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I have read the section on snapping nodes and looked at this question

Creating snap node from intersections in Inkscape

I am trying to make something that looks like a Venn diagram, but where I can duplicate the different intersections of (e.g. 3 or more circles). If these circles were somehow created using the Bezier pen, then I think I would know how to grab these partial segments and duplicate them, but as far as I can tell there doesn't seem to be an easy way to:

  • add nodes to a shape created with something other than the bezier pen tool.
  • trace over existing curve shapes with the bezier tool exactly.

http://www.gghh.name/dibtp/images/compact_and_exploded.png This is the type of image I am trying to recreate.

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Inkscape's circles are not Bezier curves. The node tool and many other path editing methods do not work as expected.

Select a circle, apply Path > Object to Path. The circle is now editable path like those you have drawn with the pen. You can add new nodes with the node tool and use all available other path editing methods.

Warning: "Stroke to Path" convert curves and lines to closed fillable areas, it's totally different than "Object to Path".

A suggestion: Learn path operations such as Union, Intersect, Difference etc... I guess you make Venn diagram style shapes best with them. Have spare copies of the original shapes because the originals vanish in path operations. Learn also snapping options because you need snapping to get the generated slices placed exactly.

About tracing: It's difficult to draw manually a copy of an existing curve with the pen although many of us must do it if the original happens to be a photo or other bitmap image. Path > Bitmap Trace can sometimes be good enough, but as often manual drawing is better.

Copying a Bezier curve with the pen is wasting of time. Make a duplicate and separate the wanted parts with the node tool.

  • This was super helpful. To add, if you make intersections or something it is possible to make the intersection, copy them to the clipboard and then use the undo command to put the original object back as it was. Undo does not erase the clipboard, so you can still paste a copy of the new shape and keep the old one. – marlow Oct 17 at 20:17
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I don't think you need to add nodes to achieve your desired result.

Here's one method that works well for complex overlapping shapes you want to cut out:

  1. Draw overlapping circles

  2. Select all the circles, click Path > Combine

  3. Draw a rectangle, click Object > Lower to Bottom

  4. Select all shapes and the rectangle, and click Path > Division. This will make all the pieces separate. Might be easier at this stage to apply a fill so you can select the pieces easily.

  5. Delete the outer rectangle

  6. Fill and apply white strokes to the pieces as required

Example showing steps 4 to 6:

enter image description here

Example

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