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THE SPACE CURVE AS A FOLDED EDGE
THE SPACE CURVE AS A FOLDED EDGE Ronald D. Resch
University
of Utah
Since a folded edge can determine a space curve, this research focused on the question: given any space curve, can one develop a two dimensional score line such that its folding will produce the desired space curve as a folded edge? The images on the following pages exhibit the use of a given space curve as a folded edge in an architectural model. The model was designed with the aid of the computer images· A numeric control tape, which determined the layout of the sheets to be devel oped, was used in the fabrication of the physical models. Ephriam Cohen (now at Applicon Corp., Burlington, Mass.) was responsible for the mathematical defini tion and the computer programming of a folded, curved edge. The research reported in this paper was directed by the author during 1972-73 under ARPA-IPT DOD Con tract #F30602-70-C-0300. References 1.
Resch, R., "The Topological Design of Sculptural and Architectural Systems11, AFIPS - CONFERENCE PROCEEDINGS, Vol. 42, NCC, 1973, 643-650.
2.
Resch, R., "Portfolio of Shaded Computer Images", Proceedings of IEEE, Vol. 62 no. 4, April 1974, 496-502. 255
Top: computer simulated image. Bottom: photograph of physical model· Plan view of a model built from devel opable surfaces with folded edges. 256
COMPUTER AIDED GEOMETRIC DESIGN
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Top: computer simulated image. Bottom: photograph of physical model. Elevation and oblique views, respec tively, of same structure. 257
RONALD D. RESCH
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Top: computer simulated image of interior elevation view of a variation of the previous structure· Bottom: computer simulated image of suggested architectural structure.
258
University
of Utah
Since a folded edge can determine a space curve, this research focused on the question: given any space curve, can one develop a two dimensional score line such that its folding will produce the desired space curve as a folded edge? The images on the following pages exhibit the use of a given space curve as a folded edge in an architectural model. The model was designed with the aid of the computer images· A numeric control tape, which determined the layout of the sheets to be devel oped, was used in the fabrication of the physical models. Ephriam Cohen (now at Applicon Corp., Burlington, Mass.) was responsible for the mathematical defini tion and the computer programming of a folded, curved edge. The research reported in this paper was directed by the author during 1972-73 under ARPA-IPT DOD Con tract #F30602-70-C-0300. References 1.
Resch, R., "The Topological Design of Sculptural and Architectural Systems11, AFIPS - CONFERENCE PROCEEDINGS, Vol. 42, NCC, 1973, 643-650.
2.
Resch, R., "Portfolio of Shaded Computer Images", Proceedings of IEEE, Vol. 62 no. 4, April 1974, 496-502. 255
Top: computer simulated image. Bottom: photograph of physical model· Plan view of a model built from devel opable surfaces with folded edges. 256
COMPUTER AIDED GEOMETRIC DESIGN
:\&(-../Γ&£*:-λ. '*: <&Λ"'ί%
Top: computer simulated image. Bottom: photograph of physical model. Elevation and oblique views, respec tively, of same structure. 257
RONALD D. RESCH
WËË*'&* |*n- jfi >~,
HE$
, >
^»C^>,H- -?' ' ^ e ^ W ' - ' î "·^ ^ B l ^ f : ^ -■
Silslif*!! ^ep^%r, , ;
^^S?>>' ', '%-* , -, ' '
Hj^<~-1* £f, -,»f
Top: computer simulated image of interior elevation view of a variation of the previous structure· Bottom: computer simulated image of suggested architectural structure.
258