Because 3D shape-measuring machines on the market are mainly developed for measuring precise objects, they are very expensive and difficult to operate for medium-sized and small enterprises. So we developed a new type of 3D shape-measuring machine in cooperation with some companies, which is large in size, low in cost and easy to operate. In this paper, firstly, outline of the 3D shape-measuring machine is introduced. Next, coordinate equations of the measured point are derived, and format of the measured data is described. Then, information of a measured triangle (side length and angle) or of a free-form curve, least-square methods and algorithms for rendering any spatial plane, circle, cylinder and sphere are expressed with higher precision, as well as their rendering results obtained by using the software developed in this research with Visual C++ and OpenGL are illustrated. Finally, some conclusions and discussions are summarized.