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Abstract
The Author describes Sculptor, a three-dimensional computer modelling system
that allows the use of sculptural methods for the construction of objects.
These objects can be subsequently realised as physical sculptures through
the use of a contour-slicing routine, though the major use of the system
has been in the production of computer images of 3D 'scenes'. The origins,
structure, and usage of the system are described, followed by a discussion
of the author's personal exploration of its possibilities.
Introduction
Computer solid modelling systems are aimed mainly at commercial animation,
engineering, product design or architectural users, and are usually based
on a polygon-mesh description of objects. There are two main methods of
constructing objects described in this way; constructive solid geometry
(CSG), where complex forms are created by the intersection of 'positive'
or 'negative' primitive volumes, or surface modelling, where surfaces are
created in 3D using sets of control points. Artists and sculptors have used
these systems, but are presented first with the problem of modelling techniques
more suited to other applications, and secondly with the problem of 'photo-realistic'
rendering techniques. Artists have traditionally applied a personal feel
for depth, perspective, light and shadow, which they are robbed of with
computer graphics systems, as these use more and more the laws of optics
in the precise renderings of objects. The rendering software can only be
tuned to certain degrees by the artist, so the main area of expression lies
with the modelling. The modelling in Sculptor presents an alternative to
the techniques more suited to engineering, and also some limited departures
in the methods of rendering. Sculptor comes closer to CSG than surface modelling
in that objects are built up only by the intersection of positive volumes,
starting with a single sphere as the primitive.
1) Description of the system and its origins
Sculptor allows the interactive creation and editing of arbitrary objects
composed of spheres overlapping in three dimensions. The system allows the
user to create a three-dimensional object by successively adding spheres
of the desired radius at arbitrary positions in space. Further manipulations,
such as scaling, rotating, translating, copying, mirroring and deleting
are provided by the system. Perspective viewing of a single object, or scenes
composed of a number of objects, is provided, along with provision for adjusting
the viewing parameters for close or far perspectives.
Sculptor was originally conceived as a simple 3D modelling system, built
by the author as a test bed for investigating user interface design in interactive
graphics media. More recently it has been used by the author as a system
for generating a very personal style of imagery. Some of the interface design
concepts arising from Sculptor have been used in a 2D painting/drafting
system called ICAS (Integrated Computer Art System) [1]. Using the sphere as the only
primitive reduced development effort, and also resulted in an unusually
organic imagery, in contrast to the more geometrical imagery of conventional
3D modelling systems. The system uses the techniques of object representation
and display described by Badler et al. [2] and Knowlton [3] to achieve
the organic shapes, rather than, for example, the approach adopted by Wyvill
et al. in SOFT [4] and [5].
Because of the unique symmetry of the sphere as a primitive, three concurrent
views can be easily provided to help the user visualise the object. A first-angle
projection system is employed where circles are used to represent the spheres;
the computational expense of doing this being negligible compared to using
other kinds of primitive. Fig. 1 shows the screen layout, consisting of
the first-angle views of the object (elevation, plan, and side view) and
also the menus and various symbols informing the user of the status of the
system.
In order to create objects of reasonable complexity a large number of spheres
are needed (at present the system allows a maximum of around 20,000), and
this can make editing of an object very difficult once the sphere count
is more than even 100. To counter this problem a technique is used called
hiding where spheres can be made invisible (though not lost from
memory). In order to do this in a practicable way, spheres are added to
the current object in groups, of which the system provides 12. A current
group is selected for editing, while the remaining groups can be made invisible
to facilitate the editing process. Hence objects are usually created or
sculpted in parts, where the spheres in each part are grouped together.
Various operations are provided to allow ungrouping, regrouping, transferring,
and merging of existing groupings. Groups can also be loaded from and saved
to memory allowing the user to build up libraries of sculptural 'components'.
The blocks of little squares on the right of the plan view show a tree-structure
of groupings which allow the user to select and make visible any combination
of the twelve available groups.
Operations for manipulating the medium are grouped in five sub-menus, and
each operation that has variations is provided with a menu of 'switches'
which appear whenever the operation is selected. The main menu is always visible; sub-menus are called
up from the main menu and appear below the main menu, while switches appear
below the submenu (refer to fig. 1). The tree-structure of menus, sub-menus
and switches is shown in fig. 2.
