1. A method to process data comprised of a triangulated mesh representation of an object, comprising: establishing a continuous bijective mapping between a first triangle mesh representation of the object and a second polygonal mesh representation of the object during application of at least one mesh connectivity operation selected from a set of mesh connectivity operations, establishing the mapping comprising computing a set of charts where an individual chart encodes a mapping of a single face of the second mesh representation to a plurality of triangles or portions thereof of the first triangle mesh representation that the single face of the second mesh representation overlaps with parametrically; and dynamically updating at least one chart of the set of charts in response to each application of the at least one mesh connectivity operation.