Curve-stitch Isometric Cube
The figure above is an instance of a design I
created more than fifty years ago. (This figure is covered by a Creative Commons
license. For more information, click
here.) A framed version of it hangs on my kitchen wall.
That picture is a negative print (i.e., white on black) of an India ink drawing
on vellum. It is a minor conversation piece—first-time viewers are often
surprised to learn that the drawing contains no curves. More amazing to me is
that I drew it with drafting pen and straightedge without introducing
major imperfections. I cannot imagine repeating the feat! The figure shown
here is a conversion of output generated using Adobe
PostScript. It doesn’t
reproduce the razor-sharp lines of the original, but it does capture the spirit
of the figure. I recently replaced most of the graphics on this page with PNG,
rather than GIF images. These images are much sharper, but the page
loads slowly because the image files are bigger. (Sorry about that.) A SVG graphic of this figure can be found
here,
although not all browsers will render it properly. (Try zooming in and
out and notice how the image changes.)
My talent as a graphic artist is limited, but I have
always enjoyed drawing designs on paper. Designs employing only straight
lines—such as this one—permit me to masquerade as a real artist, so long as I
don’t have to draw in public.
This design resulted from combining two designs—the
curve-stitch parabola and the isometric
cube. I encountered the former in a junior
high school math class. A drawing such as the following can be made with
needle and thread, punching holes in cardboard and stretching the thread along
its surface:
Somewhere, I picked up the technique of making
isometric drawings. Isometric drawings represent
three-dimensional objects in two dimensions. The x- y- and z-axes are inclined,
respectively, 30, 150, and 90 degrees from the horizontal. Isometric drawings
look like perspective drawings, but parallel lines do not converge at a
distance. Lines parallel to the axes are proportional to the lengths of the
corresponding lines of the actual object, though oblique lines are not. The
nature of an isometric drawing is most easily appreciated by studying an opaque
cube drawn using this technique:
My design simply took an isometric
cube and added curve-stitch parabolas on all adjacent edges. Simple. One feature I’ve always
liked about the design is that the impression it makes on the viewer is quite
changeable. Knowing its origin, it is easy to see it as a patterned cube, but it
can also be viewed two-dimensionally as a hexagon whose vertices have been
connected to the middle before the parabolas are applied. It looks very
different upside down (somewhat face-like, I think):
or rotated:
NOTES: Those interested in
curve-stitch designs may enjoy Jon Millington’s attractive book,
Curve
Stitching: The Art of Sewing Beautiful Mathematical Patterns, Diss,
England: Tarquin Publications, 1989. (The book has been reprinted, most
recently, I think, in 1999.) This full-color paperback includes
a brief quotation from Mary Boole, who invented curve stitching in 1904;
numerous photographs of curve-stitch designs executed in colored
thread on cardstock; a collection of BASIC programs for generating
designs; a discussion of the mathematics of curve stitching; photographs
of art works using curve-stitch techniques; a collection of tools for
executing designs; and a bibliography.
The curve-stitch designs on this site
were all coded originally in PostScript and converted to one of several image
formats that can be viewed in a browser. Information about how I have created
designs and how you might make some in a similar fashion can be read in “Make
Your Own Designs.”
— LED, 8/9/2001, rev. 3/14/2023 |
