[R] Linear Integration

[Michael Bedward]

Hi Alex,

I remember that you had the discussion recently about identifying grid
cells that were crossed by a line...

http://tolstoy.newcastle.edu.au/R/e11/help/10/09/8431.html

So, following on from those posts, for any cell crossed by a line you
will know the coordinates of the cell corners and the densified
vertices of the line (referring to David W's approach of using a
sequence of points along the line). You could then use the following
simple function to get the area of the polygon defined by those
coordinates...

function(x, y=NULL) {
# Calculate unsigned area of a simple (ie. no holes) polygon
#
# x, y vertex coordinates

  coords <- xy.coords(x, y)
  x <- coords$x
  y <- coords$y
  N <- length(x)

  if (!(x[1] == x[N] & y[1] == y[N])) {
    x <- c(x, x[1])
    y <- c(y, y[1])
    N <- N + 1
  }

  px <- sum(x[-N] * y[-1])
  py <- sum(y[-N] * x[-1])

  abs((px - py) / 2)
}

The position of your cells and lines in the real number plane will
determine which cell corners you include with the line vertices to
calculate an area appropriate for your integral.

Michael


On 6 October 2010 01:31, Alaios <alaios at yahoo.com> wrote:
> Hello
> I would like to calculate a weighted line integral.
> The integral is calculated by the cells that this lines trasverses (the small
> cells belong to  matrix (m*n) that represent the value that a specific area has.
>
> I need to calculate the weights by finding out how much the line touches or
> impinges inside a cell.
> The weight is less if a line just touches one of the four edges of a square and
> much more if it traverses inside the cell. I think there might be some function
> to calculate this in any image processing packages.
> So far I could not find anything appropriate.
> Could you please help me with that?
>
> I would like to thank you in advance for your help
> Best Regards
> Alex
>
>
>
>
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