sculpting with computer graphics: an approach to the design and fabrication of abstract sculpture

Leonardo

Sculpting with Computer Graphics: An Approach to the Design and Fabrication of AbstractSculptureAuthor(s): Michael O'RourkeSource: Leonardo, Vol. 21, No. 4 (1988), pp. 343-350Published by: The MIT PressStable URL: http://www.jstor.org/stable/1578695 .

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Sculpting with Computer Graphics: An Approach to the Design and Fabrication of

Abstract Sculpture

Michael O'Rourke

Abstract-The author describes a computer-based approach intended to facilitate the design and fabrication of his abstract sculpture. After explaining how he models the three-dimensional shapes, determines the color composition and fabricates a detailed aluminum maquette, he examines the usefulness and the limitations of his techniques. Finally, he discusses some ways in which this approach allows him to address his aesthetic concerns.

Fig. 1. The modeling of one component of the sculpture on the real-time Fig. 2. The various elements of the sculpture combined on the real-time vector machine. (Courtesy of the New York Institute of Technology. Photo: vector machine. (Courtesy of the New York Institute of Technology. Photo: Ariel Shaw.) A curved section is being subtracted from the pointed Ariel Shaw.) The view here is from the back of the piece. Note that, as more component by the cylinder. This is an example of the use of the Boolean elements are added, the wireframe image becomes harder to read clearly.

operators as a modeling tool.

I. INTRODUCTION

As would be expected of any powerful technology, computers offer many poten- tial advantages to the design and fabrication of sculpture. Some of those advantages are already familiar to the general public, even if most people may not have thought of them specifically in relation to sculpture. The three-dimensional look of the computer graphics that we see daily on television is one example. The computer-assisted manufacturing that takes place in Detroit, Michigan, is

Michael O'Rourke (sculptor), Computer Graphics Laboratory, New York Institute of Technology, Old Westbury, NY 11568, U.S.A.

Received 20 May 1987.

another. Given visualization and fabrication capabilities like these, it would seem reasonable to expect computer technology to be in wide use by sculptors.

In fact, sculptors have used computers very little, especially in comparison with, for example, animators, photographers and painters. Three-dimensional design tasks present an intricate set of problems to any computer graphics system, and sculpture, with its irregular forms, can be particularly difficult. There can be potentially as many disadvantages to the use of computers in sculpture as there might be advantages. These disadvantages can range from difficulty in gaining access to equipment, to the inherent limitations of that equipment.

Over the last several years, and with a great deal of support from my colleagues

at the New York Institute of Technology (NYIT), I have been developing a computer-aided design (CAD) and a computer-aided manufacturing (CAM) system for my own sculpture [1]. Now that this system has been developed to the point where the advantages genuinely outweigh the disadvantages, it is, I think, worth sharing with others. Although the system I am about to describe remains a research-level tool at NYIT and is not available commercially, many of the individual capabilities of the system are available in a variety of commercially available software packages that can be pieced together to produce a system suited to an individual sculptor's needs.

To describe my own CAD/CAM system, I will trace the development of a single piece of sculpture [2] from first

? 1988 ISAST Pergamon Press pic. Printed in Great Britain. 0024-094X/88 $3.00+0.00

LEONARDO, Vol. 21, No. 4, pp. 343-350, 1988



Fig. 3. Four hidden-surface views of the digital sculpture model. (Courtesy of the New York Institute of Technology. Photo: Ariel Shaw.) The entire composition has been modeled as sets of flat, polygonal

surfaces. An actual physical object does not yet exist at this point in the process.

sketches through to a detailed aluminum maquette. In the course of doing so, I will also draw some implications about CAD systems generally, particularly those intended for sculpture.

II. MODELING

As is the case for most sculptors, my

first ideas for a sculpture are in the form of quick sketches. While some sculptors prefer to work initially with clay, others with wax or plaster, I prefer to begin with pencil drawings on paper. These not only allow me to record and develop ideas quickly but also immediately force me to consider the relationship between two dimensionality and three dimensionality,

Fig. 4. A hidden-line plotter drawing of the sculpture, ink and graphite on paper, 8 X 10 in, 1986. (Courtesy of the New York Institute of Technology. Photo: Ariel Shaw.) The thinner ink lines were plotted with the computer; the heavier pencil marks were done by hand afterward. These sketches are especially important in that they allow the artist to think about the piece and work on it while away

from the machines.

one of the issues with which I want my sculpture to deal.

