How do I split a circle into equal sections in Inkscape?

Question

Illustrator has the polar grid tool (as mentioned in this question) but how do I properly split a circle into equal sections in Inkscape?

Answer 1

The naive way is to use the circle tool and its sector (pie chart) mode to draw sectors with the same angle. Press ctrl while drawing the sectors to enable snapping every 15° (snapping angle can be changed in Edit > Preferences > Behaviour > Steps > Rotation snaps every ... degrees).

The naive method is viable for a few cases (coarse subdivision, angles are multiples of 15°, ...).

With some effort, you can emulate the linked polar grid tool using Inkscape's tiled clones. For the following steps enable the snapping options »center of bounding boxes«, »cusp nodes«, and »rotation center« as in the following picture.

🞱 Snapping is essential here. This whole approach only works if the lines we are about to generate touch each other at the center. This is easy with snapping but nearly impossible freehand.

Divide circles/disks into N pie chart pieces / sectors**

1. Draw a circle.
2. Draw a line from the circle's center 🞱 outwards so that the line is longer than the radius of the circle.
3. Move the rotation center of the line to the center of the circle.
   To do so, click the line twice but do not double click; just make a pause between the clicks. A + should appear in the middle of the line. Drag the + to the center 🞱 of the circle.
4. Select the line and click Edit > Clone > Create Tiled Clones... *
5. In the tab Symmetry, choose »P1: simple translation« and click Reset.
6. In the tab Shift, check Exclude tile Per row.
7. In the tab Rotation, enter 360/N into the field Angle Per row (replace N with the desired number of sectors and yes, Inkscape can calculate 360/N, you don't have to use a calculator)
8. At the bottom of the dialog, choose Rows, columns and enter N and 1 into the related fields.
9. Click Create.
10. Select the resulting clones and unlink them (shift+alt+d or Edit > Clone > Unlink Clone).
11. Combine the unlinked clones (ctrl+k or Path > Combine).
12. Divide the circle using the combined object (select both objects, ctrl+/ or Path > Division).

Divide circles/disks into N rings/annuli

1. Draw a circle.
2. Duplicate the circle (ctrl+d) and click Edit > Clone > Create Tiled Clones... *
3. In the tab Symmetry, choose »P1: simple translation« and click Reset.
4. In the tab Shift, check Exclude tile Per row.
5. In the tab Scale, enter -100/N into the fields Scale X and Scale Y Per row (replace N with the desired number of sectors and yes, Inkscape can calculate 100/N, you don't have to use a calculator)
6. At the bottom of the dialog, choose Rows, columns and enter N and 1 into the related fields.
7. Click Create.
8. Select the resulting clones and unlink them (shift+alt+d or Edit > Clone > Unlink Clone).
9. Combine the unlinked clones (ctrl+k or Path > Combine).
10. Divide the circle using the combined object (select both objects, ctrl+/ or Path > Division).

You can also combine both approaches to create a "radar". Simply combine the unlinked clones ("star" and "bulls eye") and use the result to divide your circle.

* In Inkscape 0.91 Create Tiled Clones is a bit buggy. Often the clones will be shifted all over the canvas (probably due to transformation matrices in the xml file). The issue was fixed in Inkscape 0.92.
Workaround:

1. Create and place the object which should be cloned.
2. Copy the object.
3. Create a new layer.
4. Change to the new layer.
5. Paste the object to the same place (ctrl+alt+v) and use the tiled clones.

Update: There is also an addon to draw polar coordinate systems. It may be easier to use such an coordinate system to divide the circle instead of using tiled clones, but I have not tested the addon so far.