Right angles, curves and node control for a ring-road starter district

[Blueberry Muffins!]

So you can make right angles without reference to a grid, you can make perfect arcs with any diameter and center you like, and you can put intersections and road/footpath connections exactly where you want them. This is harder to describe than it is to do, I'm trying to be exact here.

The thing to notice is, the measurement tool gives you two distances: end-to-end direct "air" distance, and every-step-of-the-path-following "ground" distance. You and Pythagoras can hijack this.

To make right angles without reference to a grid, the two triples I use most are 5,12,13 and 9,40,41, that latter one to start my example here: a 400m-diameter ring road around a walkable, reasonably good-looking starter enclave that easily handles up to about 2000 workers with the starter buildings. There are easier and arguably better layouts to start with, but this one illustrates the techniques so I'm going with it.

400m diameter is 40×10. The other leg of a right triangle would be 90m, so draw the 400m diameter, then drag out a 90m leg and put its tip where the air distance is 410m. Zoom in real close to get fiddly with the positioning if you want. Run a straight mud-road temporary segment along the short leg, notice how the placement display acts at 5m-length intervals and where the measurement dots are, and you've got your tangent, now draw a half-circle to the start point, cancel the short leg and complete the circle.

That's the ring road, nodes at the diameter tips, as accurate as your ground was level (which a little judicious excavator-and-bulldozer work could make "perfect") and your mouse hand was steady. For the *really* fussy, zooming in to get the placement juuust right, noticing details like how the placement display behaves at 5m-length intervals and such can take the precision to ridiculous levels, but really? on any reasonably-level ground you won't need the fussy.

Now move the third measurement point, the tip of the starter tangent leg, to the circle's center: the ground path length will be 600m, the air path length 200m and the measurement-path dots will be all pretty in a row. I drop a temporary small fountain there to start, it's useful to highlight that point so I can casually reset all the measurements and still easily see when I've drawn through the center.

Now you're going to make two footpath rings, one 85m in from the ring road and one 35m out from the fountain: drop a new point on the diameter to make the ground distance 635m and the air distance 165m, delete the first two points and you've got a 35m radius for your inner walkway ring. 35 is 5×7, 13×7 is 91, 12×7 is 84, plus the 35 is 119, so your other right-angle tip is at 119 ground-path length, 91 air-path length, your tangent's along the 91m leg, you got this,right? Finish it up,move the right-angle tip point back to the outer road node, drop a new leg 85m back along that radius, 85 is 5×17, air path is 13×17 is 221, tangent leg is 12×17 is 204, ground path is 17×17 is 289. Make a footpath ring 85m in from the ring road.

Now to make radial walkways at pleasingly-exact symmetrical points along the circles.

To set this up, re-measure the ring road diameter through the two existing road nodes, re-add the center point to make the ground path length 600m, and drop a radius to make the ground path 800m and the air path 200m. Ta-daa, an equilateral triangle. Bounce back trhough the center point to make a diameter, ground path length 1200m now, add a chord to ground path 1400m air path 200m and another diameter from there: guides for radial footpaths from the road to the inner ring.

With some practice this paragraph takes me about two, three seconds per node to execute, maybe five when I get sloippy: cancel—don't bulldoze, pretty sure that wipes and recalculates nodes, use the road and footpath cancel tools to cut existing paths without recalculating—maybe 50m-100m of ring road either side of one of the new diameter ends you just dropped, re-extend road from a freshly-cut tip back to the diameter's end and you can precisely place it so the calculated curve radius extends exactly along the drawn diameter. Reconnect from the the other cut end and you've got a road node exactly where you want the radial walkway to end. Do this again with proportionately-shorter stretches of the two footpath rings and connect the perfect radial walkway through the nodes you just made. Three more new radiii and that's done.

Now drop a chord between adjacent road nodes (notice when you extended from a cut end that moved the end node, it didn't add a new one), a third point back to the halfway mark, most of a diameter through the center then a full diameter back through the center again, Add new walkways from the road to the outer walkway ring.

I pack in eighteen high-quality medium flats, two each in eight consecutive lots and one overflow at each end, leaving lots of room for pub/shopping/utilities in the remaining lots, the central area for kindergarten and whatnot. Nonpolluting services can run around the outer ring, la la. At capacity you'll want the asphalt walkways with lights, probably the lighted-and-walkwayed roads too