Surface command for vector-valued functions
I have been working with implicit curves defined by functions of the type g: R² -> R³. Unfortunately, the Function command only works for scalar functions.
It is possible to define simple vector functions with the Surface command though: s(a,b) = Surface(f(a,b), a, 0, 0, b, 0, 0) defines a vector function, where f is a linear combination of vectors depending on a and b. It is then possible to compute the value of s at a point (u,v) by simply writing s(u,v). The first screenshot illustrates this use of the command, with all quantities other than a and b being 3d vectors.
When f is more complicated (in my case, when I use UnitVector), the parameters a and b are replaced by their lower bound (as defined by the parameters to Surface), producing a constant value for the surface. This can be seen on the second screenshot.
Is there a way to define a vector function containing commands such as UnitVector, or an easier way to define g: R² -> R³ vector functions?
Thank you for your help.