A method, a data storage medium storing a computer program, and a data processing system are disclosed to process data comprised of a triangulated mesh representation of an object. The method includes establishing a continuous bijective mapping between a first triangle mesh representation of the object and a second polygonal mesh representation of the object during the application of at least one mesh connectivity operation selected from a set of mesh connectivity operations. Establishing the mapping includes using a set of charts where an individual chart encodes a mapping of a single face of the second polygonal mesh representation to a plurality of triangles of the first triangle mesh representation that the single face of the second mesh representation overlaps with parametrically. The method further includes updating at least one chart of the set of charts in response to each application of the at least one mesh connectivity operation. An edge smoothing operation may be applied to smooth the continuous bijective mapping across chart boundaries.