"Warren" wrote in
:

Salty Thumb wrote:

pick a set of reference coordinates. You know the east, south and
west are tangent to the circle. equation of line is y-b=m(x-a),
circle (x-c)^ 2 + (y-d)^2 = r^2. Solve for c, d, r. Choose the r the
fits your criteria.


Gee. I didn't realize it was that simple.

Nor have I felt as dumb as I do right now looking at that equation. I
have no idea where to even start.

Well if you start with y=0 as your south line, it should be easier and
you should be able to find m the slope and (a,b) the offset for the other
two/three lines by measuring from your reference point. Then plug into
your circle equation to solve. You also have your r approximation, you
can interatively go through possibilities till you find an acceptable c,
d. Should be pretty easy with a spreadsheet. If you have access to
Mathmatica or Mat(h)lab or maybe even some Internet applet you could
probably just type in the equations to get an answer.. As far as the
west side, I just assumed they were close enough to be straight using the
southwest line, but if you don't get an acceptable answer, you could
always try again with the northwest line. It is also possible that I am
off my nut, and you won't be able to get an answer with just those
equations.

One of the things complicating this is that there are two segments on
the west side. I'm not sure if the circle will be touching both, or
just one.

It's to the point that I'm ready to scrap this project. Solving this
problem in a practical way looks like I'm going to have to clear the
whole area at once, which isn't something I'll be able to have enough
labor to do at the right time of the year in the available window. I
could just put in a smaller circle that doesn't touch the edges, and
hope it's placement doesn't look too "off", but then I'll have some
left-over scrap areas that'll need to be cared for in some way. (It's
hard to describe it all, as it is such an irregular space.)

I'm ready to just toss the whole concept of repeating circles, and go
with something more free-form. I did think that the repeating circles
vs. the odd angles of things I can't move (like the driveway, the
house, the street and the lot line) would look good, but I obviously
underestimated the difficulty of the geometry when one can't just
clear the land, and use more practical methods like stakes, strings,
and chalk lines that can be easily erased if drawn wrong.


There might be some easy theorem that would solve you easily, but the
hell if I could tell you what it is. As for practical methods, there
might be a way, but again, I couldn't tell you how. There must be some
Pyramid or Stonehenge builders hanging out in other groups.