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The Space Curve as a Folded Edge (1971)
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The Space Curve as a Folded Edge (1971)
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![[i-90-.10]](http://www.ronresch.com/gallery/space-curve-as-a-folded-edge/bw%20colin%20print%20090-.10.png/image_thumb "This White Space Curve Fold with 3-fold Symmetry is based on work I did in the early 1960’s. This particular sculpture was designed and folded ca. 1971-1972. It was shown in the 1972 Exhibition: \"Ron Resch and the Computer\", Utah Museum of Art, University of Utah, Salt Lake City, Utah.
It was designed with a custom CAD program that I and my staff developed specifically to enable the design of space curves and physically fabricate them as folded curves with bent developable surfaces on either side of the folded curved edge. The mathematics and the program were based on my discovery of how to geometrically define a folded, curved crease that would conform to any predefined space curve. I believe I was the first to ever solve this geometric problem.
First, I used the program to define a target space curve. This particular pre-defined 3-dimensional space curve is a b-spline. Secondly, the program enabled the completely generalized design of the folded sheet developable such that it would conform to the predefined, 3-D space curve. This folded sheet developable which has this pre-defined space curve embedded in it as the folded edge was then rendered both as a shaded raster-video image (see examples) and as a line drawing showing the generator lines of the developable surfaces on either side of the curved folded edge.
Next the 2-dimensional developable geometry was computed and output. This included both the fold lines to be subsequently scored and the edge lines to be cut. This output graph was then used to drive a custom make NC-machine that I built that scored and cut the physical sheet. The sheets were then hand folded and assembled, as you see here. This model is about 48” across.")
![[i-90-.10]](http://www.ronresch.com/gallery/space-curve-as-a-folded-edge/bw%20colin%20print%20090-.10.png/image_large "This White Space Curve Fold with 3-fold Symmetry is based on work I did in the early 1960’s. This particular sculpture was designed and folded ca. 1971-1972. It was shown in the 1972 Exhibition: \"Ron Resch and the Computer\", Utah Museum of Art, University of Utah, Salt Lake City, Utah.
It was designed with a custom CAD program that I and my staff developed specifically to enable the design of space curves and physically fabricate them as folded curves with bent developable surfaces on either side of the folded curved edge. The mathematics and the program were based on my discovery of how to geometrically define a folded, curved crease that would conform to any predefined space curve. I believe I was the first to ever solve this geometric problem.
First, I used the program to define a target space curve. This particular pre-defined 3-dimensional space curve is a b-spline. Secondly, the program enabled the completely generalized design of the folded sheet developable such that it would conform to the predefined, 3-D space curve. This folded sheet developable which has this pre-defined space curve embedded in it as the folded edge was then rendered both as a shaded raster-video image (see examples) and as a line drawing showing the generator lines of the developable surfaces on either side of the curved folded edge.
Next the 2-dimensional developable geometry was computed and output. This included both the fold lines to be subsequently scored and the edge lines to be cut. This output graph was then used to drive a custom make NC-machine that I built that scored and cut the physical sheet. The sheets were then hand folded and assembled, as you see here. This model is about 48” across.")
![[i-92-.10]](http://www.ronresch.com/gallery/space-curve-as-a-folded-edge/bw%20colin%20print%20092-.10.png/image_thumb "This White Space Curve Fold with 3-fold Symmetry is based on work I did in the early 1960’s. This particular sculpture was designed and folded ca. 1971-1972. It was shown in the 1972 Exhibition: \"Ron Resch and the Computer\", Utah Museum of Art, University of Utah, Salt Lake City, Utah.
It was designed with a custom CAD program that I and my staff developed specifically to enable the design of space curves and physically fabricate them as folded curves with bent developable surfaces on either side of the folded curved edge. The mathematics and the program were based on my discovery of how to geometrically define a folded, curved crease that would conform to any predefined space curve. I believe I was the first to ever solve this geometric problem.
