Mesh parameterization is a primary task in many computer graphics applications

such as texture mapping

digital geometry processing and geometry compression

etc. This paper proposes a global parameterization method of meshes with arbitrary topology. For a given manifold triangle mesh with zero genus

it is firstly turned into a PM representation by means of edge collapse

the two vertices of the age to collapse are locally parameterized over the neighborhood of the new vertex obtained through pair contraction. Edge collapse is iteratively carried out until a simple convex base mesh with local parameterization information is reached

then this base mesh is center protected onto a unit sphere

and vertices deleted during edge collapse are added back and positioned on the unit sphere according to the local parameterization information one by one with an inverse order which they are deleted until an isomorphic mesh of original mesh is produced. By this means

global parameterization over the unit sphere of the original mesh is completed. To avoid fold back

relaxation operator is adopted.