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We present an algorithm that constructs compact and realistic descriptions of colored 3D objects using texture mapping on compressed triangulations. A highresolution triangular mesh model is created by integrating measurements from a color 3D laser sensor. Each vertex is attributed with a RGB color value. The high-resolution triangulation is transformed into a compressed triangulation and a texture map. This map embeds the color information of the vertices removed during the geometric compression and projected on the lower resolution triangulation. We describe the algorithm for the rapid and efficient construction of a texture map for compressed triangulations of arbitrary topology. Experiments show that high compression rates can be achieved while maintaining good visual similarity between the original and compressed models.