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Fig.1 Sculptor
screen layout
This shows three orthogonal views of the object under construction in 1st
angle projection. The user drives the system through the menus to the right
of the views, using a mouse or a tablet and puck. The small boxes to the
right of the plan view are used to select one or more groupings to work
with and make visible or invisible - this is needed in the construction
of complex objects. |
Fig.2
Sculptor menus
The operations for the Sculptor system are arranged in five menus, which
group related operations together. Operations which have variations can
have these set by switches arranged below the operations on the screen.
The Sculptor system was originally built as a test-bed for user interface
design and considerable development effort has gone into this aspect of
the system.
Kenneth Knowlton's paper entitled 'Computer-Aided
Definition, Manipulation, and Depiction of Objects Composed of Spheres'
[6]
outlines the algorithm I have used in Sculptor for object representation
and rendering. I have modified the rendering algorithm in several ways to
give a choice of finished imagery. The illusion of solid objects is created
using two types of filled disc, called respectively the facade and the outliner
which are sorted by depth and drawn in order from the rearmost to the foremost.
The outliner is always drawn as a filled black disc, painted directly into
the frame buffer (i.e. overwriting pixels). Originally the facade was drawn
in OR mode which allows previously drawn highlights to 'shine' through;
now an alternative technique is used involving the comparison of colour
values to see which is brighter - brighter colours are drawn over darker
colours, never the other way round.
Different rendering styles are achieved by drawing different types of facade:
a white disc for 'outline', and a series of up to 256 discs with smoothly
interpolating colour values, giving the 'smooth' rendered option. The two
types of rendering take different times; 'outline' being the fastest and
'smooth' being the slowest. While the 'smooth' rendered version is usually
used for the final result, the 'outline' version is useful for a quick 3D
visualisation to guide the user in the creation of the object. These rendering
algorithms are essentially a 'fudge', in that no 3D data is used for drawing
a given sphere, but are performed much more quickly than any true 3D rendering
could be.
Sculptor, written in C, runs on an IBM AT compatible driving an Digisolve
Ikon frame-store. The frame-store has 768 x 576 resolution with 8 bits per
pixel, and its own 68000 processor and Hitachi ATRTC graphics chip and graphics
commands in firmware. I have also adapted it to run on the Hercules Graphics
Station card, which is controlled by the TIGA graphics processor, and is
significantly faster.
2) Constructing objects (modelling)
In looking at creative computer media in the visual arts for my PhD research
at the Royal College of Art (London, England) [7], I identified the principle
of synthesis from primitives as a useful concept. In Sculptor the only primitive
is the sphere, and all the operations provided allow for the construction
or synthesis of some end-result from the (single) primitive. In considering
the processes involved I proposed a distinction between arbitrary and
algorithmic synthesis from primitives. Arbitrary synthesis from primitives
implies a sequence of operations on the medium determined solely by the
artistic discretion of the user, while algorithmic synthesis from primitives
implies a sequence of operations determined by a set of rules embodied in
the machine as an algorithm. I discuss this further in [8], and point out a relationship
between algorithmic synthesis and different types of geometry. Sculptor
provides several geometrical operations, or geometrical primitives, which
are simple examples of algorithmic synthesis from primitives: cylinder,
cone, arc and torus. In the first two cases spheres are added at small distances
apart along a straight line specified by the user, while in the others spheres
are added along a circular arc, again specified by the user. In the following
examples of constructing an object using Sculptor, arbitrary and algorithmic
synthesis feature in different proportions, with different effects on the
end-result. Fig. 3 shows the construction of a chair, and illustrates how
much of the construction work arises from copying groups of spheres that
have already been sculpted. The cylinder, and part of a torus are also used
in the construction.
Fig.3 Stages in the construction of a chair
Top left: a column of spheres have been added using the elevation view,
and constrained to align their centres vertically. Top right: a smaller
column has been added in front of the previous column, using the side view,
and both columns copied using the copy group command. Bottom left: cross
pieces are added; each new element is added as a new 'group' to facilitate
correction of any errors. Bottom right: the finished chair includes part
of a torus (ring of spheres).
