Messages from Usenet group comp.lang.idl-pvwave, compiled by Paulo Penteado
counting points falling inside a Voronoi cell
hey there, i'm looking for ideas on how to best solve this. I have 2 sets of x, y data that I will, non-creatively, call 'data1' and 'data2'. Using data1 I have built Voronoi cells/polygons to represent the x,y space. Now I need to discover how many points from data2 fall in each of the Voronoi cells built from data1. In other words, I need to be able to assign each of the data1's Voronoi cell to all points in data2 falling inside that cell. Firstly I was suggested to use INSIDE function, but that doesn't look good to me because it involves going through a double loop: for every x,y point in data2, test each of the voronoi polygons until I discover a match. That FOR+WHILE structure will be slow, specially given that data2 is much larger than the number of Voronoi polygons (I'm "FOR-looping" through the largest of the data arrays, besides I know IDL "hates" loops :)). I'm wondering how I can build an algorithm differently... if I think about the two datasets as if they were 2D images, I could FOR-loop through the Voronoi cells (the smallest dataset) and use them as a mask. It would be something like: 1) build a 2D image from data2 2) FOR loop: for each voronoi polygon, make a 2D image where the inside of the loop polygon equals to 1, everything else equals to 0 3) multiply the "voronoi mask" in step 2) by the image built in step 1) The non-zero results of the multiplication in step above are exactly the points in data2 that I'm looking for (in true, I only need the total number of points, so i don't even need to track back to the original x,y data2 values). 4) Write out the number of non-zero points, close the FOR loop. Done! (done in only 1 FOR loop, looping through the smallest dataset) Does that reasoning make sense? How can I efficiently build an image from a) a set of x,y points and b) a polygon? If I don't find a way to efficiently built the images, better to stick to the inefficient loop over the larger x,y array using INSIDE I guess... (or not?) thanks, Paula
Re: counting points falling inside a Voronoi cell
Hello, I expect the most efficient solution is dependent on some parameters of your problem, particularly the number of points in data1 and data2, how much overlap there is in the area covered by a polygon surrounding each of them, and how homogeneous/clustered the points are. Going for a third alternative - not the double loop or the masking method: Since your polygons are Voronoi cells, each point in data2 will be inside either 0 or 1 polygon in data1. Therefore, I see the point in doing a while loop, to stop searching for a polygon once one is one is found. But calling a function to test a single data point/polygon pair is so inherently inefficient, that I suspect this approach would be better: 1) Loop over data1's polygons, since there are much fewer polygons than points in data2. For each polygon, call a function that accepts an array of points to test, so that there is only one function call per polygon, testing for all of data2's points. Such as IDLanROI::ContainsPoints (www.exelisvis.com/docs/idlanroi__containspoints.html). 2) If data2 has many points, and the polygons in data1 cover a large fraction of the area covered by a polygon encircling data2's points, this can be significantly sped up if, after searching for data2's points on each data1 polygon, the matches are removed from data2, since we know a point in data2 cannot be in more than one Voronoi cell. Since data2 will be decreasing in size, the loop iterations will speedup as the code moves through the polygons. It would be something like data2_work=data2 matches=long64arr(N1) foreach roi,rois,iroi do begin print,'processing polygon ',iroi match=roi.containspoints(data2_work) w=where(match eq 1,count,complement=wc,ncomplement=nc) matches[iroi]=count if (nc gt 0) then data2_work=data2_work[*,wc] else break endforeach Where N1 is the number of polygons in data1, and I am guessing that data2 is a 2xN2 array, with x,y for each of the N2 points. And rois is an array of N1 IDLanROIs, created from the Voronoi cells you have found. If data2 still has too many points, so that the first loop iterations are taking too long (or, worse, memory fills up), this can be easily parallelized by splitting data2 into smaller chunks. The combined result is just a sum over the matches array produced on testing each chunk of data2. The code above is only looking for points falling inside each Voronoi polygon. You must also consider that a point can be on the edge or on a vertex of the polygon (in which case ContainsPoints returns 2 or 3), and decide what to do with those, since they do not clearly belong to just one polygon. The way I wrote it, edge and vertex points will not be counted on any polygons. Another possible approach is to count them only in the first polygon where they hit the edge/vertex, which would be done just changing the test to w=where(match ne 0,count,complement=wc,ncomplement=nc) Paulo On Friday, May 1, 2015 at 12:33:04 PM UTC-3, Paula wrote: > hey there, > i'm looking for ideas on how to best solve this. > > I have 2 sets of x, y data that I will, non-creatively, call 'data1' and 'data2'. Using data1 I have built Voronoi cells/polygons to represent the x,y space. Now I need to discover how many points from data2 fall in each of the Voronoi cells built from data1. In other words, I need to be able to assign each of the data1's Voronoi cell to all points in data2 falling inside that cell. > > Firstly I was suggested to use INSIDE function, but that doesn't look good to me because it involves going through a double loop: for every x,y point in data2, test each of the voronoi polygons until I discover a match. That FOR+WHILE structure will be slow, specially given that data2 is much larger than the number of Voronoi polygons (I'm "FOR-looping" through the largest of the data arrays, besides I know IDL "hates" loops :)). > > I'm wondering how I can build an algorithm differently... if I think about the two datasets as if they were 2D images, I could FOR-loop through the Voronoi cells (the smallest dataset) and use them as a