Largely as a result of my work with three-dimensional computer graphics, in which volumetric models are first developed in a three-dimensional mathematical space and then displayed as pictures on a two-dimensional screen, I have become interested in the interplay between two- dimensional and three-dimensional representation and in the questions these raise about perception and our notions of dimensionality. For example, what do we mean when we say that one physical object-a sculpture-is three-dimensional but that another equally physical object-a painting-is two-dimensional? When, and why, do we feel comfortable ignoring the three-dimensional surface irregularities of a painting in order to classify it as two-dimensional? How do we answer similar questions concerning the color patterns that might be part of the surfaces of a sculpture? And then, on a more general, epistemological level, what is the connection in our minds between calling something 'real' and calling it three- dimensional, or between calling something an 'artifact' and calling it two-dimensional?

I approach my sculpture with these sorts of questions in mind, and I immediately begin dealing with them by roughing out, in two dimensions and on paper, the first versions for what eventually will be a three-dimensional object. These first ideas take into account other intended characteristics of the final piece as well. For example, as I start working on a piece, I know that I would like the final sculpture to be somewhat larger than a person [3], to be constructed of steel and to be painted. I also know that I want it to establish several formal counterpoints- those between volume and space, between straight lines and curved lines and between regular, geometric shapes and irregular, unpredictable shapes.

In short, my compositional goals and my working method are interdependent. I develop my compositions with my method and materials in mind and, conversely, develop my working method to help me best realize my compositional goals. As a result, my method is not universally effective. It handles certain types of sculpture better than others. It would be foolishly tedious, for example, to use my working method to model a naturalistically rendered human figure. On the other hand, my approach does handle quite well the flat surfaces, tubular curves and abstract compositions for which it was developed.

Once my pencil sketches have begun to yield a coherent composition, I begin

O'Rourke, Sculpting with Computer Graphics 344



modeling the sculpture in the computer. Within the computer's memory, this modeling consists of a list of three- dimensional points (x,y,z) and how they are connected together [4]. At the user level at which I am working, however, I do not need to think in terms of these numbers. Instead, I specify points and surfaces interactively with a powerful set of software modeling tools [5]. Since these programs run on a real-time vector machine [6], the models are displayed on a screen as see-through wireframe images, which I can move around, rotate and look at from other points of view simply by turning a dial or by pressing a 3-axis joystick.

The software modeling package that I use at NYIT is polygon based, i.e. all objects are composed of flat surfaces connected together. Curved surfaces are approximated by a stepped sequence of flat surfaces. The package is powerful and includes the following modeling capabilities: 'extrusion', in which an outline (for example, a hand-drawn curve) is pushed straight back into space to produce a block with that outline; 'geometric primitives', such as spheres, cones and cylinders; 'lofting', in which a set of map- like contours at different heights are connected together to form a surface; and 'surfaces of revolution', in which a two- dimensional curve is rotated about an axis to form a surface that is similar to what might be modeled on a lathe.

Another powerful tool that plays a major role in my sculptures is known as spatial set operators, or Boolean operators. These allow one to add and subtract pairs of three-dimensional shapes to produce new shapes. As a simple example, a cube minus a cylinder might yield a cube with a cylindrical hole through it.

A final modeling tool that I employ throughout my process is a program that I call "draw3d". This program allows me to use a 3-axis joystick to move a cursor interactively through space and trace a three-dimensional curve. This sort of floating, ephemeral 'space curve' becomes a crucial element in the composition as I play it off against the heavier, more regular and more volumetric solid shapes [7].

