1. Apparatus for mapping an object, comprising: an illumination assembly, comprising: a single transparency containing a fixed pattern of spots; and a light source, which is configured to transilluminate the single transparency with optical radiation so as to project the pattern onto the object; an image capture assembly, which is configured to capture an image of the pattern that is projected onto the object using the single transparency; and a processor, which is coupled to process the image captured by the image capture assembly so as to reconstruct a three-dimensional (3D) map of the object.