How do I use inkscape to divide a circular ring into sections?

Question

I'm using inkscape 0.92.3 and want to break a circular ring into 3 equal sections. I've created a ring from two circles and used Path > Difference, then Extensions > Modify Path > Add Nodes... with a selection of By number of segments, 3. The screenshot shows the result.

Now I need to create 3 divisions of the ring. Using a coordinate system where 0/360 degrees is to the centre right of the ring, I want to connect the nodes from the outer ring to the inner ring with straight segments as follows,

outer  inner
 90     30
210    150
330    270

The dashed lines in the next screenshot show the segments.

I need the segments to break apart and be fitted back again with precision and no gaps. It is absolutely necessary that the radius remains the same when all three segments are rotated as a group.

For anyone who's interested, this is a trivial flower snark with the inner nodes rotated 60 degrees clockwise. In this case the nodes are infinitely small and the 3 sections will be coloured.

Answer 1

To my understanding, what you need is /Path -> Division/. Check the manual here.

If you call your dashed segments are 1, 2 and 3, using the Bezier tool create a closed shape that includes segments 1 and 2, and then overlaps the ring:

Then use /Path -> Division/ to cut the ring using the shape.

Repeat for segments 1 and 3.

To aid in making the precise shape for cutting, enable node snapping.

Answer 2

I am far from a wizard when it comes to Inkscape, but I enjoy a challenge of this nature.

One must presume that you can create an ordinary circle. Once created, you'll see there is two square nodes and one circular node:

Grab the circular node and watch the start or end degree boxes change values:

Note also that the icon on the tool bar has the non-pie-slice option selected, keeping the endpoints open.

A smaller circle has been added and the numbers for start and finish have been changed to match your requirements. The numbers don't match your references and require a bit of math to find the correct "reverse" direction figures.

The inside circle has been adjusted as well, to match your figure. Once you've selected the circle, you can type the numbers in, or drag to get the same figures.

Select both figures and convert to path.

There may be a smarter method than this one, but I simply select the line tool, with snap on (default) and join the inner circle and outer circle.

I'd bet that there's some sequence to automatically join the line being created to the node used as the anchor, but I had to do that manually after creating the lines.

That is, I selected the node tool and then selected the two nodes, one for the outside circle and one for the line that attached to it, then used the combine node toolbar icon to make them a single node. If this isn't done, the fill won't work properly. The object has to be a closed figure for a proper fill. I did a quick Google search and did not find an easy answer about adding a line to a previously placed path and have the nodes automatically joined. That doesn't mean it doesn't exist, but when I know how to do it manually, a long search is longer than the manual method implementation.

You can now take this shape and copy/paste/rotate/clone-rotate to get the three segments required in the original objective.

Answer 3

ADD: This method isn't valid. See the explanation in the end

==============

Dividing the ring with a closed polygon is already presented in an older answer. I recommend it, too:

The black line is the division line. The 30 and 150 degrees rotated lines only mark the corners of the divider for easy, but still exact drawing.

This is new: Have a copy of the original (=undivided) ring below all. You can well delete the bigger part after making the division or directly by making an itersection instead of dividing. The wanted slice (=One part in the objects panel) has a red fill.

Make a copy of the "One part" by duplicating. Color it differently, here it's green:

Select the "One part" and the original ring, rotate them 120 degrees:

Now it's the right time to stop. You do not need the third copy. It's better to have the full ring below all, because in Inkscape perfectly fitting seams leak. That's because SVG shapes are rendered to visible bitmap images with anti-alias. That makes 1px wide transparent gap between exactly fitting parts.

Here the background ring is removed and the splices have dark color. The bright background can be seen through the gap. It will get worse, when exported to PNG.

The invalidity:

Path operations Division and Intersect produce inaccurate result. The parts will not fit. A proof:

Orange line, blue circle and its copy green circle all meet at the corner node of the black polygon. After making intersection between the black polygon and blue circle, the intersection has been shifted away:

The circle radius has been reduced. The questioner seemingly had knocked his head to something resembling, because he demanded that the radius must stay same.

I do not know is it a bug or a specified property. I would say "a bug" if I must guess.