The reasons for using the computer for these modeling operations are speed and flexibility. Most of the shapes I want to use in my sculptures can be modeled and modified more quickly by working with this software than by working in a physical medium. In addition, different versions of a given shape can be saved and recalled as needed. This not only saves time but also makes me psychologically more willing to experiment with new

Fig. 5. Calculation of the intersections and flattening of the parts. (Courtesy of the New York Institute of Technology. Photo: Ariel Shaw.) On the left, a hidden-surface rendering of one of the sculpture's elements after it has had subtracted from it any parts that were touching it. The line drawing on the right is the two-dimensional flat pattern that is the 'unwrapping' of this three-

dimensional element.

ideas. I know that, if an idea does not work, I can easily return to my saved original.

Figure 1 illustrates the modeling that takes place at this wireframe stage. The smaller, secondary window in the lower right displays a side view of the configuration I am working on. The larger, main window shows the same configuration from another point of view. Two shapes are involved here. The first is a cylinder (seen on the right in the small window). The second shape, a wedge-shaped section of a sphere with a long point growing from its top, is visible on the left side of the small window. The Boolean operation of subtraction has been performed: originally the inner edge of the wedge-shaped piece went in a straight line from the tip of the point (upper left in the small window) to the very bottom of the shape (bottom middle in the small window). Now, however, the cylinder has been subtracted from the wedge-shaped object to produce an arc- shaped curve along the inner side of that object.

As I model the individual elements of a sculpture, I use the same equipment to begin combining them together to form the whole composition [8]. Figure 2 shows an early version of the sculpture that I will be using as my example throughout this article. The various individual parts of the sculpture have

been brought together and are being positioned and scaled relative to one another on the real-time vector equipment.

As this compositing proceeds, the complexity of the image increases to the point where the see-through vector representation no longer suffices. It becomes impossible to see what is in front of what and exactly where one piece intersects another. A more realistic representation of the model is needed, which I achieve by creating shaded, hidden-surface images of the model [9]. These images are viewed on a separate monitor, which is placed next to my initial workstation. This second monitor displays a 'raster scan' image, that is, an image consisting of areas of color, not just of monochrome lines. Figure 3 shows several views of the sculpture in progress, displayed in this hidden-surface raster representation.

The advantage of this sort of image over the wireframe image is that now I am able to look at the opaque surfaces of the objects rather than merely at lines representing the edges of those surfaces. Surfaces that are behind others are no longer visible-obviously a closer approximation of our physical world, for which the sculpture is intended.

The disadvantage of this raster scan image technique, however, is that using it is slower than using the wireframe images. On NYIT's system, I cannot turn




Fig. 6. The completed paper-and-wire maquette of the sculpture, 6 X 9 X 3 in, 1986. (Photo: Ariel Shaw) Once the two-dimensional flat patterns of each element have been plotted onto paper, the paper is cut out and taped together to form this model. The wire elements are made of electrical wire. These have been bent by hand into shape using the calculated locations of some key points on the

curves as guides.

the raster images around in real time with a joystick control, which I am able to do with the wireframe images. Instead, I have to type a command at my terminal and wait about 30 seconds for each static image to appear-a delay that, though not ideal, is, in the context, workable.

I consider this issue of feedback time vitally important. One of the principal reasons computer modeling has not been generally useful to sculptors is that most available systems have an unacceptable delay in the image/feedback loop. If one has to wait too long to see one's results each time one makes a modeling change or each time one wants to look at the model from a different point of view, the system being used simply will not be very helpful. Waiting too long for visual feedback can be annoying but, more importantly, distracting and disruptive to the flow of ideas. After all, the sort of feedback a computer design system must compete with is what a sculptor tradi- tionally gets by pushing a thumb into a lump of clay and turning the clay around for viewing. To the extent that a CAD system does not match this sort of feedback, it must compensate by offering other advantages-for example, speed of modeling, or flexibility of change.

In addition to the wireframe representation of the model and the hidden- surface raster representation, I use a third visualization technique as the modeling progresses. This technique, which involves

hidden-line plotter drawings, proves to be enormously useful. In making these drawings, I work on yet a third type of monitor-a simple, non-real time monochrome graphics monitor. I first select a specific point of view. The model data are then processed to remove any edges (i.e. lines) that, in the physical world, would be obscured by other parts of the model. The 'hidden-line' image that results is then plotted onto paper with a laser plotter.

