True 3D Computer Modeling: Sculpture of Numerical Abstraction

Abstract

ly. The mechanism between the endpoints is a series of translations necessary to implement the mathematics in a machine-executable form and to condense the abstract problem into a spatial representation. New compilers of natural mathematical language make the condensation transparent. A two-dimensional (2D) picture representing threeor higher-dimensional form is a lower-dimensional abstraction of the higher-dimensional actuality. I claim that creating sculpture of numerical abstraction increases the immediacy of the abstraction over what a picture can convey. Computeraided prototyping technologies make a direct projection of three-dimensional (3D) abstraction into physical reality. An interactive computer graphic of a 3D space exists behind the glass front of a cathode-ray tube. Even a hologram or stereo projection is only an illusion in light. A sculpture occupies and shares the physical space occupied by the viewer. A sculpture has its own presence, one that dominates these alternate presentation media. ? 1992 ISAST Pergamon Press Ltd. Printed in Great Britain. 0024-094X/92 $5.00+0.00 EARLY WORK ABSTRACT I saw my first interactive, visual computer workstation in 1984. The author gives an account It was a DEC pdpll/40 with of his experience in progamming a Vector General scope that interactive computer graphics. Observations are made of the logiran Tom DeFanti's GRASS incal connections between a computerteractive graphical operating generated picture and the computer system [5] and programming program that generated the picture. language. The first incarnation The action of condensing abstracof GRASS was known as the tion into visual form as an aid in understanding the abstraction is Graphis Sybosis at Ohio State studied in the context of scientific University. It later became the visualization. The author presents Circle Graphics Habitat at the his work in making sculptures of University of Illinois at Chimathematically defined surfaces via direct, three-dimensional computercago. This is the machine Larry p t 6 7 printing technologies. Cuba used to create the Death Star hologram simulation sequence in the original Star Wars motion picture. My experience in computer graphics up to that time consisted of writing FORTRAN batch programs for an electrostatic plotter at AT&T Bell Labs in Naperville, Illinois. Despite the fact that the pdpl 1/40 had only 32k bytes of magnetic core memory, the Vector General had hardware display capability for interactively manipulating 3D objects in vector-list form in real-time. The GRASS language also had some very interesting features. Among them were character string manipulation tools that allowed me to write primitive compilers, such as those for evaluating Lindenmayer [6] systems and Boolean operations. The experience of GRASS was an immediate acceleration of all the techniques I had been developing for making pictures up to that time. From amidst the creative explosion, there emerged a technique of construction that is becoming increasingly important to me. I discovered that aligning circular arcs with the vertices and edges of a polyhedron yields a shape that can be repeated in the manner of an atomic crystalline lattice, but that can define a smoothed topological surface of many handles. Achieving the surface requires triangulating closed wireframes made of connected circular arcs. In implementing the program to do this, I came up with a linear approxiStewart Dickson (computer-graphics progammer), The Post Group Digital Center, 6335 Homewood Avenue, Hollywood, CA 90028, U.S.A. Fax: (213) 464-1953. E-mail: Received 22 March 1991. LEONARDO, Vol. 25, No. 3/4, pp. 2281-287, 1992 This content downloaded from 157.55.39.55 on Tue, 23 Aug 2016 04:15:58 UTC All use subject to http://about.jstor.org/terms Fig. la. Circles oriented at the edges and vertices of a tetrahedron. Dots show edgeoriented circle centers at the points of intersection of vertex-tangent planes and edge-normal planes. Fig. Id.