The invention provides a system for modeling three-dimensional objects using hybrid geometric/volumetric representation, wherein sharp edges are created by a geometric representation that is connected to the volumetric representation. The system creates, maintains, and updates the hybrid representation according to user input. The system also provides for conversion of the hybrid representation into either a wholly geometric representation or a wholly volumetric representation, as may be needed for output to a given device, such as a display device, a printer, and/or a fabricating device.