| Re: Compute area between curves [message #62908 is a reply to message #62821] |
Mon, 13 October 2008 06:24   |
jameskuyper
Messages: 79
Registered: October 2007
|
Member |
|
|
frankosuna wrote:
> On Oct 12, 3:17 pm, James Kuyper <jameskuy...@verizon.net> wrote:
>> frankosuna wrote:
>>> Dear IDLers,
>>> How can I compute the area between two curves given two functions?
>> Are the curves closed? That is, do you create the complete curve by
>> drawing a line from the final <x,y> pair to the first <x,y> pair?
>>
>> Are the x values the same for the two curves? Are they evenly spaced?
>>
>> Note: you don't need to post the same question multiple times, this is a
>> newsgroup, not a chat room. Your message will stay up indefinitely. As a
>> general rule, you might have to wait 24 hours or more before getting an
>> answer.
>
> The curves are not closed... I posted some images of the actual rings
> I am trying
> to compare. They look like parabolas.
Given the geometry involved, I think it's more likely that they are
sections of an ellipse, not parabolas.
The rings might differ in shift
> and slight rotation from each other. So because the rings might be
> shifted, they probably have different x-values. Also the x-values are
> continuous..meaning that once the ring starts.. there is an (x,y)
> value until the end of the ring. When I was extracting the (x,y)
> location of every pixel that makes up the rings I noticed that a lot
> of x values had multiple y's. To fix this I used the MIN x value for
> that group in order to be able to compute the area. I'm not sure if
> that's bad or good.
I'm not sure I follow that. You describe those groups as having the same
x value, so MIN(x) doesn't make sense. If you meant MIN(y), that would
make more sense, but taking the average makes more sense than using the
minimum.
> I am using INT_TABULATED and TSUM currently and get very close values
> for the most part. I compute the area under the curve for both rings
> and then subtract but I'm not sure if that is correct either.
That approach should produce reasonable results, if you use the average
y value rather than the minimum y value. However, this approach a
assumes that for any given value of x, a vertical line at x intersects
each curve only once. Since I suspect that these are actually sections
of an ellipse, it's entirely possible that some images will violate that
condition. If you had an image of the entire ellipse, any given x value
would cross 0, 1, or 2 times, depending upon the value of x. If you have
such an image, the simplest approach would be to break the images into
two sections, breaking them at the point where the tangent to the curve
is vertical. Calculate the area between the curves separately for each part.
A more general approach would would work regardless of the shapes of the
two curves. Just connect the two curves to create a single combined
curve that starts by listing all the points on one curve in clockwise
order, then continues by listing all of the points of the other curve in
counter-clockwise order. As a result, the combined curve encloses the
area that lies between the two curves. Then use POLY_AREA to calculates
the area enclosed by the combined curve. If you've got lots of data
points and a very thin area between the two curves, you'll almost
certainly need to do the calculations in double precision in order to
get useful results; otherwise the algorithm used will be dominated by
round-off errors. Note that you should connect the two curves in such a
way that the combined curve goes around the area between them in a
counter-clockwise direction. If you do it in the wrong order, you'll get
the negative of the correct area.
If you are taking this approach, there's no need to remove cases where
you have multiple y values for the same value of x. You'll get more
accurate results by keeping all of those points, rather than by
replacing them with the average value of y.
|
|
|
|
comp.lang.idl-pvwave archive
Members
Search
Help
Login
Home
