Curve-stitch Designs

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More Generalizations (Page 13)

 
Just as a 5-pointed star is formed from a pentagon by connecting the vertices in a different order, we can do the same thing with the points of a square, forming a kind of hourglass or figure-8. In the figure below, our path goes through the points at the lower left, lower right, upper left, upper right, and back to the lower left. The point in the center of the figure is not part of our “polygon.” Twenty segments are used on each side, and the offset is 20:

Figure-8 with segments=20 and offset=20

If our “polygon” really is a polygon but is not convex—that is, it is possible to connect two points on the perimeter and have at least some of the points on the line between them be points outside the polygon—we get a kind of 3-D effect, resulting from parabolas being drawn on both the inside and outside of the figure. Here, for example, is a hexagon with a “waist”:

Hexagon with "waist" with segments=20 and offset=20

 

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