First, I used the program to define a target space curve. This particular pre-defined 3-dimensional space curve is a b-spline. Secondly, the program enabled the completely generalized design of the folded sheet developable such that it would conform to the predefined, 3-D space curve. This folded sheet developable which has this pre-defined space curve embedded in it as the folded edge was then rendered both as a shaded raster-video image (see examples) and as a line drawing showing the generator lines of the developable surfaces on either side of the curved folded edge.
Next the 2-dimensional developable geometry was computed and output. This included both the fold lines to be subsequently scored and the edge lines to be cut. This output graph was then used to drive a custom make NC-machine that I built that scored and cut the physical sheet. The sheets were then hand folded and assembled, as you see here. This model is about 48” across.")
![[i-92-.10]](http://www.ronresch.com/gallery/space-curve-as-a-folded-edge/bw%20colin%20print%20092-.10.png/image_large "This White Space Curve Fold with 3-fold Symmetry is based on work I did in the early 1960’s. This particular sculpture was designed and folded ca. 1971-1972. It was shown in the 1972 Exhibition: \"Ron Resch and the Computer\", Utah Museum of Art, University of Utah, Salt Lake City, Utah.
It was designed with a custom CAD program that I and my staff developed specifically to enable the design of space curves and physically fabricate them as folded curves with bent developable surfaces on either side of the folded curved edge. The mathematics and the program were based on my discovery of how to geometrically define a folded, curved crease that would conform to any predefined space curve. I believe I was the first to ever solve this geometric problem.
First, I used the program to define a target space curve. This particular pre-defined 3-dimensional space curve is a b-spline. Secondly, the program enabled the completely generalized design of the folded sheet developable such that it would conform to the predefined, 3-D space curve. This folded sheet developable which has this pre-defined space curve embedded in it as the folded edge was then rendered both as a shaded raster-video image (see examples) and as a line drawing showing the generator lines of the developable surfaces on either side of the curved folded edge.
Next the 2-dimensional developable geometry was computed and output. This included both the fold lines to be subsequently scored and the edge lines to be cut. This output graph was then used to drive a custom make NC-machine that I built that scored and cut the physical sheet. The sheets were then hand folded and assembled, as you see here. This model is about 48” across.")
![[069-C12]](http://www.ronresch.com/gallery/space-curve-as-a-folded-edge/bw%20colin%20print%20069-C12.png/image_thumb "This White Space Curve Fold with 3-fold Symmetry is based on work I did in the early 1960’s. This particular sculpture was designed and folded ca. 1971-1972. It was shown in the 1972 Exhibition: \"Ron Resch and the Computer\", Utah Museum of Art, University of Utah, Salt Lake City, Utah.
It was designed with a custom CAD program that I and my staff developed specifically to enable the design of space curves and physically fabricate them as folded curves with bent developable surfaces on either side of the folded curved edge. The mathematics and the program were based on my discovery of how to geometrically define a folded, curved crease that would conform to any predefined space curve. I believe I was the first to ever solve this geometric problem.
First, I used the program to define a target space curve. This particular pre-defined 3-dimensional space curve is a b-spline. Secondly, the program enabled the completely generalized design of the folded sheet developable such that it would conform to the predefined, 3-D space curve. This folded sheet developable which has this pre-defined space curve embedded in it as the folded edge was then rendered both as a shaded raster-video image (see examples) and as a line drawing showing the generator lines of the developable surfaces on either side of the curved folded edge.
Next the 2-dimensional developable geometry was computed and output. This included both the fold lines to be subsequently scored and the edge lines to be cut. This output graph was then used to drive a custom make NC-machine that I built that scored and cut the physical sheet. The sheets were then hand folded and assembled, as you see here. This model is about 48” across.")
![[069-C12]](http://www.ronresch.com/gallery/space-curve-as-a-folded-edge/bw%20colin%20print%20069-C12.png/image_large "This White Space Curve Fold with 3-fold Symmetry is based on work I did in the early 1960’s. This particular sculpture was designed and folded ca. 1971-1972. It was shown in the 1972 Exhibition: \"Ron Resch and the Computer\", Utah Museum of Art, University of Utah, Salt Lake City, Utah.
