TRAN2A computer graphics program to make sculpture

by ROBERT MALLARY The University of Massachusetts Amherst, Massachusetts

INTRODUCTION

Historically the techniques of sculpture have ten-ded to reflect the technological character and level of the society in which the sculpture was made. If primitive man carved bone and the Greeks cast in bronze it should not be surprising that sculptors today are using plastics, lasers, strobes, electronic circuitry and transducers to link art with contemporary technology. Even so, this still does not account for why some of us have been using the computer, as-signing it a status above other "art-and-technology" possibilities and viewing it as nothing less than por-tentous in its implications for art. *

The computer is special among the technical re-sources previously available to the artist because for the first time he has a tool, not only for executing a work of art, but for conceiving one as well. Once a computer has been programmed to generate a first rate work of three-dimensional art with no direct as-sistance from a sculptor it will be legitimate to speak of cybernetic sculpture in the fullest sense of the word. Until then computer sculpture will qualify as cyber-netic only in the sense that the design process is sub-stantially facilitated by "intelligence amplification" which is to say, by the use of advanced computer graphic interactive systems.2

The core problem in computer sculpture is to pro-gram the machine to take in, manipulate and give back three-dimensional information which can be used to make sculpture. For example, a Massachusetts sculptor, Alfred Duca, with the help of IBM pro-grammers, has used a computer tape and an N /C machine tool to carve out a large and intricate spherical sculpture in metal.3 Michael Noll of the Bell Telephone Laboratories has programmed linear stereo-drawings which appear three-dimensional when seen in a stereo-

viewer. On the other hand, he has apparently made no provision for constructing an actual sculpture from this authentically three-dimensional information.4 Others have used 2-D plotter drawings to "suggest" sculpture, or* have used computer graphic material to embellish the surfaces of a sculpture, or have used computer graphic output to determine the flat shapes to be incorporated into a sculpture. But in none of these latter programs has the computer generated, processed or delivered up the real thing in the way of three-dimensional form information.

TRAN2

In beginning about three years ago to work on TRAN2 our intention was not so much to anticipate the computer sculpture of the future, with its awesome kinetic and form transformational capabilities, as to take a small but real step ahead within our immediate resources. However, TRAN2 does qualify as a basic, or prototype, computer sculpture program in the sense that it provides for a full description of volumetric objects within the machine, processes this information in a meaningful way, and generates a usable output. Moreover, the program is workable in that it has ac-tually been used to make a series of sculptures (see Figure 1 and Figure 2). Now written in Fortran IV for the IBM 1130 computer and plotter, when it has been rewritten for the display it will be upgraded as a more fully interactive program allowing for the almost instant manipulation and transmutation of forms.

Form description

Crucial to the processing of three-dimensional form informationbe it architecture, sculpture or indus-

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Figure 1"QUAD III" TRAN2 computer sculpture in laminated veneer. 60" high1968. The sculpture was made from plotter templates provided by the Amherst College IBM 1130 computer

trial objectsis the 3-space depiction of the object within the machine.5'6 Perhaps there is no "best" way of doing this, keeping in mind that some methods of

form and space description are more suitable than others only in respect to the purpose of the program. For example, MAGI uses a system called "combina-torial geometry"7 to assemble forms within the com-puter, but it is difficult, using this system, to revise and further develop the forms as freely as a sculptor would like. Other methods, which refer to surfaces rather than volumes, would seem to be more promising for shaping and processing three-dimensional material assuming, that is, that provision is made at some point for fully enclosing and defining these surfaces as bound-ed and complete sculptural volumes.8 But whatever the system used, if the computer is to be involved with sculpture in an authentic way it must be given either a comprehensive numerical description of the material it is to work with or the means to generate this ma-terial for itself.

In this respect TRAN2 does both, using contour sectioning, or "slicing," as the basic method of form

Figure 2"QUAD IV" A TRAN2 computer sculpture in laminated marble. 11" high1969

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description and form generation. In effect, the form is slicedmuch as an apple or a chunk or baloney might be sliced, into a series of thin parallel cross sec-tions of equal thickness. These two-dimensional slices comprise a vertical set, or array, of modular form in-formation units which are then graphed, digitized and encoded onto computer punch cards. Each of the slices has an axis point and a reference ("tick") mark to position it on the vertical axis relative to all the other slices comprising the set. It is by means of this "stack-ing" of two-dimensional data that the program converts standard computer graphic capabilities to the require-ments of three-dimensional form description.

