- #1
mnb96
- 715
- 5
Hello,
if one wants to represent a parametric curve in a N-dimensional vector space, the straightforward way is to express it as:
[tex]\mathbf{v} = f_1(t)\mathbf{e}_1 + \ldots + f_n(t)\mathbf{e}_n[/tex]
However there are infinite representations!
I could make any substitution [tex] t = g(t)[/tex] as long as g is invertible and I would get the same curve in the space.
How should a curve (or surface) be expressed in a general way, independent of the type of parametrization?
if one wants to represent a parametric curve in a N-dimensional vector space, the straightforward way is to express it as:
[tex]\mathbf{v} = f_1(t)\mathbf{e}_1 + \ldots + f_n(t)\mathbf{e}_n[/tex]
However there are infinite representations!
I could make any substitution [tex] t = g(t)[/tex] as long as g is invertible and I would get the same curve in the space.
How should a curve (or surface) be expressed in a general way, independent of the type of parametrization?