Four related but independent aspects are described: (1) a method and a system to derive mesh surface descriptions (also called connectivity-wireframes) and material properties from objects represented as a scalar field (e.g. discrete multi-dimensional data), scalar functions (e.g. implicit surfaces) or any other surface description, (2) a compact, optionally multi-scalable, optionally view-dependent, optionally animation-friendly, multi-dimensional surface representation method and system comprising a combination of a surface mesh description and material properties associated with a reference grid, (3) a digital coding and decoding method and system of a combined surface mesh representation with connectivity information and material properties and a reference grid, and (4) a method and system for conversion of other surface descriptions to the combined surface mesh representation and reference grid. The presentation of the surface of an object may be transmitted across a communications channel by means of a bit stream.