This paper introduces a new and powerful technique to determine the workspace shape of a general n-joint manipulator by utilizing geometric modeling. A complete three-dimensional geometric model of the workspace shape can be generated which is compatible with the computer graphics. The resulting workspace image can be visualized in three-dimensions realistically, manipulated interactively and analyzed for topological and volumetric features. The first part of the paper presents a general discussion of the workspace geometry and boundary representation concept. The remainder of the paper focuses on two workspace boundary extraction methods in a CAD environment: Radial-Slice-Layering method (RSL) and Apparent-Contour method (AC). Several specific examples are presented to illustrate the basic technique.