1. A method to process data comprised of a triangulated mesh representation of an object, comprising: using a processor, 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 without updating an entire mapping, dynamically updating overlap portions of at least one chart of the set of charts in response to each application of the at least one mesh connectivity operation.