I can make these plotter drawings easily and quickly, and I do so quite often throughout the modeling process. Their usefulness lies primarily in the fact that they free me from the machines. Computer graphics can be seductively counter- productive. There is a great tendency to become so engrossed in the details of the process that one loses sight of the more global issues. The hardcopy plotter drawings allow me to make a quick record of what I have been thinking-and allow me to take them home. Looking at the drawings later, I often am able to think more clearly about the composition than I was able to do while working directly at the computer. Once a set of plotter drawings has been made, I normally draw by hand on top of the original plots to notate new ideas and changes. Figure 4 is one such drawing. The thin black ink lines were plotted with the computer; the pencil drawing was done by hand.

All of these imaging techniques are

used as the modeling of the sculpture progresses; there is no fixed sequence to their usage. I use the different techniques as often as the need arises. In this way, the modeling progresses from selecting the individual elements of the composition, to combining those elements to form the whole composition, to refining the individual elements, to changing the whole, and back again, as often as necessary.

III. FABRICATION

Once the composition has stabilized and I do not want to make any more changes, the next task is to transfer the design, which so far has existed only digitally and within the memory of the computer, from the computer into the real world. I could use the various renderings and drawings of the model simply as approximate visual guidelines for fabricating the physical model; however, since the digital model is an extremely accurate representation of what I want, I prefer a more precise translation from digital information to physical object.

My first step is to calculate the exact shape of all the intersections of all the elements. So far in the process, this has not been an issue. In fact, one of the more significant advantages of modeling with

computer graphics is that I do not have to concern myself with intersecting parts (except insofar as the intersections might be treated as elements of the visual composition). Because the computer model is only digital and not physical, pieces can pass readily through one another: I can make repeated changes to the way two parts intersect without having to remodel the separate parts.

Now, however, in order to transfer my digital model into the physical world, I must explicitly concern myself with the shape of each of these intersections. In the physical world, these intersections will be important, because each part must fit snugly up against the other parts it touches. The task of computing the shapes of these intersections is handled by the Boolean operators-specifically, the 'difference' operator [10]. By doing a Boolean subtraction on a pair of elements that intersect, I can determine the precise shape of the hole cut in one by the other. In this way, each element has 'scooped' out of it the shape of any intersection it may have with other elements. All of the elements, with their intersections properly scooped out, will fit together like a three- dimensional jigsaw puzzle in the final

physical version. The image on the left side of Fig. 5 is one of the elements from




my sculpture. This element can be seen in its relation to the whole sculpture by referring to the image in the lower right of Fig. 3, where the element in question can be found near the lower left of the rectangular shape. Referring back again to Fig. 5, note that this element, which was originally a solid, squashed cylinder, has had several areas 'scooped' out of it. These are the areas where it intersected other elements.

Once I have calculated all of the intersections one by one, I then flatten each resulting part out into a plane-I effectively 'unwrap' it. The concept is analogous to removing the staples from a cardboard box and then spreading it out so that it lies flat on the floor forming a two-dimensional pattern of cardboard. This two-dimensional configuration can then be folded back up and restapled to form the original three-dimensional box [11].

Like the cardboard box, all of the elements of my sculpture are composed of flat, polygonal surfaces. Each element can be mathematically unwrapped into a two-dimensional pattern of surfaces, all lying in a plane [12]. The line-drawing on the right side of Fig. 5 is the unwrapped two-dimensional pattern that corresponds to the three-dimensional element to its left.

The point of this unwrapping approach is twofold. The first is that once one has a two-dimensional plan of an element, one can easily plot it as a line drawing onto a piece of paper and thereby transfer the three-dimensional object into the physical world of hardcopy. Moreover, one can do so without the considerable expense of a numerically controlled milling machine, which is the more common method of transferring three-dimensional data to the physical world. The second is that any three-dimensional object that has been defined to consist of flat polygonal surfaces can be unwrapped in this way. Some objects are more complex than others, and some must be broken apart into sub-objects, but ultimately any such three-dimensional shape can be unwrapped. So, this approach is not only practically feasible but also conceptually powerful.

