Methods, structures and systems for encoding and decoding isosurface data. An encoder process takes volume data and an isolevel as input and produces compressed isosurface data as output. The compressed isosurface data produced by an encoder process is composed of an occupancy image record, an optional intersection points record, and an optional normal vectors record. An occupancy image is compressed with a context-based arithmetic encoder. Compressed isosurface data can be stored in a data storage device or transmitted through a communication medium to a remote computer system, where the decoder process is executed. The decoder processes take compressed surface data as input and produce surface data as output. The decoder processes first reconstructs the occupancy image by decoding the occupancy image record. An in-core isosurface decoder process produces a polygon mesh as a surface representation. An out-of-core isosurface decoder process produces a set of oriented points as a surface representation.