I am trying to implement a harmonic map from a surface with a boundary to a unit circle in python. I found this algorithm by Xianfeng Gu, which is almost straight forward:

harmonic mapper algorithm

  1. Trace the boundary vertices
  2. Write linear discrete equation of laplace beltrami operator
  3. Solve the system of equation Ax=b

The solution of this system of equations gives the discrete values of a harmonic function namely f at each vertex. How is it possible to compute the harmonic/isothermal/uv co-ordinates?

The code is attached in the tutorial but my C++ skills are poor to understand it.


f is not a scalar field, however; a vector field. Is there then two systems of equations for each co-ordinate?



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