I flatten out each element of the sculpture in this way to produce a two- dimensional pattern. Then, making sure to keep the scale of all the drawings constant, I plot each two-dimensional pattern onto paper. Each of these paper patterns is in turn cut out, folded back up into its original three-dimensional configuration and taped together. Each three-dimensional paper element cum puzzle piece is then positioned and taped

to the others to form a three-dimensional paper model of the sculpture.

While theoretically it would be possible to deal with the tubular components of the sculpture in the way I have just described-flattening them out and reassembling them in paper-it would be practically infeasible. So many tiny polygons would be required to obtain a good approximation of the tube's curvature that their unwrapping would be a programmer's Everest, and their assembly a kindergartner's nightmare.

Another possible approach would be to approximate the curvature of the tubes by a series of straight cylindrical sections and then to calculate the angle of intersection between each cylinder [13]. Unfortunately, using this approach for my sculptures would similarly result in a hellish myriad of tiny cylindrical sections.

Rather than force the issue, the approach I use with the tube structures is to calculate certain key pieces of information for each curve, for example, the length of the curve or the highest point of the curve. With these numerical guidelines, which can be scaled up according to the scale of the model, I then bend electrical wire by hand to conform to the model, looking at my plotter drawings for reference as I work. Figure 6 shows a completed paper- and-wire model of the sculpture. The sizes of these paper models range in height from about 5" to about 8".

When the paper model has been built, there is an uncanny sense of deja-vu. As

with any sculptural process, the modeling of my composition has taken a long time. I have spent many hours over many days and weeks thinking about it, adjusting it, refining this component, shaving down that component. I have become intimately familiar with it and all its details. And yet, it has not even existed! So far there has been no physical 'reality' to the model. Yet, when the first paper model is built, there is a strong sense of seeing something that has existed.

Anyone who develops a detailed design of an object-whether a sculpture or a building or a carburetor-will sense this feeling to some degree. In my experience, however, the thoroughness of the digital model is such that this feeling passes beyond the usual pleased surprise to a sort of stunned recognition. Given the strength of this reaction, there would seem to be some sense in which the a- physical model did have some sort of 'reality' to it. In which case, we must ask ourselves, I believe, what we mean by 'real'.

This issue touches on what I have referred to elsewhere as 'virtual' sculpture-sculpture that does not have, and is not intended to have, any physicality [14]. It is perfectly possible to make such virtual sculpture one's goal and to find an appropriate medium for displaying it. The implications of this for all of sculpture are fascinating. In the sculptures here under discussion, however, I have specifically decided to bring the com-

Fig. 7. The image-mapping technique used to develop sketches for the color composition of the piece. (Courtesy of the New York Institute of Technology. Photo: Ariel Shaw.) Each of the line drawings is the flat pattern of one element. By positioning each flat pattern within the color picture (here reproduced in black and white), the artist determines which areas of color will be applied to which

surfaces.




Fig. 8. A digitally composited picture of the final aluminum maquette along with a human reference to indicate the scale intended for the final sculpture. (Courtesy of the New York Institute of Technology.

Photo: Ariel Shaw.)

positions into the physical world and to fabricate them in physical materials.

As with all the other stages of the design process, there is no fixed sequence that the fabrication of the paper model must follow. If the paper model reveals something in the composition that I am not pleased with, I change it. Sometimes this is done directly on the paper model; sometimes it is easier to go back to the digital model, make the changes there and then resume the fabrication process. In any case, the modeling process is eventually complete. I began with purely digital modeling and now have an accurate, and physical, maquette of the sculpture.

This maquette, however, has some obvious limitations. It is quite small, relative to its intended size. A scaled-up version would be helpful in trying to refine the details of the composition. Also, being made of paper and wire, the maquette is not fabricated of the same sorts of materials I intend to use in making the final sculpture. A lot would be learned by making a version in sheet metal. And finally, I cannot readily experiment on my fragile paper model with the spray-painted colors I intend to use for the final sculpture.

Consequently, my next step is to fabricate another, larger model out of aluminum. The procedure here is basically the same as for the paper-and-wire version. The flat plan drawing of each element is re-plotted onto paper, using much larger paper this time. Each of these drawings is transferred by hand to sheet aluminum. The aluminum sheets are cut using traditional metal working tech-

niques, then ground, filed, folded and joined to form the three-dimensional parts. These are then fitted together and joined to form the whole model. The tubular structures are also handled just as they were in the earlier model, only now I use 1/4" solid aluminum wire rather than thin electrical wire.

