)
given $$f(t)=(u(t),v(t))$$ $$g(t)=(x(t),y(t))$$ to draw f around g will be: $$w(t)=g(t)+u(t)T(t)+v(t)N(t)$$
now i can draw circle around another circle: