[R] Interpolate? a line

[David Winsemius]

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