Nice posts David. I like the way that 'simple' problems such as this one give rise to an interesting assortment of approaches and gotchas :)
Michael On 15 September 2010 22:41, David Winsemius <dwinsem...@comcast.net> wrote: > > On Sep 15, 2010, at 7:55 AM, David Winsemius wrote: > >> >> On Sep 15, 2010, at 7:24 AM, David Winsemius wrote: >> >>> Replacing context: >>> >>>>> Hello everyone. >>>>> I have created a 100*100 matrix in R. >>>>> Let's now say that I have a line that starts from (2,3) point and ends >>>>> to the >>>>> (62,34) point. In other words this line starts at cell (2,3) and ends >>>>> at cell >>>>> (62,34). >>>>> >>>>> Is it possible to get by some R function all the matrix's cells that >>>>> this line >>>>> transverses? >>>>> >>>>> I would like to thank you for your feedback. >>>>> >>>>> Best Regards >>>>> Alex >>> >>> On Sep 15, 2010, at 6:52 AM, Michael Bedward wrote: >>> >>>> Hello Alex, >>>> >>>> Here is one way to do it. It works but it's not pretty :) >>> >>> If you want an alternative, consider that produces the Y cell indices >>> (since the x cell indices are already 2:62): >>> >>> > linefn <- function(x) 3+((34-3)/(62-2)) *(x-2) >>> > findInterval(linefn(2:62), 3:34) >>> [1] 1 1 2 2 3 3 4 4 5 5 6 6 7 7 8 8 9 9 10 10 11 11 12 >>> 12 13 13 14 >>> [28] 14 15 15 16 17 17 18 18 19 19 20 20 21 21 22 22 23 23 24 24 25 25 26 >>> 26 27 27 28 >>> [55] 28 29 29 30 30 31 32 >>> # that seems "off" by two >>> > linefn(62) >>> [1] 34 >>> > linefn(2) >>> [1] 3 # but that checks out and I realized those were just indices for >>> the 3:34 findInterval vector >>> >>> > (3:34)[findInterval(linefn(2:62), 3:34)] >>> [1] 3 3 4 4 5 5 6 6 7 7 8 8 9 9 10 10 11 11 12 12 13 13 14 >>> 14 15 15 16 >>> [28] 16 17 17 18 19 19 20 20 21 21 22 22 23 23 24 24 25 25 26 26 27 27 28 >>> 28 29 29 30 >>> [55] 30 31 31 32 32 33 34 >>> >>> ( no rounding and I think the logic is clearer.) >> >> But I also realized it didn't enumerate all the the cells were crossed >> either, only indicating which cell was associated with an integer value of >> x. Also would have even more serious problems if the slope were greater than >> unity. To enumerate the cell indices that were crossed, try: >> >> unique( floor( cbind( seq(2,62, by=0.1), linefn(seq(2,62, by=0.1)) ) ) ) >> [,1] [,2] >> [1,] 2 3 >> [2,] 3 3 >> [3,] 4 4 >> [4,] 5 4 >> [5,] 5 5 >> [6,] 6 5 >> [7,] 7 5 >> [8,] 7 6 >> snipping interior results >> [83,] 58 32 >> [84,] 59 32 >> [85,] 60 32 >> [86,] 60 33 >> [87,] 61 33 >> [88,] 62 34 >> >> That could probably be passed to rect() to illustrate (and check logic): >> >> rect(cellidxs[,1], cellidxs[,2], cellidxs[,1]+1, cellidxs[,2]+1, >> col="red") >> >> #redraw line : >> lines(2:62, 3+(34-3)/(62-2)*(0:60)) > > And then I got to wondering if every 0.1 was sufficient to catch all the > corners and discovered I could identify 3 more cell traversals with by=0.01 > >> cellid2 <-unique( floor(cbind(seq(2,62, by=0.01), linefn(seq(2,62, >> by=0.01) )) ) ) >> NROW(cellid2) # 91 cells >> rect(cellid2[,1], cellid2[,2], cellid2[,1]+1, cellid2[,2]+1, col="blue") >> rect(cellidxs[,1], cellidxs[,2], cellidxs[,1]+1, cellidxs[,2]+1, >> col="red") >> lines(2:62, 3+(34-3)/(62-2)*(0:60)) > > (Trying by=0.001 did not change the count, but did take longer) > > -- > David. > >>> - >>> David. >>> >>>> >>>> interp <- approx(c(2, 62), c(3, 34), method="linear", xout=2:62) >>>> m <- matrix(c(interp$x, round(interp$y)), ncol=2) >>>> tie <- m[,2] == c(-Inf, m[-nrow(m),2]) >>>> m <- m[ !tie, ] >>>> >>>> You might want to examine the result like this... >>>> >>>> plot(m) # plots points >>>> lines(c(2,26), c(3, 34)) # overlay line for comparison >>> >>> you can add a grid with >>> abline(v=2:62, h=3:34) >>>> >>>> Michael >> > > > David Winsemius, MD > West Hartford, CT > > ______________________________________________ > R-help@r-project.org mailing list > https://stat.ethz.ch/mailman/listinfo/r-help > PLEASE do read the posting guide http://www.R-project.org/posting-guide.html > and provide commented, minimal, self-contained, reproducible code. > ______________________________________________ R-help@r-project.org mailing list https://stat.ethz.ch/mailman/listinfo/r-help PLEASE do read the posting guide http://www.R-project.org/posting-guide.html and provide commented, minimal, self-contained, reproducible code.
