Curve-stitch Designs

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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:

Standard parabola with three segments

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:

Standard parabola with four segments

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:

Alternate parabola with three segments

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:

Mirror-image parabolas, standard construction

The second method results in:

Mirror-image parabolas, alternate construction

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:

Back-to-back parameters, standard construction

The alternate construction gives us the following instead:

Back-to-back parameters, alternate construction

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, Standard Construction
Segments = 10, Wedges = 5, Levels = 2, Alternate Construction
Segments = 10, Wedges = 5, Levels = 2, Alternate Construction

Click on Next for more on the two possible constructions for curve-stitch parabolas.

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