Two modes for form description input

TRAN2 provides for two modes of form description input, though others might be devised. The first, called INITL, requires an antecedent hand-made "proto-type" form which must be traced three-dimensionally using a special contour grapher designed for this pur-pose (see Figure 4). The grapher has a swinging probe which, when held gently against the slowly revolving form, traces off the contour levels one-by-one and transfers them to graph paper. These graphs are then digitized with X / Y coordinates, using the vertical axis as the Z coordinate, and transferred to punch cards. Between 48 and 100 contours are needed, which is insufficient to guarantee a smooth, continuous defi-nition of the form (i. e., without a visible demarcation, or "step," between each contourand the next), but is a practical minimum considering the relatively small capacity of the computer which has been available

Figure 4Contour sections are being traced from a styrofoam prototype form mounted in the contour grapher. The contour "slices" are then graphed and punched onto cards to provide

the form description input for the INITL input mode

INPUT TRANSFORMATIONS OUTPUT

TRAN2 SUBROUTINE SEQUENCES AND OPTIONS

Figure 3Block diagram showing the basic program structure of TRAN2

to us and the amount of hand work required to trans-late the computer output into an actual sculpture in-the-round.

The second input mode, called PROFIL, dispenses with the prototype form, but in its place the computer must be given coded profile drawings (see Figure 5). Eight profiles are stored at a time, though the computer needs only one to generate a form with radial sym-metry. Two profiles generate a form having two planes of symmetry and three generate a form with bilateral symmetry. A set of four different profiles generates an asymmetrical form, this being the number which is normally specified unless one of the symmetrical schemes is used.

By following the typed instructions given to it at the console the computer "fills in" the form between the profiles (see Figure 6). In calling up subroutines

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Figure 5Profile drawings for use with the PROSA input mode. Needed are two facing profiles on the Y-Z plane, making four in all. The profiles are generally designed as matching sets, though eight are filed in the computer at a time and are inter-

changeable

such as ELIPS, OVAL1, OVAL2, and SUPER the sculptor can generate forms for which all the cross sections at all levels along the vertical axis are either perfect circles, ellipses, super-ellipses, or are one of two kinds of ovals. In other words, the coordinate values taken from the profile drawings are used by the com-puter to shape these geometrical cross sections (see Figure 7).

While this ability to generate an asymmetrical sculp-ture characterized by a uniform, and perhaps sym-metrical, geometry throughout all the cross sections is no guarantee of "beauty," it at least unlocks some interesting possibilities for sculpture which deserve further exploration. For that matter, the extensive use (or should we say over-use?) of symmetry in so much current computer art has yet to be applied to three-dimensional structures and configurations, and even in our use of TRAN2 we have hardly begun to

Figure 6Diagram showing how the computer uses the PROSA input mode to combine 4 profiles and from them derive a contour slice ADBC. 48 of these sections are stacked on the vertical axis to define a complete form. It can be seen that if the same profile were to be used in all positions ( + X and X, and + F and Y) the form would have radial symmetry and all the sections would be circles. Available as options are yet other systems of symmetry

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scratch the surface in this area. Evidence of our con-tinuing commitment to asymmetry, as against sym-metry, is the fact that QUAD, which shapes an asym-metric contour section based on quadrants taken from four different ellipses, is still the most used subroutine within the PROFIL group of input subroutines.

The transformation subroutines

The computer, once it has either been given or has generated for itself the form description data it re-