Many types of object can be constructed using the short cuts that Sculptor,
as a typical computer medium, offers the artist. However in order to create
a more figurative, or biomorphic kind of piece, a similar amount of effort
is required as in any traditional medium. Fig. 4 shows some different renderings
of an object which has required this kind of approach. These renderings, involving the mapping of 3-D textures
onto the surface were carried out on high-performance parallel processing
machines by Ian Curington of Amazing Array Productions in London [9] using
the stored data-file describing the object.
The construction of the chair was mainly through
arbitrary synthesis from primitives with some algorithmic synthesis (using
the definitions made above), while the amorphous shape of fig. 4 involved
only arbitrary synthesis from primitives. William Latham extends the concept
of algorithmic synthesis from primitives towards a rule-based system for
evolving complex form called 'Form Synth' [10], and the type of results are
different again. William Latham, who is now developing the system as Research
Fellow at the IBM UK Research Centre, used Sculptor to realise some of his
early ideas, though the execution of the rules within his system was carried
out 'manually'; there would however be the potential to drive Sculptor from
an expert system which formalised the rules by which he works. Fig. 5 is
an example of his use of the Sculptor system, again rendered with 3D texturing
by Ian Curington.
Fig.5 'Form II'
William Latham has been the only artist to use the system apart from myself,
and saw the possibilities of exploiting it to implement some of his ideas
on rule-based evolution of form ('Form Synth'). Artist: William Latham,
photographer: Ian Curington.
I have extended the use of Sculptor with a contour-slicing routine, which
will take any Sculptor object (i.e. any object composed of spheres) and
plot out a series of cross-sections. The reverse process, that of converting
a set of surface points or contours into a set of spheres to define the
same object, has been described by O'Rourke and Badler [11]. However the techniques I
have used are not a simple reversal of their process, which in any case
was restricted to certain types of object. Briefly, the technique involves
extracting a set of circles for each slice through the object, finding their
points of intersection, and creating an ordered sequence of'exposed' arcs
that make up the contour. The routine looks likely to benefit from a spatial-subdivision
approach.
The main purpose of developing the contour-slicing routine was to allow
solid sculptures to be built from lamina defined by the contour-slices.
Fig.6 shows a sectioned version of the object in fig. 4, where 100 slices
were drawn of an object in an orthogonal projection; the figure also shows
the resulting sculpture made from plywood lamina. The individual contours
were plotted out, stuck onto plywood sheets, cut out with a fretsaw, and
nailed and glued together.
Other sculptures have been created as maquettes using expanded polystyrene
sheets, which can be rapidly cut to the contour using a hot-wire cutter.
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Fig.6 'Morph1' as a physical sculpture
The upper part of the figure shows 'Morph1' as a series of contour-slices
in orthogonal projection. The lower figure shows the corresponding sculpture
made from plywood laminae. Individual contours (100 of them in this case)
are plotted, cut out and stuck to sheets of plywood; the laminae are then
cut out and pinned or glued together to form the sculpture. Alignment of
successive slices is secured by the use of a grid of numbered register marks
overlaying the contour plot. Artist: Mike King, photographer: Mike King.
12cm x 8cm x 8cm. |
The idea of producing sculpture from computer-generated
contour slices is not new - Robert Mallary has produced sculptures in marble
from contour plots (described by Ruth Leavitt [12]), and more recently Mark Dunhill
showed series of sculptures in the Cleveland Gallery (UK) computer art exhibition
[13].
I have so far only constructed a few small sculptures by this method, and
have made no attempt to smooth the stepped surfaces, but the potential is
there for the construction of sculptures on a large scale (several metres
high) and for the smoothing of the surface by either removing or adding
material.
3) The potential and limitations of Sculptor
As with any other sculpting medium, the medium itself imposes limitations,
in this case arising from the sole provided primitive, the sphere. Given
that one is willing to adapt one's sculptural techniques to circumvent this
limitation, what advantages are there in working with Sculptor? I would
claim the same advantages as for other creative computer media, such as
word processing, paint systems and drafting systems. These advantages lie
chiefly in the infinite editability of the medium (though this in turn requires
a special kind of discipline). However, the main appeal to a sculptor may
be the saving in materials and mess that goes with the use of a computer
medium, though offset by the cost of purchase or access-time. Sculptor also
offers the sculptor a computer system for making maquettes, with the ability
to view the created object from any angle on the screen, and finally with
the option of creating a physical sculpture from lamina, once the development
is complete and satisfactory.
