Methods of hidden surface removal and shading for computer-displayed surfaces are proposed. If the surface to be displayed is approximated by a large number of square faces of restricted orientation, the methods proposed in this paper work at least an order of magnitude faster than previously published methods. A situation in which such approximation is natural is the display of organs based on data obtained by the reconstruction of the internal structure of a body from multiple shadowgraphs such as X-ray photographs (computed tomography). The methods can also be used for rapidly achieving some but not all of the aims of surface modeling in more general situations. The hidden surface removal method is based on the Z-buffer algorithm (no sorting is required), with modifications which make use of the nature of the assumed surface approximation. The artifact caused by approximating the curved surface with squares is reduced by low-pass filtering of the picture to be displayed. The results are demonstrated by displays of actual human organs based on data provided by computed tomography.