It was designed with a custom CAD program that I and my staff developed specifically to enable the design of space curves and physically fabricate them as folded curves with bent developable surfaces on either side of the folded curved edge. The mathematics and the program were based on my discovery of how to geometrically define a folded, curved crease that would conform to any predefined space curve. I believe I was the first to ever solve this geometric problem.
First, I used the program to define a target space curve. This particular pre-defined 3-dimensional space curve is a b-spline. Secondly, the program enabled the completely generalized design of the folded sheet developable such that it would conform to the predefined, 3-D space curve. This folded sheet developable which has this pre-defined space curve embedded in it as the folded edge was then rendered both as a shaded raster-video image (see examples) and as a line drawing showing the generator lines of the developable surfaces on either side of the curved folded edge.
Next the 2-dimensional developable geometry was computed and output. This included both the fold lines to be subsequently scored and the edge lines to be cut. This output graph was then used to drive a custom make NC-machine that I built that scored and cut the physical sheet. The sheets were then hand folded and assembled, as you see here. This model is about 48” across.")
![[074-.10]](http://www.ronresch.com/gallery/space-curve-as-a-folded-edge/bw%20colin%20print%20074-.10.png/image_thumb "This White Space Curve Fold with 3-fold Symmetry is based on work I did in the early 1960’s. This particular sculpture was designed and folded ca. 1971-1972. It was shown in the 1972 Exhibition: \"Ron Resch and the Computer\", Utah Museum of Art, University of Utah, Salt Lake City, Utah.
It was designed with a custom CAD program that I and my staff developed specifically to enable the design of space curves and physically fabricate them as folded curves with bent developable surfaces on either side of the folded curved edge. The mathematics and the program were based on my discovery of how to geometrically define a folded, curved crease that would conform to any predefined space curve. I believe I was the first to ever solve this geometric problem.
First, I used the program to define a target space curve. This particular pre-defined 3-dimensional space curve is a b-spline. Secondly, the program enabled the completely generalized design of the folded sheet developable such that it would conform to the predefined, 3-D space curve. This folded sheet developable which has this pre-defined space curve embedded in it as the folded edge was then rendered both as a shaded raster-video image (see examples) and as a line drawing showing the generator lines of the developable surfaces on either side of the curved folded edge.
Next the 2-dimensional developable geometry was computed and output. This included both the fold lines to be subsequently scored and the edge lines to be cut. This output graph was then used to drive a custom make NC-machine that I built that scored and cut the physical sheet. The sheets were then hand folded and assembled, as you see here. This model is about 48” across.")
![[074-.10]](http://www.ronresch.com/gallery/space-curve-as-a-folded-edge/bw%20colin%20print%20074-.10.png/image_large "This White Space Curve Fold with 3-fold Symmetry is based on work I did in the early 1960’s. This particular sculpture was designed and folded ca. 1971-1972. It was shown in the 1972 Exhibition: \"Ron Resch and the Computer\", Utah Museum of Art, University of Utah, Salt Lake City, Utah.
It was designed with a custom CAD program that I and my staff developed specifically to enable the design of space curves and physically fabricate them as folded curves with bent developable surfaces on either side of the folded curved edge. The mathematics and the program were based on my discovery of how to geometrically define a folded, curved crease that would conform to any predefined space curve. I believe I was the first to ever solve this geometric problem.
First, I used the program to define a target space curve. This particular pre-defined 3-dimensional space curve is a b-spline. Secondly, the program enabled the completely generalized design of the folded sheet developable such that it would conform to the predefined, 3-D space curve. This folded sheet developable which has this pre-defined space curve embedded in it as the folded edge was then rendered both as a shaded raster-video image (see examples) and as a line drawing showing the generator lines of the developable surfaces on either side of the curved folded edge.
Next the 2-dimensional developable geometry was computed and output. This included both the fold lines to be subsequently scored and the edge lines to be cut. This output graph was then used to drive a custom make NC-machine that I built that scored and cut the physical sheet. The sheets were then hand folded and assembled, as you see here. This model is about 48” across.")