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Figure 7This diagram shows how the computer, using OVAL 2, moves the minor chord AB to the center of the major cord CD, making a cross section which is a perfect oval (AB and CD are opposite points on two adjacent profile drawings). OVAL I moves the major chord to the center of the minor chord, ELIPS moves each chord to the center of the other to form a perfect ellipse, and QUAD shapes a cross section comprised of quadrants

from 4 different ellipses

quires, in effect is converted into a sculptural modeling and shaping tool. This is accomplished by calling up one or more of the transformation subroutines such as EXPND, EXPNT, ROTES, or MOVES. These gener-ate permutations on the form description data by means of various mathematical functions which stretch and compress the form in a variety of ways.9 The computer requests instructions regarding the kind of transfor-mation which is wanted and the specific values in-volved. For example, EXPND is used to stretch or compress a contour section on the X or Y coordinate or on both. If 1.0 is typed for X and the same for Y there is no change in contour section or in the over-all form. But if 0.5 is typed for X and 2.0 for Y the form is halved on X and doubled on Y. Because the comput-er calculates these values for only one contour at a time, and in sequence, it is possible to specify incre-mental transformations, either of a positive or negative kind. In this way the sculptor can induce a more drastic transformation at the top of the form than at the bot-tom (or vice versa).

In understanding the action of these transforma-tion "templates" it is important to bear in mind their dependence on the underlying structure of the program, based on the stacked layers of contour sections, which limits them to the X / Y horizontal plane. As yet no provision has been made in TRAN2 to introduce trans-formations on the Z, or vertical, coordinate. EXPND, which is TRAN2's most basic "modeling tool," evenly stretches or compresses the contour section over the X /Y plane of transformation. In other words, the form, in respect to its length and breadth, is uniformly stretched or compressedwhich means that the kind of transformation is constant even when the values are changed.

EXPNT (for exponential) surmounts this invariance in offering the sculptor a wider range as regards the kind of transformation permutations available to him. Crucial to this much enlarged transformational capa-bility are various logarithmic and exponential func-tions and values which can be typed in.10

For example, using EXPNT the form can be com-pressed on one side and expanded on the other, or the degree of expansion or compression can be made to vary continuously along the X / Y plane of transforma-tion. Once TRAN2 has been given a graphic console and provided with proper instrumentation it should be possible for the sculptor, using the typewriter and function keys, to specify the class of transformation he is seeking while he spins a knob in order to con-tinuously vary the values. This will enable the sculptor to scrutinize his creation, which is slowly swelling and contracting on the display, while he waits to seize the moment it "gells"either as the original image in

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Figure 8TRAN2 perspective plotter drawing of a sculptural form, which can be thought of as a preliminary sketch or "study." The sculptor decides on the basis of these drawings whether to

complete the sculpture in some durable material

his mind's eye or as an unexpected discovery. The sculptor should also have the option of subjecting his form to a series of transformation sequences which are more or less automatic in their operation. As programmed transformation "scenarios" they will be

Figure 9Photo of a complete set of plotter drawn contour sections ready for projection onto the material to be used in

making the TRAN2 sculpture

Figure 10A contour section has been projected and traced onto a %" thick piece of luaun veneer and is being cut out with a bandsaw. Marked on the veneer are the center hole and a registry mark used to properly orient the slices in the stack as

the sculpture is being assembled and laminated

only partially under the control of the sculptor in the sense of his fully anticipating what happens next. They will be useful, not only as an expanded computer-aided design resource, but for their cinematic possibilities. As a third option the sculptor should also be able to "harden," or "fix," any of the transformation permu-tations at any given strategic point in the procedure, using this new data set to replace the original form description material as the basis for a further round of transformation sequences.

Using ROTES incremental transformations can also be used in order to rotate, or twist, the contour sections sequentiallythe final result being to twist the form as a whole. Using this subroutine forms have been twisted 360, and even 720, about the axis (with rather bizarre results, it might be added). In general a subtle, less drastic, rotation is preferablefor ex-

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ample, the 60 rotation used in designing QUAD III (see Figure 1).

It should be emphasized that the TRAN2 trans-formations are cumulativei.e., in being added to-gether in sequence they are in effect combined. For example, the initial input form can first be expanded using EXPND, then have its center point shifted on the X / Y plan using MOVES, then be twisted using ROTES. Sorely needed is a subroutine on the order of MOVES, but more versatile and drastic in its trans-formations. This subroutine would completely re-orient the sculpture relative to its axis, thereby as-signing it a new top and bottom and a new set of con-tour sections. By enabling the transformations to work on the form from any direction, and along any desig-nated plane of transformation, the number of trans-formation possibilities would be multiplied many times over.

