First of all, I am sorry if some concepts in this description are not accurate. I have no knowledge of topology, but my research has brought me to a situation in which topology is necessary.
I have a series of datapoints in 3D that lie along a 2D surface (for example a Mobius strip, but it is actually a bit more complicated than that and cannot be easily interpreted by simple visualization). Let us assume that the density of points is high enough (relative to the maximum curvature) to describe the surface unambiguously, so that you cannot have a sudden twist in the space between two data points.
Are there any methods to compute whether this surface is orientable or not?
Thanks in advance for any insights into this.