Some Circular Designs (Page 3)
Most authorities construct curve-stitch parabolas using
s+1 distinct lines, where s is the number of
equal-length segments into which each axis is divided. For example, if
s = 3, we would have a figure like the following:
In this construction, a
point on either axis is connected directly to a point on the other axis s
segments away, counting toward the vertex and moving along the other axis once
the vertex is reached. For s = 4, we have something like:
When I was taught how to
construct curve-stitch parabolas in junior high school, I learned to use s+2 distinct lines, following the rule of spacing endpoints at a separation of
s+1 segments, with the axes as the scaffolding on which the entire
construction is built. This produces figures like the following, for s =
3:
Notice that this is
actually the same construction as the earlier one, but using longer axes
segmented into s+1 units and with the final segment on each axis lopped
off.
Each construction method
approximates parabolas, in that they result in tangent lines along a parabola
that is never explicitly drawn. The first method approximates a parabola
actually tangent to the axes at the endpoints. This is a useful property in some
constructions. For example, if two curve-stitch parabolas share an axis and
endpoint, and they are mirror images of one another, using the first
(or standard) construction prevents a minor discontinuity where the parabolas meet:
The second method results in:
Nonetheless, the standard
construction does not always seem to be the “right” one. In some combinations,
standard parabolas produce very
“spiky” elements, which one might prefer to avoid. Consider this juxtaposition
of standard parabolas:
The alternate construction gives us the following
instead:
I generally prefer the second method of construction,
which gives many figures points that look like stars, rather than like antennas.
Judge for yourself in the following pictures. (Click on a design to see a
larger image.)
Segments = 10, Wedges = 5, Levels = 2, Standard
Construction
Segments = 10, Wedges = 5, Levels = 2, Alternate
Construction
Click on Next for more on the two possible
constructions for curve-stitch parabolas. |
