Sampling in COLLADA objects

Hi all,

Basic problem is that I need to sample on the 1D curves (in 3D space), 2D surfaces (in 3D space) or 3D volumes specified in COLLADA. Mathematically it leads to the mapping, e.g., of the 3D surface to the 2D limited plane (XY). So that by choosing point x in [0,1] and y in [0,1] we could get a unique point on the surface. The same stands for arbitrary 1D curves in 3D space and searching for a function that maps an arbitrary curve to the interval [0,1].

I would be grateful for any hints or suggestions. Please excuse me, if the question has no relation to this forum.

Best regards,