![[082-.10]](http://www.ronresch.com/gallery/space-curve-as-a-folded-edge/bw%20colin%20print%20082-.10.png/image_thumb "This White Space Curve Fold with 3-fold Symmetry is based on work I did in the early 1960’s. This particular sculpture was designed and folded ca. 1971-1972. It was shown in the 1972 Exhibition: \"Ron Resch and the Computer\", Utah Museum of Art, University of Utah, Salt Lake City, Utah.
It was designed with a custom CAD program that I and my staff developed specifically to enable the design of space curves and physically fabricate them as folded curves with bent developable surfaces on either side of the folded curved edge. The mathematics and the program were based on my discovery of how to geometrically define a folded, curved crease that would conform to any predefined space curve. I believe I was the first to ever solve this geometric problem.
First, I used the program to define a target space curve. This particular pre-defined 3-dimensional space curve is a b-spline. Secondly, the program enabled the completely generalized design of the folded sheet developable such that it would conform to the predefined, 3-D space curve. This folded sheet developable which has this pre-defined space curve embedded in it as the folded edge was then rendered both as a shaded raster-video image (see examples) and as a line drawing showing the generator lines of the developable surfaces on either side of the curved folded edge.
Next the 2-dimensional developable geometry was computed and output. This included both the fold lines to be subsequently scored and the edge lines to be cut. This output graph was then used to drive a custom make NC-machine that I built that scored and cut the physical sheet. The sheets were then hand folded and assembled, as you see here. This model is about 48” across.")
![[082-.10]](http://www.ronresch.com/gallery/space-curve-as-a-folded-edge/bw%20colin%20print%20082-.10.png/image_large "This White Space Curve Fold with 3-fold Symmetry is based on work I did in the early 1960’s. This particular sculpture was designed and folded ca. 1971-1972. It was shown in the 1972 Exhibition: \"Ron Resch and the Computer\", Utah Museum of Art, University of Utah, Salt Lake City, Utah.
It was designed with a custom CAD program that I and my staff developed specifically to enable the design of space curves and physically fabricate them as folded curves with bent developable surfaces on either side of the folded curved edge. The mathematics and the program were based on my discovery of how to geometrically define a folded, curved crease that would conform to any predefined space curve. I believe I was the first to ever solve this geometric problem.
First, I used the program to define a target space curve. This particular pre-defined 3-dimensional space curve is a b-spline. Secondly, the program enabled the completely generalized design of the folded sheet developable such that it would conform to the predefined, 3-D space curve. This folded sheet developable which has this pre-defined space curve embedded in it as the folded edge was then rendered both as a shaded raster-video image (see examples) and as a line drawing showing the generator lines of the developable surfaces on either side of the curved folded edge.
Next the 2-dimensional developable geometry was computed and output. This included both the fold lines to be subsequently scored and the edge lines to be cut. This output graph was then used to drive a custom make NC-machine that I built that scored and cut the physical sheet. The sheets were then hand folded and assembled, as you see here. This model is about 48” across.")
![[096-.10]](http://www.ronresch.com/gallery/space-curve-as-a-folded-edge/bw%20colin%20print%20096-.10.png/image_thumb "This White Space Curve Fold with 3-fold Symmetry is based on work I did in the early 1960’s. This particular sculpture was designed and folded ca. 1971-1972. It was shown in the 1972 Exhibition: \"Ron Resch and the Computer\", Utah Museum of Art, University of Utah, Salt Lake City, Utah.
It was designed with a custom CAD program that I and my staff developed specifically to enable the design of space curves and physically fabricate them as folded curves with bent developable surfaces on either side of the folded curved edge. The mathematics and the program were based on my discovery of how to geometrically define a folded, curved crease that would conform to any predefined space curve. I believe I was the first to ever solve this geometric problem.
