Here’s the skinny: I’ve got FEMA 100-year flood maps, and I’ve got plat maps and site surveys of different tracts of land. Using my handy-dandy Deed Plotter program, I can quickly and easily find the exact area of my tracts of land if I do not have a reliable or precise figure. BUT, sometimes I’ve got some of that land in a flood plain, based on my FEMA maps, and I’d like to know exactly (or close to exactly) how much of my land is in the flood plain.
To start with, I guess I should note that I’m no engineer or mathematician, but I do remember enough from my college calculus courses to find the area of irregular shapes GIVEN the equations of the upper and lower curves that define the shape. Presumably, all of these floodplains can be expressed as some nth-order polynomial, only I don’t know what it is.
SO, my question is, is there maybe some kind of software where I could take the digital image of the curves I want defined, and then spit back out whatever polynomial best approximates the area? Like maybe an add-in to Photoshop or something like that? I’m not at all opposed to buying new and expensive software to do this, but at the same time if it can be easily and reliably done with some kind of shareware or freeware (or maybe Adobe Photoshop, which I own, can already do this?) that would be all the better.
In case it matters at all, this is for a pretty speedy brand-new wintel based machine, so serious iteration crunching shouldn’t be too much of a problem.
NIH Image can probably do what you want.
If for some reason you actually want to have the boundaries in polynomial form, check out Lagrange polynomials.
I do this kind of thing in AutoCAD fairly regularly - I don’t know if you have access to anyone who uses it or not, because AutoCAD is probably a bit more expensive than you want to deal with for a one-off project.
Anyway, let’s assume that you can get access to someone who uses it.
Using the “measure area” function in AutoCAD, you can plot points on curves, etc and have the software do the math. In your case, you’d figure it in acres probably (but then, AutoCAD is actually unitless.)
You’d have to be able to import an image of your maps into the program (easily done with a scanner - AutoCAD will accept most standard graphics file types) and then overlay a set of lines, arcs, curves, polylines, etc. on the image. Then you measure the area enclosed by the lines you just drew.
Thanks, Squink and TVGuy! Right now I’m in the middle of downloading Scion Image to see if that will do what I want… although I would really like to actually have the polynomial, ultimately all I really need to do is accurately estimate an oddly shaped area. Maybe programming myself a little lagrange polynomial program is the way to go, but the problem is that I’d have to do some measuring to get my x and y coordinates… what I’m starting with, after all, is a picture (that’s already in digital format, in fact it’s a bitmap) and I want to find the area. What makes it complicated is that often times the flood plain looks like a ball of mud thrown at a wall, so overlaying a set of lines and curves would be a tedious job… what I’m looking for is something that isn’t very time consuming, although it could be as complicated as it wants to be.
That being said, even though I remember a fair amount of college calculus, I’m still no mathematician. I only vaguely remember the term “lagrange multipliers” and this whole concept of lagrange polynomials is all new to me… 'course, I guess fighting ignorance is why we’re all here
I’ve done a lot of curve fitting and I can tell you it’s not worth the trouble. If you’ve got an image or diagram, find the area by brute force - i.e. by using a CAD program’s area function, or use a graphics software (image editing or drawing program) and counting the number of pixels within a specified shape/area. It’s notoriously difficult to automate function fitting routines even when the shape looks similar every time.
I’m afraid I don’t know off hand which software is most suitable, but maybe someone else here can help.
As for the curves themselves, they’re most likely constructed from arcs of circles. The three standard ways of drawing smooth curves on paper are using a compass, a spline (a doohickey like a flexible ruler), or a French curve, and the latter two won’t give you any particular standard type of curve.
Chronos, the curves are, I believe, essentially defined by contours on a topographic map.
I tried using the software Squink recommended, and it ultimately does what I’m trying to do: it tells me what the area is of my flood plains. It would be cool if I could easily fit some kind of nth-order polynomial, but it’s certainly not necessary. I just like to have the equations so that I can integrate them by hand… call me old-fashioned or just stupid, but I like to work out all of my math by hand whenever possible.
I’ll probably play around with writing some program to calculate lagrange polynomials or something though, I like to learn math whenever possible.
Now, if somone could furnish me with sales comparables of full-service car washes in the Fayetteville area, I’ll be all set
I use a program titled Surfer (~$500) from Golden Software that will allow me to generate, via on-screen digitizing, an ascii file of X and Y values describing any curve I can import in many graphical file formats. The resulting ascii files can be imported into Excel, whose charting function will generate n-th order polynomial functions for you when you generate a trendline for the chart, and display the function if you remember to hit that check-box.
Alternatively, from my toolbox anyway, I can use DesignCAD (a relatively cheap CAD program) to give me areas from any polygon.
