Color gamut mapping plays a crucial role in color management. Accurate techniques for defining and visualizing a device's gamut boundary are very important in the design of robust color gamut mapping algorithms. A novel technique for defining the surface of a color imaging device's gamut in CIELAB L*C_ab*h_ab color space using a triangulation and interpolation process is presented. This process provides an accurate approach for gamut surface fitting, from measured or modeled data, that is independent of gamut concavity or convexity. The results of a goodness-of-fit test indicate that the gamut surface can be predicted to a mean ΔE_ab* of 1.1, for the CRT gamut tested. In addition the L*C_ab*h_ab space has been shown to be useful for several gamut mapping and visualization tasks. Finally, an L*C_ab*h_ab gamut is given for an HP Deskjet 870Cxi inkjet printer that was derived from measured data.