Figure 11The center hole is drilled

Figure 12The cut out luaun sections are stacked on a steel rod preparatory to gluing and laminating

The output subroutines

The group of output subroutines determines the kind of drawing the computer is to make. PERSP specifies a perspective drawing (see Figure 8), the sculptor typing in the angle of vision he wantsat, above or below eye level. He also specifies the view or views he wishes, which is apt to be a complete set taken at regular intervals around the form. By instructing the plotter to make a series of drawingssay, at 15 or 30 increments, he in effect revolves the form before his eyes and achieves a rough idea of what it would look like if he were actually to construct it. I t is in this sense that TRAN2 is an example of how computer graphic techniques can be exploited by the sculptor to extend and enhance the usefulness of drawing as a way of sorting and clarifying visual ideas preparatory to executing them in a three-dimensional medium.

CONTR calls up a plot of the entire set of contour sections as orthographic projections (see Figure 9).

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Figure 13The stacked sections have been laminated together and the irregularities ground down and smoothed

Each of the contours includes both a center point and a reference mark to orient the contours in the proper position one to the other. The entire set of contours is photographed as an 8 X10 inch positive transparency, inserted into an overhead projector, projected onto some appropriate material such as wood or plastic, and traced. The set of traced contours is then cut out (see Figure 10), the center holes are drilled (see Figure 11), and the contours are stacked over a metal rod (see Figure 12). Finally the contours are glued, lami-nated together under pressure, ground down to remove the "steps" and irregularities (see Figure 13), and smoothed and polished. These, of course, are manual operations at the handicraft level, but in principle, inasmuch as the computer has generated all the es-sential three-dimensional information, the sculpture could also be made using an N /C milling machine.

Capabilities of an improved TRAN2 program

TRAN2 is slow in its operation when measured against the potential of a large c.p.u. and a true inter-active program. I t is also limited in that it can handle solid, volumetric forms oriented around a central axis; concavities are possible using the INITL input mode, but undercuts are ruled out. Nor is it possible, using PROFIL and its maximum of four profiles, to generate a concavitythough the addition of, say, 12 profiles might improve the situation in this regard (see Figure 14). It will be necessary either to enormously expand the resources of TRAN2, or to develop a library of specialized computer sculpture programs, if planar, linear and open-form sculptures are to be made using the computer.

An ideally interactive program along the lines of TRAN2 would allow the sculptor to draw his profiles directly on the display using a light pen11 or sketch pad arrangement.12 He should then be able to evaluate his work by referring to a graphic display which shows the form slowly revolving about its axis. Next he should be able to set in motion a series of transformation scenarios of the type already described, then switch back to the sketch modeperhaps to refine the details of the form with the light pen or stylus. If he should

Figure 14A diagram showing how 12 profiles, instead of the 4 now used in PROSA, will permit the sculptor to introduce concavities into his form and generate more complicated and interesting surfaces. Needed is an elegant algorithm to generate

the smooth continuous curve which links the 12 points

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decide he has taken a wrong turn at some point he should be able to call upon the computer's memory and return to an earlier stage in order to try some-thing else. In other words, the program should have what amounts to a quick rewind and playback capa-bility based on a complete and permanent log of the entire design process. Apart from its value to the sculptor, a record of this kind might also be valuable as a way of investigating systematically the dynamics of the creative process and determining how one sculp-tor works as against another in creative problem solving.

I t might also be helpful for the computer sculptor, as for the architect as well, if he could rely on multiple displays, each unit providing information regarding a different aspect of the on-going problem. For example, he might study several views of the same sculpture at once, compare two or more current versions, or refer back to an earlier version for comparison. Even-tually a practical stereo display, and possibly a holo-graphic display,14 will optimize the efficiency of com-puter graphic systems for communicating three-di-mensional form information with maximum visual clarity and precision. In fact, we might define the eventual goal of computer graphic systems as pro-viding the sculptor, architect or designer with a virtual real-life experience of the form-in-progress so he may design it better, more rapidly and with more assurance that it will conform to his expectations once it has actually been made.

