I was wondering if there are methods for specifying a vector field which have the versatility and intuitiveness of a bezier curve. Like a Bezier curve, I'd like to be able to 'patch' entities together to ensure smoothness by constraining the rate of change at the boundary. Just as a cubic bezier can approximate almost all curves, I'd like this vector field tool to be versatile enough to approximate almost all possible vector fields.
Does something like this exist?
Thanks!
If you want to "patch together" the individual fields in a smooth way, then you probably ought to be looking at b-spline techniques. Very roughly speaking, b-splines give you a way to joint together polynomial pieces with prescribed continuity.
I would guess that you probably know the values of your vector field at certain points, and you want to interpolate these values with some smooth function. Either Bezier or b-spline techniques will allow you to do this. But b-splines will probably work better because they allow you to increase the number of interpolated points without increasing degree.
Here is one reference. You can find many others by searching for terms like "vector field visualization".