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General view

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Computational conformal geometry (CCG) is an interdisciplinary field that related to algebraic topology, differential geometry, Riemann surface, harmonic analysis, etc. Also related to physical fields that electrodynamics, elastic deformation, thermal dynamics, and modular space theory in super string theory.

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The space formed by all Riemann surfaces sharing the same topology and geometry of the modular space is called Modular Space, which also a finite dimensional manifold.

 

The power of CCG is the following fact: all surface in real life can be deformed to three canonical shapes, the sphere, the disk and hyperbolic space. The deformation preserves angles and is determined by a set of parameters such as the landmarks. Thus all geometric problem in three dimensional Euclidean space can be concerted to two dimensional problem on plane.

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