[R] Interpolate? a line

[Michael Bedward]

I think that's because of your definition for "touches".

If I read it correctly, David's code assumes that a "cell" is a square
1 unit wide and then followed the normal geometric definition of
"touches", ie. the line intersects with at least one point on the
cell's boundary.

You seem to have a different definition: cell centers perhaps ? or
cell lower-left corner points ?  Whether or not any particular
definition is valid depends on your requirements.  In other words -
it's all up to you :)

Michael


On 17 September 2010 21:22, Alaios <alaios at yahoo.com> wrote:
> I would like to thank you again for your help.
> But it seems that the floor function (ceiling, round too) create more dots in
> the matrix that line really "touches".
>
> unique( floor( cbind( seq(2,62, by=0.1), linefn(seq(2,62, by=0.1)) ) )  )
>
> You can see that in the picture below
>
> http://yfrog.com/5blineswj
>
> So, how to select the only the cells that the line "touches"?
>
> I would like to thank you in advance for your help
> best Regards
> Alex
>
>
>
>
> ________________________________
> From: David Winsemius <dwinsemius at comcast.net>
>
> Cc: Rhelp list <r-help at r-project.org>
> Sent: Wed, September 15, 2010 1:55:10 PM
> Subject: Re: [R] Interpolate? a line
>
>
> 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))
>
>
>>
>> --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
>>>
>>> ______________________________________________
>>> R-help at 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.
>>
>> David Winsemius, MD
>> West Hartford, CT
>>
>> ______________________________________________
>> R-help at 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.
>
> David Winsemius, MD
> West Hartford, CT
>
>
>
>        [[alternative HTML version deleted]]
>
> ______________________________________________
> R-help at 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.
>