In this paper, an extendable volumetric representation based on run-lengths called spatial run-length encoding (S-RLE) is presented. The S-RLE representation is developed for a haptic shape modeling system that is based on simulated machining processes. In the system, shape modeling is simulated as virtual material removal processes similar to machining processes with volume-based haptic rendering. The object and the tools are represented by S-RLE. The data structure of S-RLE consists of two cross-referenced databases: one is a stack of lists in geometrical domain, recording the runs describing the space occupation of the object; the other is a table in physical domain, describing the physical properties of each element. The latter is exten...