Abstract: The disclosure describes a system for measuring three-dimensional coordinates comprising a position detector which detects orthogonal coordinate positions of X-, Y-, and Z-axes on a surface to be measured; a noncontact-type displacement measuring instrument which moves along the surface to be measured; a device which controls the attitude of the displacement measuring instrument; a coordinate operation processor which converts the data from said position detecting means, from said noncontact-type displacement measuring instrument, and from said device into three-dimensional coordinates of the surface to be measured; a computer which files and transfers to an external unit the data that are operated by said coordinate operation processor; and a singular point determination processor which introduces the coordinate data from said coordinate operation processor, which extracts any singular points, and which transfers the coordinates thereof to said computer.