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# Program for the Interactive Design of Polyhedra

IP.com Disclosure Number: IPCOM000075912D
Original Publication Date: 1971-Dec-01
Included in the Prior Art Database: 2005-Feb-24

IBM

## Related People

Appel, A: AUTHOR [+2]

## Abstract

In the three-dimensional modeling of polyhedra using a computer, a polyhedron is generally described to the computer as two lists: 1) A vertex list, which is the table of numbered points in space in their three-dimensional coordinates. 2) A topological map, which indicates which points are connected together to form the boundaries of planes. The boundary of a surface comprises one or more closed loops. The methodology of computer manipulation of three-dimensional objects are summarized in the publication of Arthur Appel entitled "Modelling in Three-Dimensions", IBM Systems Journal, Vol. 7, #3, 4.

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Program for the Interactive Design of Polyhedra

In the three-dimensional modeling of polyhedra using a computer, a polyhedron is generally described to the computer as two lists:
1) A vertex list, which is the table of numbered points in space

in their three-dimensional coordinates.
2) A topological map, which indicates which points are connected

together to form the boundaries of planes. The boundary of

a surface comprises one or more closed loops. The methodology of computer manipulation of three-dimensional objects are summarized in the publication of Arthur Appel entitled "Modelling in Three-Dimensions", IBM Systems Journal, Vol. 7, #3, 4.

The salient problem of three-dimensional modeling is the preparation of the vertex list and the topological map of a typical polyhedron. For example, as shown in Figs. 1A, 1B and 1C wherein it is desired to encode an approximation of a human head, the encoding requires about 40 hours of man-time and about five hours of computer time. There are required for such encoding, a front view 1A, a side view 1B and a top view 1C. It can be readily appreciated that methods for rapid encoding would be of great value.

In this latter connection, a computer program for drawing in three dimensions is set forth under the title "Sketchpad III", T. Johnson, AFIPS Proceedings SJCC, 1963. This program will provide the vertex list but does not produce a topological map. The reason for the deficiency is that the latter program stores only lines in space. It does not store the arrangement whereby lines form the boundaries of planes, or the manner in which planes enclose specific volumes to form objects.

Programs exist whereby drawings of polyhedra can be analyzed to associate features in two perspective views and, thereby, yield, by computer analysis, equivalent of the vertex list. These programs, however, cannot analyze hidden features, such as internal detail and in addition, they are quite voluminous and noninteractive.

In this description, there is set forth a simple, fast technique whereby one can readily design polyhedra of any topological complexity. In the operation of the technique, as the designer works, he simultaneously records the vertex list and the topological map. Hence, the computer can punch cards or telecommunicate the data for high quality rendering by known programs, such as LEGER and SIGHT. The novel technique can be utilized on a combination such as the IBM 1130 computer in conjunction with the IBM 2250 interactive graphics unit, and may also be utilized with a tablet.

In the carrying out of the technique, a designer sketches on an interactive graphics screen, two views of the polyhedron, as shown in Fig. 2. The T-square tracking spot is shown. Thereafter, the designer describes, in the front view, a particular surface boundary. He then places the tracking spot over successive vertex points in the front view and closes the light-pen switch at every vertex point.

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Thereby, ther...