Stencils!
After the nightmare that was compass-and-straightedge construction on fabric, I decided to make grid templates (stencils) to more easily transfer a nice euclidean grid onto the stretchy, bumpy, not-strictly-euclidean surface that is fabric.
Instructions
Step 1: Draw your grid on graph paper. It might also help to draw some of the desired pattern on the grid, so you know how large to make your circles later.
Step 2: Glue the paper to a stiff backing (eg: cardboard from a cereal box).
Tip: you might want to press/weigh everything in place while it dries, to prevent curling.
Step 3: Punch out the holes for your grid.
I used a leather punch and a stone pestle protected by felt, because it's what I had. A needle and an awl would probably also work (but be sure to clean up the backside for bumps after).
You want your hole to be large enough for your marking tool to fit, but small enough to still know where the centre of the hole is.
Step 4: Trim the template so that the edges contain punched holes. This makes it much easier to align your opaque stencil after drawing your first set of dots.
I kept the graph paper as-is on the template, because this helps me set my compass to the correct distance for my circles. So like, if for some reason I should forget how big to make the circles, or forget what this stencil is good for, I can just look at the graph paper.
