How to split a shape based on a grid?

Question

I'm using Photoshop and Inkscape.

1. I have a circle shape.
2. Based on a grid, I want to generate say thousand other smaller shapes that fill that circle nicely (and perhaps without gaps).
3. I want those smaller shapes to be vector and separately selectable.

How do I do that? I can’t do it without automation because the number of smaller shapes can be large. For a small number of filler shapes I could use masks.

Answer 1

1. Suppose this is your shape:

   

2. Create a single square of your desired size:

   

3. Activate Snapping (%) and Snap to Cusp Nodes.

4. Duplicate your square (Ctrl + D).

5. Drag the duplicate to touch the original in exactly one corner (it should snap):

   

6. Duplicate both squares; drag the duplicates to form a checkerboard pattern; duplicate all four squares; drag; duplicate; … Soon you should have your entire object covered:

   

7. Combine all squares (Ctrl + K).

8. Select your squares and then your object.

9. Intersection (Ctrl + *):

   

10. Break apart (Ctrl + Shift + K). You can now manipulate your individual shapes separately.

Now, obviously that only half the battle, but it’s more instructive to do this once first. To get your real result change the above as follows:

• After Step 7, duplicate your combined squares and move the duplicate squares to fill the gaps of the other ones, i.e., such that the whole shape is covered.

• Duplicate your original shape.

• Perform Steps 8 to 10 twice, once with the original squares and shape and once with the duplicates. To avoid confusion, I recommend to have a separate layer for each of the two iterations, so you can hide while you perform the other one. Alternatively, use separate colours for each object.