ProbeGetTangentspaces

ProbeGetTangentspaces returns the List of tangent spaces of the already calculated points given by ProbeGetPoints. The tangent space itself is represented as a List of (orthonormal) basis vectors.

Be aware that not all points must have well defined tangent spaces, i.e. a list of basis vectors given by ProbeGetTangentspaces can be empty. This mostly depends on the ProbeScan option MaxEV and on the surface itself. For example, self-intersecting surfaces do have singular points.

Also note that in general the set of basis vectors is not oriented.

This method admits no arguments nor options.

Example

<< BProbeM`

(* initialization *)
t = PauliMatrix[{1,2,3}];
ProbeInit[t];
ProbeScan[];

(* calculate normal vectors to the tangential surfaces; *)
(* since in this case the tangent spaces are two-dimensional, they *)
(* can also be charactarized by their normal vectors *)
normals = Cross[#[[1]],#[[2]]]& /@ ProbeGetTangentspaces[];

(* the normals can for example be used to reconstruct a surface *)
(* from the given pointcloud *)