In this paper we present a novel method to calculate the gamut boundary of a color printing device using a sparse number of measured values. This method belongs to the SMGBD (Segment Maxima Gamut Boundary Descriptor) family. At first, we construct an inverse printer model based on a set of printed color patches. This model allows us to find the colorant values that have to be sent to the printer in order to obtain a given color appearance, or to show that such a colorant value does not exist. Then we construct a GBD (Gamut Boundary Descriptor) with the measured color patches, using the segment maxima method. After calculating the GBD every segment contains exactly one color value, which might not necessarily be part of the device gamut boundary. Therefore we sample along the line determined by the contained color value and the middle grey value (L, a, b) = (50, 0, 0) for every segment, using a bisection method based on the inverse printer model, and store the printable color value on the line with the largest distance from the middle grey value in the GBD. Due to this approach practical gamut boundaries can be calculated based on a sparse number of measured colors. Measurement results and a comparison with other methods are given in the text.