Computing parametric coordinates


I have been using BAMG to construct anisotropic meshes for a while now. I am interested in knowing how to construct meshes on curved geometries. From the BAMG documentation, I see that I can provide tangents at edges and this will then be used to construct mesh vertices on the second or third order representation of the geometry. I wanted to know how exactly the parametric coordinates of these mesh points are calculated.

To be specific, in the mesh file they are called “VertexOnGeometricEdge” and I am given a vertex number, geometric edge number and a floating point. I wanted to know how the third floating point is calculated.

Please let me know how to compute these exactly given two tangents at edges. It would be very useful for my work.

Best regards