A look over the horizon

The computer sculptor will make better use of the computer to evaluate his work-in-progress when he no longer has to rely on the rather crude wire cage drawings to which graphic displays are now generally restricted. A minimal step in the right direction would be a drawing consisting of black lines against a white field to replace the reverse image of white on black. More remote, though beginnings are being made,13-14 would be a simulated light and shadow version of the form on the display giving the sculptor the option of simulating a procedure he is apt to follow in his own studionamely, to adjust and vary the light-ing on the form for the clearest effect. Sequencing the shifting patterns of mobile lighting configurations, either with real lighting equipment or as simulated images on displays, is an obvious computer potential.

Cybernetic sculpture

Ultimately interactive programs will become truly cybernetic in the sense that the computer will move

beyond computer-aided intelligence amplification (com-puter-aided design, in other words) into the more creative aspects of the design process. The computer will be more than a "slave"; it will be more like a col-laborator or a virtual surrogate for the sculptor him-self. According to his inclinations the sculptor will vary the manner and degree of his involvement with the computer. He will use and interact with it, monitor it or leave it, as it were, to its own resources.

CONCLUSION

The sculpture now made with the help of TRAN2 does not forecast the look of the computer sculpture of the future, which will be mainly kinetic, have multi-media features and will probably be based on a cinema type projection system linking the computer with holographic techniques. The relevance of TRAN2 in this connection is thatapart from the claims to be made for it as one of the very first pioneering efforts in the fieldit does forecast, in its use of mathematical methods, an approach to form description, as well as form manipulation and metamorphosis, which will be crucial to these kinetic media of the future.

In conclusion I feel it an obligation to remind those who know more about computers than they do about art that I am at outs with some of my more conserva-tive artist colleagues who deny that the computer can make any constructive contribution to art at all. But what is more nettling is that I am also at outs with some of my more avant-garde colleagues who will acknowledge (or even insist) that the computer can play a role in art but that TRAN2, which according to them is involved in an anachronistic kind of "ob-ject" art, is not a valid way to go about it. I differ with these latter critics in holding that "object" sculp-ture (which is the kind most people think of, whether it be realistic or abstract, when they think of sculpture at all and which is the only kind we can as yet make with TRAN2) still offers unexplored potentialities for the computer to help uncover.

In any event, a beginning must be made at some point, and for the present it may be a sufficient achieve-ment to have demonstrated that the computer can play a role in the making of sculptureall apart from the question of how well it has done so.

REFERENCES

1 J REICHARDT Cybernetic serendipity, the computer and the arts Studio International London and New York 1968

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2 R MALLARY Computer sculpture: six levels of cybernetics Artforum Vol 7 No 9 pp 29-35 May 1969

3 R CHANDLER Design for numerical control machining Machine Design pp 4-24 February 15 1968

4 A M NOLL The digital computer as a creative medium I E E E Spectrum Vol 4 pp 87-95 October 1967

5 W F E T T E R Computer graphics Annual meeting of the American Society for Engineering Educators 1966

6 C M THEISS Computer graphic displays of simulated automobile dynamics AFIPS Conference Proceedings Spring Joint Computer Conference Vol 34 p 289 1969

7 MAGI Description of the MAGI technique for accurate modeling and graphic display of three-dimensional objects Mathematical Applications Group Inc White Plains New York 1967

8 T M P L E E A class of surfaces for computer display AFIPS Conference Proceedings Spring Joint Computer Conference Vol 34 p 309 1969

9 C CSURI J SHAFFER Art, computers and mathematics AFIPS Conference Proceedings Fall Joint Computer Conference Part 2 Vol 33 p 1293 1968

10 C CSURI Leonardo: circle to square transformation The Magazine of the Institute of Contemporary Art Number 5 London pp 27-28 August 1968

H I E SUTHERLAND Sketchpad: a man-machine graphical communication system M I T Lincoln Laboratory Technical Report No 296 January 1963

12 M R DAVIS T O ELLIS The rand tablet: a man-machine communication device AFIPS Conference Proceedings Fall Joint Computer Conference Par t 1 Vol 26 p 325 1964

13 C WYLIE G R O M N E Y D C EVANS* A ERDAHL Half-tone perspective drawings by computer Technical Report 4-2 Computer Science University of Utah-Salt Lake City Utah February 12 1968

14 H WILHELMSSON Holography: a new scientific technique of possible use to the arts Leonardo Pergamon Press Oxford England Vol 1 Number 2 pp 161-169 April 1968