An approximately Euclidean representation of the visible scene can be obtained directly from a range, or 'time-of-flight', camera. An uncalibrated binocular system, in contrast, gives only a projective reconstruction of the scene. This paper analyzes the geometric mapping between the two representations, without requiring an intermediate calibration of the binocular system. The mapping can be found by either of two new methods, one of which requires point-correspondences between the range and colour cameras, and one of which does not. It is shown that these methods can be used to reproject the range data into the binocular images, which makes it possible to associate high-resolution colour and texture with each point in the Euclidean representation.