When everything is assembled, I now have a maquette that is several times larger than my first one (the aluminum models tend to be about 15" high), and that simulates much more closely the surface properties and fabrication techniques of the intended final piece.

There is no question that, were I to be presented with the opportunity to build one of these sculptures at its full, intended scale, larger maquettes would be needed. There is much, from both a technical and a compositional point of view, that would change with the scale of the piece. A handful of other sculptors have indeed used their own CAD/CAM systems to produce full-scale sculpture, and their comments on this topic are worth reading [15].

IV. COLOR

At about this point in the process, I begin thinking about color. The first steps of this phase once again make use of computer graphics, specifically a technique known as 'image mapping' in which a two-dimensional pattern is applied, or 'mapped', onto the surface of a three- dimensional object. The effect is as if one had painted a picture onto a rubber sheet, then wrapped and stretched that sheet

tightly over the surface of a three- dimensional object. The object would then have its surfaces covered by the painted two-dimensional image.

I use this image-mapping approach to develop my initial ideas for the color composition of my sculpture. First, I create the two-dimensional picture-in my case, an abstract color pattern. This is all done digitally, with my picture displayed on a monitor. The techniques I use for this are standard digital image- processing techniques. These are all based on the fact that the computer represents a picture as a grid of numbers. If these numbers are changed in some way, the picture changes. For example, I can run a simple program that will look at one location in the picture grid and then change the number in that location by averaging it with the numbers in nearby locations. The new number implies a new color. Changing enough numbers will visibly change the picture.

Once I have developed a picture that has the colors and color relationships I am interested in, my next step is to 'map' portions of that picture onto my three- dimensional shapes. To do this, I position each of my flat patterns (which had been developed in the process of unwrapping the three-dimensional elements) on top of my color picture. Whatever areas of color lie beneath the line drawing will be applied to the corresponding three-dimensional surfaces. By positioning and scaling each two-dimensional flat pattern within the color picture, I can select which colors will be applied to which shapes [16]. Figure 7 is an illustration of this approach. The black-and-white reproduction here does not show the actual colors involved, but the changes in gray levels are enough to suggest where the colors change. Three unwrapped flat patterns have been positioned over this color pattern.

Once I have positioned each element within the space of the color picture, I make a new set of raster renderings of the whole sculpture, this time with the color applied to the various elements. In other words, I make pictures similar to the four illustrated in Fig. 3, but now with the color composition mapped onto the sculpture. Looking at these pictures, I adjust the positioning of the flat pattern drawings within the color picture to refine the mapping of the colors onto the three-dimensional sculpture.

The advantage of this technique is that it enables me to make a myriad of changes and tests without actually coating my aluminum maquette with layer upon false-start layer of paint. The disadvantage is, once again, that of feedback time. This technique is not extremely fast, and there


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is a delay between making a change in the color composition and seeing that change on the model. Consequently, I occasionally find it easier just to leave the computer, draw by hand with pastels or colored pens on one of my plotter drawings and then return to the image-mapping technique to work out the next level of detail.

When I feel satisfied with these first attempts at developing the color com-

position, I leave the computer behind

entirely and go to the aluminum model. The color patterns I have been using were intended to approximate the effect of

spray painting. Now, using cans of enamel paint, I spray paint the aluminum model. The color raster images are my guide as I begin working, although I make no attempt to adhere to them strictly. They are treated as sketches, just as the digital three-dimensional model was in relation to the paper model. Color Plate A No. 2 is a full-color illustration of the painted aluminum maquette in its finished state.

V. SCALE

There is one final task in which the

capabilities of computer graphics prove helpful to me. The intended scale of the final sculpture is large-approximately 8' tall. In order to refine my ideas about scale, I once again make use of the

computer. First, I photograph the finished painted

aluminum maquette. The color 35-mm slide that results is then scanned into the

computer to produce a digital version of that image. Using image-processing techniques once again, I then add to this image a picture of something of known scale, for example, a person. By changing the relative scales of the objects, I can experiment with the scale of the final

sculpture. Figure 8 illustrates this technique, as well as the intended scale for my sculpture.