First, I used the program to define a target space curve. This particular pre-defined 3-dimensional space curve is a b-spline. Secondly, the program enabled the completely generalized design of the folded sheet developable such that it would conform to the predefined, 3-D space curve. This folded sheet developable which has this pre-defined space curve embedded in it as the folded edge was then rendered both as a shaded raster-video image (see examples) and as a line drawing showing the generator lines of the developable surfaces on either side of the curved folded edge.
Next the 2-dimensional developable geometry was computed and output. This included both the fold lines to be subsequently scored and the edge lines to be cut. This output graph was then used to drive a custom make NC-machine that I built that scored and cut the physical sheet. The sheets were then hand folded and assembled, as you see here. This model is about 48” across.")
![[096-.10]](http://www.ronresch.com/gallery/space-curve-as-a-folded-edge/bw%20colin%20print%20096-.10.png/image_large "This White Space Curve Fold with 3-fold Symmetry is based on work I did in the early 1960’s. This particular sculpture was designed and folded ca. 1971-1972. It was shown in the 1972 Exhibition: \"Ron Resch and the Computer\", Utah Museum of Art, University of Utah, Salt Lake City, Utah.
It was designed with a custom CAD program that I and my staff developed specifically to enable the design of space curves and physically fabricate them as folded curves with bent developable surfaces on either side of the folded curved edge. The mathematics and the program were based on my discovery of how to geometrically define a folded, curved crease that would conform to any predefined space curve. I believe I was the first to ever solve this geometric problem.
First, I used the program to define a target space curve. This particular pre-defined 3-dimensional space curve is a b-spline. Secondly, the program enabled the completely generalized design of the folded sheet developable such that it would conform to the predefined, 3-D space curve. This folded sheet developable which has this pre-defined space curve embedded in it as the folded edge was then rendered both as a shaded raster-video image (see examples) and as a line drawing showing the generator lines of the developable surfaces on either side of the curved folded edge.
Next the 2-dimensional developable geometry was computed and output. This included both the fold lines to be subsequently scored and the edge lines to be cut. This output graph was then used to drive a custom make NC-machine that I built that scored and cut the physical sheet. The sheets were then hand folded and assembled, as you see here. This model is about 48” across.")
![[093-C12]](http://www.ronresch.com/gallery/space-curve-as-a-folded-edge/bw%20colin%20print%20093-C12.png/image_thumb "This White Space Curve Fold with 3-fold Symmetry is based on work I did in the early 1960’s. This particular sculpture was designed and folded ca. 1971-1972. It was shown in the 1972 Exhibition: \"Ron Resch and the Computer\", Utah Museum of Art, University of Utah, Salt Lake City, Utah.
It was designed with a custom CAD program that I and my staff developed specifically to enable the design of space curves and physically fabricate them as folded curves with bent developable surfaces on either side of the folded curved edge. The mathematics and the program were based on my discovery of how to geometrically define a folded, curved crease that would conform to any predefined space curve. I believe I was the first to ever solve this geometric problem.
First, I used the program to define a target space curve. This particular pre-defined 3-dimensional space curve is a b-spline. Secondly, the program enabled the completely generalized design of the folded sheet developable such that it would conform to the predefined, 3-D space curve. This folded sheet developable which has this pre-defined space curve embedded in it as the folded edge was then rendered both as a shaded raster-video image (see examples) and as a line drawing showing the generator lines of the developable surfaces on either side of the curved folded edge.
Next the 2-dimensional developable geometry was computed and output. This included both the fold lines to be subsequently scored and the edge lines to be cut. This output graph was then used to drive a custom make NC-machine that I built that scored and cut the physical sheet. The sheets were then hand folded and assembled, as you see here. This model is about 48” across.")
![[093-C12]](http://www.ronresch.com/gallery/space-curve-as-a-folded-edge/bw%20colin%20print%20093-C12.png/image_large "This White Space Curve Fold with 3-fold Symmetry is based on work I did in the early 1960’s. This particular sculpture was designed and folded ca. 1971-1972. It was shown in the 1972 Exhibition: \"Ron Resch and the Computer\", Utah Museum of Art, University of Utah, Salt Lake City, Utah.