Fisher and Masters [14] describe a large sculpture that they designed and
built with the aid of computers, though the technique differed in that a
more traditional CAD system was used. However, part of the exploitation
of the computer in their case lay in the display of the sculpture in a computer
simulation of the building in which it hung. Such a use could also be made
of Sculptor, where the computer image of the object could be used within
an environmental simulation system, either landscape, architectural, or
both. Sculptor, like any 3D computer graphics system, is not as easy to
use, in terms of control over the medium, as, for example, a paint system.
However, it is easier to use than some other interactive solid-modelling
systems because of the use of the sphere as the sole primitive, but this
also limits the range of objects that can be created. To enable a wider
range of objects to be created, e.g. those with flat planar surfaces, the
system would have to be extended. The present contour-slicing routine could
be used to yield a planar-polygon data structure for the objects, which
would allow, for example, the slicing of objects and other more conventional
CAD techniques. This is the most likely route to making Sculptor more universally
useful as a modelling tool, where it would just form part of a range of
techniques along with CSG and surface modelling that could be used by artists.
A sculptor could model crude organic volumes using Sculptor techniques,
run the data through a 'polygoniser', and continue modelling with the more
conventional tools of 3D CAD.
Another proposed development is to use a 3D input device (locator) such
as a wand. This would make it easier to work in three dimensions, because
one would not need to constantly cycle between elevation, plan and side
view in order to specify the 3D position of objects. Sculptors are used
to walking around a sculpture, or at least moving their heads, in order
to gain a 3D understanding of what they are creating. A single view, that
can take from minutes to hours to render, is frustrating and results in
a creative bottle-neck. A speed-up in rendering time to bring about real-time
or near real-time rotations of the rendered object would help here.
The disadvantage of the Sculptor system as it stands lies in the type of
objects that are natural to build with it: bulbous, amorphous, and to some
people rather disquieting or repulsive. However, while the possibilities
of overcoming this problem have been outlined above, the author is not planning
to pursue this at present, being quite content to explore the artistic possibilities
of Sculptor as it is.
4) A personal exploration
In my recent work with Sculptor I have moved away from constructing single
sculptures to building perspective scenes, where I use relatively simple
shapes to create a world into which the viewer is drawn. Although limited
in terms of geometry and topology I find that I am performing a kind of
painting in 3D, where weight and volume and juxtaposition can be directly
manipulated, following vague spatial intuitions. I have always been drawn
to the exploration of perspective in computer graphics, and I find that
Sculptor has recently allowed me to do this in a satisfying way. I take
output from the Sculptor system into a conventional paint system and cut
and paste to build up more complex scenes such as in fig. 7. Here I have
taken three separate Sculptor images and composed them together, carefully
using similar perspective settings. The bars in the foreground are added
in a semi-transparent way to partly suggest a missing vanishing-point. The
shadow in the background is another simple fudge, but is perfectly effective
for my purposes. In fig. 8 I have taken two renderings of the same scene
with different perspective settings and blended them together with a shaded
background. Although the mathematics of perspective can be a straight-jacket
to the artist in 3D graphics, using several possible viewing positions in
one scene, as in this image, is one way to become more playful with it.
In some early religious
paintings multiple viewpoints within one scene were used very expressively
to give some elements greater importance than others: this has not been
explored much in 3D computer graphics.
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Fig.7 Perspective
scene
This is created by compositing several Sculptor renderings using a paint
system. The transparent effect of the bars is the result of averaging the
pixel values of the two images, while the shadow is a shifted, flood-filled
copy of one element of the scene. The image was output to an ink-jet printer
capable of 256,000 colours. Artist: Mike King, photographer: Hugh Lacey. |
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Fig.8 Perspective
scene
This is created by blending two different views of the same set of objects.
Using more than one perspective setting in one image is one way of reducing
the tyranny of the mathematically precise viewing of 3D computer graphics.
