Cutting paths with paths in Sketch.app

Question

Goal: To come up with a set of curves on different scales to reproduce the typical "metro map" look. Also to learn what this kind of curve is called (not bezier, not rational?)

Given the following circular path, I would like to "cut" it along the lines shown in order to yield eight segments. I would repeat this process for various sized circles so that they nest as in the London tube map screenshot lower in the post.

In the end, I would remove the "fill" (the resulting paths would be "open" anyway, so unfilled anyway) and outfit it with a thick "line" to make the "tracks" of my would-be metro map.

I tried every variation I could think of, with the circle and line on "top", using intersections and masking, perhaps I'm simply doing something wrong, I never used Sketch to modify shapes before.

Any option, including using the intersection points to add additional control points to the circle (so that I could select, and duplicate just two control points to get a ^1/8 or ^1/4 radius would work for me.

My alternative would be to learn enough geometry to write this as script for Sketch (luckily I'm a software engineer) and "program" out paths with the correct curvature, but I'm quite sure that turns out to be more difficult that it appears, not to mention my knowing nothing about geometry to calculate where the line 1000,0|1000,0 intersects the circle at north-east on it's face.

If I would have the luxury of using Illustrator I suppose I could use the "Pathfinder" tool to "outline" my shapes, according to this page:

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Answer 1

I suggest a different solution where you draw the metro lines without curves to start.

1. Show the grid.

2. Draw the metro lines as lines with sharp corners that are color coded and accurate relative to each other and the underlying map.

3. Have your circle/pie handy for using as a guide when you make curves

4. Position the circle under your curve

5. Add symmetrical bezier points on either side of the corner

6. get rid of the middle corner point and adjust those new bezier points to match the guide circle.

Those are the steps I might use with Sketch. I think you were hoping for something less labor intensive and more precise, but this will work.

(If I were doing it in Illustrator I might use the pathfinder operations. As alluded to by @plainclothes)

Also, it looks like you will need more than one circle, you'll need a series of concentric circles to use as guides.

Answer 2

I'm not sure if you can do this with a quick and easy boolean operator (think pathfinder).

A reasonably quick solution:

1. Set up your orthogonals as a guide.
2. Use the Scissors tool to trim the circle down to a single section.
3. Rotate and dupe the section to create the rest.

Elegant? No.
Functional? Yes.