Polar grids generate patterns of dots that are more dense near the middle of the circle and less dense near the outer edge. Usually the diameter of the concentric circles increases at a constant rate. With these grids, the diameter increases in proportion to the distance between dots along each circle.

Install Inkscape Extensions

The generated dots are grouped per circle. The screenshot has the second circle of red dots selected. The dialog on the right shows the properties of the group. The status line at the bottom shows the number of dots on the circle, annotated with a red circle.

The diameter of the selected circle of red dots (annotated with a red circle at the right of the screen shot) is used as outer diameter (annotated with a red circle at the left of the screen shot) for the green grid with less dots per circle. The ratio of dots between the green and red grid in the example is 2:3 that difference could for example be bridged with asymmetrical spiders: four legs on the inside, six on the outside.

Think of reports to calculate the desired number of dots. For example: if the desired design has fans along the outside, the number of pins for the grid needs to be a multiple of the number of footside spaces required for that fan.

The angle of the polar grid is kept constant with the following theory.

When a is small and r large, the small edge of the pie could be considered straight.

With b = 45 degrees, r₁ equals the small pie edge.

The approximation above in math:

For the circle we get:

From the mathematical rule:

we can deduce:

This Java/SVG based proof of concept is a stripped version of the stand alone Java based BobbinWork grid generator.