THIS WAS TO HAVE BEEN a portfolio of computer simulated images of three-dimensional shaded objects
selected for their aesthetic value. Such a survey is not done here since the predominance of pictures made with these techniques are not produced for aesthetic purposes. What does exist is a highly developed output technique for producing shaded and colored video-like pictures, of numerically represented three-dimensional objects. Therefore, presented here is a selection of interesting pictures which utilize this output technique.
While most of the attention in computer graphics research and development has focused on output algorithms and devices, there has always been the inherent requirement on the input side for defining the data which represent the picture. The focus of attention has made it seem natural to classify computer graphic images by the device or technique employed in their production: line-printer images, plotter drawings, CRT pictures, or simply line drawing versus raster display. While these are obvious descriptors, it is more revealing of the picture's purpose, complexity, and sophistication to classify it on the basis of its input definition rather than its output form.
If one asks of each computer image: "How was the two- or three-dimensional data base defined?" then most computer images may be sorted into three basic groups: a) digitized data base; b) procedure-defined data base; or c) user-defined data base.
A. Digitized Data Base
A digitized data base is one which depends primarily on taking measurements of existing three-dimensional objects and processing that information by some image producing algorithm. The role of the user here is basically clerical in converting a point in space to be represented by three numbers. The resulting picture is then clearly a function of the data collected.
B. Procedure-Defined Data Base
A procedure defined data base is one which, while it may take some digitized input which represents an actual threedimensional object, the picture itself is primarily the result of computational changes or enhancement to the three-dimensional object. Examples of this are Plates XXV-XXVIII. Dr. Christiansen's distorted house frame is a result of taking measured data and computing displacements caused by structural loading and exaggerating these displacements so that they may be seen. I am pleased that Dr. Christiansen's development of colored shading to represent structural properties emerged from an earlier joint collaboration with the author on techniques for analysis of the Resch folded-plate structures (Plates I-III). I feel his work is among the most interesting involving computer images as the pictures show properties which could not otherwise be seen.
C. User-Defined Data Base
User-defined data base is, as the term implies, defined by the explicit command of the user. The explicit definition of points and lines is, of course, tedious. Therefore, this kind of data base usually employs some kind of building-block technique in which basic structures are defined once and used as component parts of more complex forms. An example of this is the tetrahedron molecule (Plates IX-XII) in which one cylinder and one sphere are defined and additional instances of these are used to create a composite picture. A variation of this approach is used by the MAGI Company in the creation of their pictures Plates XXIX-XXXII. Here the "primitives" are not defined as a collection of points and lines defining facets of some solid, but are created from a limited set of mathematically defined solids: cones, cylinders, spheres, prisms, etc. All the MAGI pictures must be created from these "primitives." All other images in this gallery were produced at the University of Utah and, therefore, must be created from planar polygons.
Manuscript received December 26. 1973.
The author is with the Department of Computer Science, University of Utah, Salt Lake City, Utah 84112.
Page 497; Prof. R. D. Resch, University of Utah:
Plate I A computer-simulated image of Resch folded-plate trusswork in a flat configuration.
Plate II A Resch folded-plate trusswork in a warped configuration.
Plate III. A Reach folded-plate trusswork in a domed configuration. Computational techniques allow the study of possible architectural forms and their structural analysis.
Plate IV. A faceted representation of a face in which each facet is a polygon whose vertices
have been digitized from an actual face by H. Gouraud, University of Utah (graduate thesis).
Plate V. Gouraud developed a shading technique which takes a faceted representation of an object and shades it as if it were smooth; an incredible breakthrough.
Plate VI. A refinement of the smooth shading technique from a faceted data base by a University of Utah graduate student, F. Parkes.
Plate VII. This computer-simulated hand by a University of Utah graduate student E. Catmull is a kind of first. While the hand was digitized in an extended finger position, the fingers may be closed by a mathematical transformation of the finger joints, thus allowing the hand to be animated on film.
Plate VIII. These sailboats by B. Hansen, University of Utah, show how effectively the smooth shading ran be employed, as well as how a single object may be replicated within a given picture.
Plates IX-XII. This series shows the historic development of shading techniques at the University of Utah.
Plate IX. Graduate student J. Warnock did shading of faceted solids.
Plate X. Warnock also did some studies in specular reflection indicating highlights.
Plate XI. Gouraud's smooth shading of this faceted object.
Plate XII. University of Utah graduate student Phong's smooth shading with highlights.
Plate XIII. This stemmed glass shows both Phong's highlight techniques and University of Utah graduate student F. Crow's transparency algorithms based on the work of M. Newell from the University of Utah.
Pages 500, 501:
Plates XIV-XXIV. These photographs are the work of the author, Associate Research Professor, University of Utah, with programming assistance from E. Cohen. All of the images are computer simulations of highly constrained three-dimensional models. Their data representation is completely defined by the program and the user, rather than being digitized, as no physical objects exist. Such computer images allow us to study the architectural and structural possibilities of nonexistent definable forms that could not otherwise be observed. For instance, Plates XIV-XXIV (with the exception of Plate XIX) are three-dimensional structures which may be developed from flat sheet material with a folded, curved edge and observed as structure.
Plate XV. This is an elevation of the plan view of Plate XXII of a roof structure formed from three identical developable surfaces. The program also allows the user to change and observe the width of the arch or its height off the ground plane, with a few instructions; and to move through it (Plates XXIII and XXIV).
Plate XVI. A close-up elevation view of a cylindrical helix, folded edge.
Plate XVII. An oblique view looking up of same.
Plate XVIII. Represented here are two instances of the form in Plate IV, which is one turn of a folded edge on a cylindrical helix.
Plate IX. This image portrays the author's technique for producing helicon seashells from a single sheet with cut strips. The physical bending property of each strip is being simulated by spline techniques.
Plates XX and XXI. Suggestions of architectural applications of developable surfaces with scale people indicated.
Plates XXIII and XXIV. Frames from an animated film. Interior views of a variation of this structure (Plates XV and XXII) as might be seen by an observer traveling through it, with some suggestion of scale people.
Plates XXV-XXVIII. The work of Dr. H. Christiansen, University of Utah. Unlike other photographs in this gallery, the coloring here represents the structural properties of torsion, compression, tension, and bending. Elastic properties of an object are exaggerated to show a distortion of the original shape (Plates XXV and XXVII).
Plates XXIX-XXXII. These pictures represent the only work in this gallery not performed at the University of Utah. The pictures, produced by MAGI Company, are good examples of alternatives to polygonally defined objects.