Read "Runabout" and thought you where talking about star trek for a second

Me mate Jim does it. He's got a good eye

I always thought these markings were made by machines, until I saw some people draw them by hand. Turns out, you can make near perfect road markings with a movable can of paint. If you use GPS to trace out your track, you can just fill them by hand.

As for construction, here's a timelapse of making one using stone tiles: https://youtu.be/gXiOt-9WCag

Here's one made of asphalt: https://youtu.be/DORBEGYVgYE Note the pre-poured blocks of concrete in the center, which likely help the round shape.

In this video you can see the imperfect temporary road markings for a short moment: https://youtu.be/SV2vSL_hiA0

This video showcases a different style of roundabout that makes two-lane roundabouts a bit easier. Note the two round, concentric lanes separated by concrete barriers: https://youtu.be/iRclLOgN-xw

This video showcases the manual driving work done to make the round roads: https://youtu.be/KCQv24BkI6Y This is a four lane roundabout. The video also shows how the line markings are applied (by a spout, in a car).

This video shows a prefab concrete roundabout installed over a weekend. All they needed to do was prepare the soil, lay down the blocks and paint the lines: https://youtu.be/J-BZWfbygkc

This video shows how the center concrete slabs can be laid on location using a specialised machine: https://youtu.be/J2g0JZzqbAs

I'm not sure if this tech is applied, but farmers use millimeter precision GPS to efficiently farm their soil. The GPS receiver itself costs a couple of grand, but making a car in a closed-off road drive in a perfect circle is hardly a technical challenge these days. That said, these people can probably do it by hand and you wouldn't notice the difference.

Firstly, roundabouts aren't perfectly round.

The city I live in is relatively small but has dozens of roundabouts. They might look round as you drive through them, but if you look from a satellite image most are just "mostly" round, and some that seem round on the ground are plain oblong.

With that in mind, you're dealing with curves, not a perfect circle.

Different points are defined with a range of methods like survey, measuring, and just plain eyeballing.

You're asking about something called surveying, if you want a term to search for. Modern surveying equipment uses lasers to measure the land, then they do a bunch of trig to create an accurate map. Once you have an accurate map that's keyed to known reference points, you can design the roundabout. When you're ready to build it, it's just following the map and using the reference points to measure it back out.

For the markings, I've seen such a small cart that just had an adjustable wheel on a pole at the side. Since the pole was fixed length, they just kept the wheel near the outer road border and thus kept the distance always the same, keeping the marking in the middle.

Have you seen these people with a weird tripod on construction sites ? They're surveyor and have tools allowing them to do very precise measure (A guy told me that one of the coolest things he has done was to make sure railway track were aligned below 1mm on both side of 2 km bridge to build) I would expect that drawing a circle isn't that complicated.

Then the rest is usual road construction, add temporary marking, close the road, do the measurement and build the roundabout

Not sure about this, but the machine that paints the line probably has its steering/turning circle set to the required radius/diameter/angle and then just drives in a circle, same as if you held your steering wheel just off centre, eventually you'd end up back where you started. If it's a few centimetres off, it probably doesn't matter.

Either that or it just follows the edge of the thing it's drawing a circle around

Well it depnds on what amount of cost you want to put in, and how are you making the roundabout, and are you going to put something on it, and essentially wht budgets you have. Where I live, we almost always have some statues or soemthing put on them.

They are made with essentially make shift compasses where I live. This is what is done for a roundabout of radius, lets say in ball park of 5-10 m. Initially marking is done (this is simply done by measuring out a tape of desired radius, and holding wwhen end at center, and other person revolvinng around it, and laying down something - could be simple as white chalk, or use jackhammer to make actual indents to ground, or lay down some bricks) This will serve as guide for curve, and any further curved elements could be made by just maintaining a constant distance from this circumference. Then the interior is usually dug to lay a foundation for whatever you put on it (could be as simple as excavating, and just plastering, but that is still expensive, often manually digging and then laying a firm dirt layer is enough). then it is covered with something (could be custom designed pizza slice shaped stone or marble wedges, but usually just bricks or cinderblocks). While making, we do not really make a great curved edge, and just make a n-gon, where n can be 20 or 50 or 100. This is simpler because straight edged bricks are cheaps, and you can lay them vertical, filling the gaps with plaster. The depending on your budget, you could get great finishing, again done with applying plaster, but this time, excess is applied, and some is removed, so we get a curved edge. Now you mostly have the exterior ready. On the top, you could have marble or stone, which can be grinded to match the curved edge, or it could be a thin plaster layer, which will take the shape of boundary.

Where I live, it’s all planned out in CAD, and then the inner concrete curb is calculated and broken up into sections, according to the plan.

Then the intersection being replaced (because that’s almost always the case) is dug up in the center and the concrete forms put in place and the center backfilled with gravel and dirt.

After the concrete has set, the asphalt machines re-level and pave the surrounding area. After this, brick is often added inside the concrete to provide an extra driving surface for large vehicles. Then plants or statues are added to the centre.

After all this, the lines and markings go on, and they’re just offset from the concrete curb, so nothing fancy needs to be done; the paint truck just has a little arm that stays over the concrete.

Well when two junctiona really really like each other......

To get a step deeper into your "how can a machine draw a circle" question. Mostly it can't. Even with an open-loop control system dragging the 'pen' at a fixed angle, you would need to have defined that curve in software somewhere, where it will be a barely-noticable set of X-Y steps, not a pure curve, otherwise you cannot be sure it would return to the origin.

Luckily, you only need a few decimals of pi to approximate that far beyond what any human eye could discern.

Break any digitally defined curve down far enough and you will see those discrete steps, but with modern technology, we just never notice it.

In my city they just put something in the center of an intersection and call it a day.