Artist: Mike King, photographer: Hugh Lacey. |
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Colour Plate
Sculptor scene
This rendering was done at Amazing Array Productions (UK) who have the specialised
software and hardware needed for high resolution rendering using multiple
light-sources and marble texturing. Attractions of the Sculptor system to
the author include the seamless joining of volumes, the ability to 'paint'
in 3D, and the release from gravity of apparently massive forms. Artist:
Mike King, photographer: Ian Curington |
The colour plate showing a Sculptor scene is
typical of recent work, though this image was rendered again by Ian Curington
at Amazing Array. The scene is shown with no perspective, but illustrates
some further use of algorithmic synthesis from primitives, where the rows
of spheres have been added using simple loops. I plan to develop the algorithmic
side of the system further using possibly fractal techniques or 3D grammars,
as I describe briefly in [15]. I have recently had access to the source code of
a ray-tracer (courtesy Richard Wright), and have adapted this to render
Sculptor objects. This takes some of the softness out of the original range
of renderings, but has the great advantage of adding shadows, which I find
very helpful in the exploration and definition of volume and space.
Conclusion
Sculptor started out as a research tool for developing interfacing ideas,
but has developed into a system for creating a rather personal type of imagery.
There are possibilities for widening the scope of the system, both in terms
of making it useful for a wider community of user, and in terms of making
physical sculptures from the computer models. It may also represent one
of many efforts by an artist to write specialised software for their own
use, or alternatively, one of many efforts of a software writer to pursue
the creative possibilities of a system that they had written.
References
[1] King, M.R., "Development of an Integrated Computer
Art System", in (Eds.) Magnenat-Thalmann, N. and Magnenat-Thalmann,
D., New Trends in Computer Graphics , proceedings of the CG International
'88, Springer-Verlag 1988., pp 643-652.
[2] Badler, N.I., O'Rourke, J. and Toltzis, H., "A
Spherical Representation of a Human Body for Visualizing Movement",
Proceedings of the IEEE, Vol.67 No.10, October 1979, pp. 1397-1403.
[3] Knowlton, K., "Computer-Aided Definition, Manipulation
and Depiction of Objects Composed of Spheres", Computer Graphics,
Vol.15 No.1, April 1981, pp. 48-71.
[4] Wyvill G, McPheeters C and Wyvill B, "Data structure
for soft objects", The Visual Computer 2:227-234 (1986).
[5] Wyvill B, McPheeters C and Wyvill G, "Animating
soft objects", The Visual Computer 2:235-242 (1986).
[6] Knowlton, K., "Computer-Aided Definition, Manipulation
and Depiction of Objects Composed of Spheres", Computer Graphics,
Vol.15 No.1, April 1981, pp. 48-71..
[7] King, M.R., Computer Media in the Visual Arts and
their User Interfaces, PhD Thesis, Royal College of Art, London 1986
(unpublished).
[8] King, M.R "Towards an Integrated Computer Art
System", in (Eds.) Lansdown, R.J. and Earnshaw, R.A., State of the
Art in Computer Art and Animation, proceedings of the 1986 conference
at the Royal College of Art, London, Springer Verlag (1988).
[9] Curington, I., "A Normal-Buffer Vectorised Surface
Shading Model", in (Eds.) Carlos, E. and Van Dani, Proceedings of
Eurographics '85 conference, Elsevier Science Publishers, pp. 365-374.
[10] Latham, W., (1986) "Form Synth, The Rule-Based
Evolution of Complex Forms from Geometric Primitives", in (Eds.) Lansdown,
R.J. and Earnshaw, .A., State of the Art in Computer Art and Animation,
proceedings of the 1986 conference at the Royal College of Art, London,
Springer Verlag 1988.
[11] O'Rourke J, and Badler N (1979) "Decomposition
of Three-Dimensional Objects into Spheres", IEEE Transactions on
Pattern Analysis and Machine Intelligence, Vol.PAMI-1, No.3, July 1979,
pp. 295-305 (1979).
[12] Leavitt, R., Artist and Computer, Harmony Press,
1976.
[13] Chettle, S. "Art and Computers", Exhibition
Catalogue, Cleveland Gallery, Middlesbrough, England, 1988.
[14] Fisher, R.N. and Masters, R.J., "Computer-Aided
Sculpture: Visual and Technical Considerations", Leonardo, Vol.18,
No.3, pp.133-143, 1985.
[15] King, M.R "Towards an Integrated Computer Art
System", in (Eds.) Lansdown, R.J. and Earnshaw, R.A., State of the
Art in Computer Art and Animation, proceedings of the 1986 conference
at the Royal College of Art, London, Springer Verlag (1988)..
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