In addition to helping me refine my ideas about the scale of the piece, this

approach serves another purpose. It

provides a visually effective way of conveying to others my intentions for the final sculpture. Although I have not yet built any of the sculptures in this series at this scale, I would expect this sort of imaging capability to be helpful in the

process of communication between sculptor and client [17].

VI. CONCLUSION

Throughout this entire process, the

point has been, not the computer graphics and not the technical novelties, but the

sculpture. The techniques were developed to make it easier for me to design and fabricate the sort of sculpture that addresses my aesthetic concerns.

One of these concerns is with setting up an interplay of tensions and harmonies between various visual elements. These in turn are intended to be visual analogs of certain emotional and psychological tensions and harmonies in our daily lives. On the visual end, in the sculpture, these include the interplay between geometric and irregular shapes, between volume and space, between curved and straight lines. I find that the computer-aided approach described here indeed allows me to develop these counterpoints in a rich and effective way.

An additional advantage of the technique is not necessarily apparent to the viewer. The structure of the computer is such that it lends itself to the reprocessing and modification of existing data. This capability can be used profitably to create subtle relationships between compositional elements-relationships that may be perceived only subliminally by most viewers [18]. For example, the data for a three-dimensional space curve may be processed to produce a two- dimensional perspective view of the curve. A portion of this might then be used as the outline of an extruded shape in the sculpture. Or, the perspective view of the curve might be rendered as a raster

picture and then that picture processed to

produce a color pattern for mapping onto the sculptural shapes. This sort of

approach has proven fertile for me. A second aesthetic concern, also

mentioned at the beginning of this article, is with how we perceive three dimensionality, and subsequently how we

represent both two-dimensionality and three-dimensionality in our image making. The sculptures that I have been developing with this technique deal directly with these issues in their compositional elements. Flat surfaces are juxtaposed with rounded surfaces, solids are juxtaposed with lines. The three-dimensional

sculpture contains a large rectangular component suggestive of the picture plane of painting. Moreover, the

computer-aided design process itself both echoes and contributes to these concerns of perception and representation. Three- dimensional objects are unwrapped into two-dimensional patterns and then folded back up into three-dimensional objects. Two-dimensional color patterns are mapped onto three-dimensional surfaces. And sculptural compositions are designed in the virtual three- dimensional space of the computer, then viewed as two-dimensional images and

finally assembled into tangible three- dimensional objects.

It is clear to me as I work with this system that it helps me in dealing with my aesthetic concerns. The degree to which the resulting sculpture communicates those concerns to others must remain for others to judge.

Acknowledgments-I would like to thank the entire staff of the New York Institute of Technology Computer Graphics Laboratory for its support throughout this work. Special thanks are also due to Frank Stella and Ken Tyler for providing the impetus for the development of the first versions of this system.

REFERENCES AND NOTES

1. The major program components of this system were developed by a number of people at NYIT, whom I cite throughout the notes. The piecing together of these components, as well as the writing of some additional software, was done by myself.

2. This sculpture is part of a series of sculptures entitled Images of Ourselves. All were designed with this approach and all deal with the same issues.

3. I have not yet had the opportunity to build any of the sculptures in this series at this intended size.

4. A particularly readable overview of common computer-graphics concepts, written for artists, can be found in A. Glassner, Computer Graphics User's Guide (Indianapolis, IN: Sams, 1984). A more comprehensive book, also written for artists, is I.V. Kerlow and J. Rosebush, Computer Graphics for Designers and Artists (New York: Van Nostrand Reinhold, 1986). An overview of computer graphics from a technical point of view can be found in J.D. Foley and A. Van Dam, Fundamentals of Interactive Com- puter Graphics (Reading, MA: Addison- Wesley, 1982).

5. Pat Hanrahan was the driving force behind the development of this modeling system. He and John Schlag did the bulk of all the programming for the system as I use it; see P.M. Hanrahan, "Topological Shape Models" (Ph.D. diss., Univ. of Wisconsin-Madison, 1985). See also P.M. Hanrahan, "The Winged Edge Geo- metry-Topology Modeler" (NYIT Internal Technical Document, 1984).

