Little snag here. Has no idea what the equation is. Oh, but there's an
area of mathematics for this too...after differential calculus and after
integral calculus. Crank up the differential equations...mathematical
equations for an unknown functions.
Wrong. It isn't a "function" -- for every x, there's TWO y's.
Maybe somehow bisect the top of the pool, symmetrically. Or not symettrically.
NOW you have TWO SEPARATE curves, each doable (unless it's *really* weirdly
shaped, parallel nooks and crannies(sp?)) via a y = f(x).
Integrating, you'll get two areas, to add together.
Long time ago, before computers, they had these mechanical complicated-linkage
based things ("planeaometer"? something like that?), at the end of which
was a tracing-needle or a pencil, etc, and when you traced around the curve,
somehow you could read the area off some dial.
Fancy stuff out there before (digital) computers.
They had tide-predictors that emulated the fourier series that
worked for that particular point (30 miles up the coast it might
be very different series).
Of course (well, maybe not "of course") the Norden bombsight was
totally (I think) mechanical, via gears, cams, linkages, etc (I guess --
I think it's still classified).
You can estimate the area by overlaying the circumference of a couple of
circles, figuring the area of each, then adding those areas together. Take
the remaining area not covered by your circles, and estimate that area,
adding it to the previous area to obtain your final rough estimate.
Circles, triangles, etc. Maybe just triangles.
That's what they've been doing since the beginning
of computer graphics, for "filling" closed curves
with colors, say.
Stupidly, I forget the generic term for computing a set
of triangles to, to some approximation, "fill" an area.
And to figure an approaching-optimum set of triangles,
ie the FEWEST number of them (differently sized, of course)
to fill an area. Triangles REALLY easy to compute, so easy
that long ago they designed chips to do it "in hardware",
A picture might contain a jillion triangles, so doing them
fast is important. Especially if you're doing it "in real time",
ie like in an animation.
Not that I've ever done any of this stuff, nor even
taken a class in it. But I am a mamber of ACM "SigGraph",
and once a year get this heavy book of the yearly "proceedings" --
man, you have to be a physicist to do some of that stuff,
and you want to see applications of REALLY hairy math,'
and REALLY clever algorithms, you'll see them there.
Again, not that I actually understand it all, but I can at
least read *parts* of *most* (well, many) of the included
"papers". Nifty stuff indeed!
Oh, there's a newsgroup that's related: comp.graphics.algorithms,
where I sometimes ask (my usual stupid) questions.
If accuracy is important, I'd use the Simpson's Rule formula, where
you take measurements across the pool at interals and plug those
distances into the formula. You also have to plug the interval
distance into the formula.
Why do you ask?
The hard part is Googling a web page that presents the formula in an
easy to understand manner for novices.
Without the dot dot dots so the link works.
You're welcome! ;)
Little bit more on it.
You're welcome! ;)
Indeed I am. ;)
I did a "copy link location" since it was a PDF - first time I ever
had an ellipsis swapped in there when I pasted. Remind me to
proofread before I post next time. Thanks in advance!
I'm curious, does anyone else here use Sketchup for determining
areas? I find it amazingly helpful when estimating. It's tailor made
for such things as SteveB is doing. Only a few measurements are
needed and then the curve is tweaked by eye.
Here's a picture of what I'm talking about. I drew four curves - drew
one curve of one end of the pool, copied it and moved the copy to the
far end of the pool, scaled it to reverse its direction, and drew two
curves tangent to the ends of the end curves. Then right clicked on
the surface and chose the area function. It took me longer to write
this than to draw it.
Looks pretty slick. Probably worth a few hours of investment time to
learn to use if you have repeated uses as Steve says he does. If it only
takes a few hrs to learn a specific use that speeds thing up, the ROI
would be great.
If designing in 3D no need to use ACAD any more
anyway. Get a solids modeler like Solid Works
The ONLY thing I would use CADA for now days is 2D
electrical schematics..... and I'm not even sure I
would use ACAD in THAT case!
I spent 12 years using ACAD and will never go back to
HomeOwnersHub.com is a website for homeowners and building and maintenance pros. It is not affiliated with any of the manufacturers or service providers discussed here.
All logos and trade names are the property of their respective owners.