Computing Fenchel-Nielsen coordinates in Teichmuller shape Space

Abstract

Teichmüller shape space is a finite dimensional Riemannian manifold, where each point represents a class of surfaces, which are conformally equivalent, and a path represents a deformation process from one shape to the other. Two surfaces in the real world correspond to the same point in the Teichmüller space, only if they can be conformally mapped to each other. Teichmüller shape space can be used for surface classification purpose in shape modeling.