6. The specific machine used here is an Evans & Sutherland Multi-Picture System. Other hardware used throughout my process includes Ikonas frame buffers, a Hewlett Packard drum plotter, an Imagen laser printer/plotter, and a network of VAX computers, which are connected by Ethernet and run UNIX.

7. I developed and programmed the interactive curve-generating program.

8. Garland Stern developed, and David Sturman refined, this portion of the software.

9. Thanks to Paul Heckbert, and subsequently Brian Whitney, for this rendering software.




10. Thanks to Jacques Stroweis for the development of this crucial portion of the system.

11. An early use of this technique by Ron Resch can be found in A. Del Zoppo, The Vegreville Pysanka (Salt Lake City, UT: R.D. Resch private publication, 1976). More recently, this technique has found commercial application in the fashion industry; see J. Nisselson, "Computer Graphics and the Fashion Industry", Proceedings of the Second Image Sym- posium, Centre d'Etudes des Systimes et des Technologies Avancees 2, 283-290 (1986).

12. This critical portion of the software was developed by Robert McDermott; see R.J. McDermott, "Geometric Modeling in Computer Aided Design" (Ph.D. diss., Univ. of Utah, 1980).

13. F.M. Smullin, "Pipedreams, A Complete CAD CAM System for Tubular Sculp- ture", Proceedings of the Third Symposium on Small Computers in the Arts, IEEE 3, 112-127 (1983).

14. M. O'Rourke, "Computers, Sculpture and Three Dimensionality", SIGGRAPH Tutorial Notes, A CM 21, 237-249 (1985).

15. R.N. Fisher and R.J. Masters, "Computer Aided Sculpture: Visual and Technical

Considerations", Leonardo 18, No. 3, 133-143 (1985). See also Smullin [13].

16. Robert McDermott produced the special purpose program that permitted this stage of the operation.

17. A discussion of how CAD can benefit this communication process can be found in Fisher and Masters [15].

18. For an interesting discussion of the link between the architecture of the computer and the imagery that results, see F. Dietrich, "Digital Media: Bridges Between Data Particles and Artifacts", The Visual Computer 2, 135-151 (1986).

Call for Papers

Art and Development

The Editors of Leonardo are preparing a special issue of the journal dedicated to art and development. Manuscripts are sought on the following topics:

1. Art as a vehicle for communication. Art for pleasure and art as incitement to thought.

2. Communication as a tool serving development.

3. Definition of development as improvement in the quality of life of members of a society. Quality of life as a function of values (material and/or spiritual).

4. The role of intelligence in achieving an improved quality of life. Intelligence as a renewable resource.

5. Information, communication and knowledge. Knowledge as information enriched through insight. Art as a means for developing the capacity for insight. Science as a branch of art.

The Editors welcome proposals for manuscripts on other topics relating to art and development. For further information please write to Leonardo, 2020 Milvia St., Berkeley, CA 94704, U.S.A.




A

No. 1. Top. Daria Dorosh, A Pedestrian Bridge for57th StreetBetween 5th and 6th A venues, oil pastel and photograph on Mylar, 24 X 34 in, 1985. Having felt the need to cross this busy thoroughfare in the most direct way possible to get to galleries on both sides of the street, the artist sought, with this visualization, to combine

art with function in the public realm.

No. 2. Bottom. Michael O'Rourke, finmal maquette for Images of Ourselves-Diana, painted

aluminum, 15 X 18 x 10 in, 1986.

A

No. 1. Top. Daria Dorosh, A Pedestrian Bridge for57th StreetBetween 5th and 6th A venues, oil pastel and photograph on Mylar, 24 X 34 in, 1985. Having felt the need to cross this busy thoroughfare in the most direct way possible to get to galleries on both sides of the street, the artist sought, with this visualization, to combine

art with function in the public realm.

No. 2. Bottom. Michael O'Rourke, finmal maquette for Images of Ourselves-Diana, painted

aluminum, 15 X 18 x 10 in, 1986.



sculpting with computer graphics: an approach to the design and fabrication of abstract sculpture

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