It was designed with a custom CAD program that I and my staff developed specifically to enable the design of space curves and physically fabricate them as folded curves with bent developable surfaces on either side of the folded curved edge. The mathematics and the program were based on my discovery of how to geometrically define a folded, curved crease that would conform to any predefined space curve. I believe I was the first to ever solve this geometric problem.
First, I used the program to define a target space curve. This particular pre-defined 3-dimensional space curve is a b-spline. Secondly, the program enabled the completely generalized design of the folded sheet developable such that it would conform to the predefined, 3-D space curve. This folded sheet developable which has this pre-defined space curve embedded in it as the folded edge was then rendered both as a shaded raster-video image (see examples) and as a line drawing showing the generator lines of the developable surfaces on either side of the curved folded edge.
Next the 2-dimensional developable geometry was computed and output. This included both the fold lines to be subsequently scored and the edge lines to be cut. This output graph was then used to drive a custom make NC-machine that I built that scored and cut the physical sheet. The sheets were then hand folded and assembled, as you see here. This model is about 48” across.")
![[081-.10]](http://www.ronresch.com/gallery/space-curve-as-a-folded-edge/bw%20colin%20print%20081-.10.png/image_thumb "This White Space Curve Fold with 3-fold Symmetry is based on work I did in the early 1960’s. This particular sculpture was designed and folded ca. 1971-1972. It was shown in the 1972 Exhibition: \"Ron Resch and the Computer\", Utah Museum of Art, University of Utah, Salt Lake City, Utah.
It was designed with a custom CAD program that I and my staff developed specifically to enable the design of space curves and physically fabricate them as folded curves with bent developable surfaces on either side of the folded curved edge. The mathematics and the program were based on my discovery of how to geometrically define a folded, curved crease that would conform to any predefined space curve. I believe I was the first to ever solve this geometric problem.
First, I used the program to define a target space curve. This particular pre-defined 3-dimensional space curve is a b-spline. Secondly, the program enabled the completely generalized design of the folded sheet developable such that it would conform to the predefined, 3-D space curve. This folded sheet developable which has this pre-defined space curve embedded in it as the folded edge was then rendered both as a shaded raster-video image (see examples) and as a line drawing showing the generator lines of the developable surfaces on either side of the curved folded edge.
Next the 2-dimensional developable geometry was computed and output. This included both the fold lines to be subsequently scored and the edge lines to be cut. This output graph was then used to drive a custom make NC-machine that I built that scored and cut the physical sheet. The sheets were then hand folded and assembled, as you see here. This model is about 48” across.")
![[081-.10]](http://www.ronresch.com/gallery/space-curve-as-a-folded-edge/bw%20colin%20print%20081-.10.png/image_large "This White Space Curve Fold with 3-fold Symmetry is based on work I did in the early 1960’s. This particular sculpture was designed and folded ca. 1971-1972. It was shown in the 1972 Exhibition: \"Ron Resch and the Computer\", Utah Museum of Art, University of Utah, Salt Lake City, Utah.
It was designed with a custom CAD program that I and my staff developed specifically to enable the design of space curves and physically fabricate them as folded curves with bent developable surfaces on either side of the folded curved edge. The mathematics and the program were based on my discovery of how to geometrically define a folded, curved crease that would conform to any predefined space curve. I believe I was the first to ever solve this geometric problem.
First, I used the program to define a target space curve. This particular pre-defined 3-dimensional space curve is a b-spline. Secondly, the program enabled the completely generalized design of the folded sheet developable such that it would conform to the predefined, 3-D space curve. This folded sheet developable which has this pre-defined space curve embedded in it as the folded edge was then rendered both as a shaded raster-video image (see examples) and as a line drawing showing the generator lines of the developable surfaces on either side of the curved folded edge.
Next the 2-dimensional developable geometry was computed and output. This included both the fold lines to be subsequently scored and the edge lines to be cut. This output graph was then used to drive a custom make NC-machine that I built that scored and cut the physical sheet. The sheets were then hand folded and assembled, as you see here. This model is about 48” across.")