mask. It would be something like: > > 1) build a 2D image from data2 > 2) FOR loop: for each voronoi polygon, make a 2D image where the inside of the loop polygon equals to 1, everything else equals to 0 > 3) multiply the "voronoi mask" in step 2) by the image built in step 1) > The non-zero results of the multiplication in step above are exactly the points in data2 that I'm looking for (in true, I only need the total number of points, so i don't even need to track back to the original x,y data2 values). > 4) Write out the number of non-zero points, close the FOR loop. > Done! (done in only 1 FOR loop, looping through the smallest dataset) > > Does that reasoning make sense? > How can I efficiently build an image from a) a set of x,y points and b) a polygon? > If I don't find a way to efficiently built the images, better to stick to the inefficient loop over the larger x,y array using INSIDE I guess... (or not?) > > thanks, > Paula
On Sunday, May 3, 2015 at 4:49:37 PM UTC-4, Paulo Penteado wrote: > Hello, > > I expect the most efficient solution is dependent on some parameters of your problem, particularly the number of points in data1 and data2, how much overlap there is in the area covered by a polygon surrounding each of them, and how homogeneous/clustered the points are. > > Going for a third alternative - not the double loop or the masking method: > > Since your polygons are Voronoi cells, each point in data2 will be inside either 0 or 1 polygon in data1. Therefore, I see the point in doing a while loop, to stop searching for a polygon once one is one is found. But calling a function to test a single data point/polygon pair is so inherently inefficient, that I suspect this approach would be better: > > 1) Loop over data1's polygons, since there are much fewer polygons than points in data2. For each polygon, call a function that accepts an array of points to test, so that there is only one function call per polygon, testing for all of data2's points. Such as IDLanROI::ContainsPoints (www.exelisvis.com/docs/idlanroi__containspoints.html). > > 2) If data2 has many points, and the polygons in data1 cover a large fraction of the area covered by a polygon encircling data2's points, this can be significantly sped up if, after searching for data2's points on each data1 polygon, the matches are removed from data2, since we know a point in data2 cannot be in more than one Voronoi cell. Since data2 will be decreasing in size, the loop iterations will speedup as the code moves through the polygons. > > It would be something like > > data2_work=data2 > matches=long64arr(N1) > foreach roi,rois,iroi do begin > print,'processing polygon ',iroi > match=roi.containspoints(data2_work) > w=where(match eq 1,count,complement=wc,ncomplement=nc) > matches[iroi]=count > if (nc gt 0) then data2_work=data2_work[*,wc] else break > endforeach > > Where N1 is the number of polygons in data1, and I am guessing that data2 is a 2xN2 array, with x,y for each of the N2 points. And rois is an array of N1 IDLanROIs, created from the Voronoi cells you have found. > > If data2 still has too many points, so that the first loop iterations are taking too long (or, worse, memory fills up), this can be easily parallelized by splitting data2 into smaller chunks. The combined result is just a sum over the matches array produced on testing each chunk of data2. > > The code above is only looking for points falling inside each Voronoi polygon. You must also consider that a point can be on the edge or on a vertex of the polygon (in which case ContainsPoints returns 2 or 3), and decide what to do with those, since they do not clearly belong to just one polygon. The way I wrote it, edge and vertex points will not be counted on any polygons. Another possible approach is to count them only in the first polygon where they hit the edge/vertex, which would be done just changing the test to > > w=where(match ne 0,count,complement=wc,ncomplement=nc) > > Paulo > > On Friday, May 1, 2015 at 12:33:04 PM UTC-3, Paula wrote: >> hey there, >> i'm looking for ideas on how to best solve this. >> >> I have 2 sets of x, y data that I will, non-creatively, call 'data1' and 'data2'. Using data1 I have built Voronoi cells/polygons to represent the x,y space. Now I need to discover how many points from data2 fall in each of the Voronoi cells built from data1. In other words, I need to be able to assign each of the data1's Voronoi cell to all points in data2 falling inside that cell. >> >> Firstly I was suggested to use INSIDE function, but that doesn't look good to me because it involves going through a double loop: for every x,y point in data2, test each of the voronoi polygons until I discover a match. That FOR+WHILE structure will be slow, specially given that data2 is much larger than the number of Voronoi polygons (I'm "FOR-looping" through the largest of the data arrays, besides I know IDL "hates" loops :)). >> >> I'm wondering how I can build an algorithm differently... if I think about the two datasets as if they were 2D images, I could FOR-loop through the Voronoi cells (the smallest dataset) and use them as a mask. It would be something like: >> >> 1) build a 2D image from data2 >> 2) FOR loop: for each voronoi polygon, make a 2D image where the inside of the loop polygon equals to 1, everything else equals to 0 >> 3) multiply the "voronoi mask" in step 2) by the image built in step 1) >> The non-zero results of the multiplication in step above are exactly the points in data2 that I'm looking for (in true, I only need the total number of points, so i don't even need to track back to the original x,y data2 values). >> 4) Write out the number of non-zero points, close the FOR loop. >> Done! (done in only 1 FOR loop, looping through the smallest dataset) >> >> Does that reasoning make sense? >> How can I efficiently build an image from a) a set of x,y points and b) a polygon? >> If I don't find a way to efficiently built the images, better to stick to the inefficient loop over the larger x,y array using INSIDE I guess... (or not?) >> >> thanks, >> Paula Paolo's solution is definitely going to be the easiest to code, but if memory isn't outrageous then I think you can modify INSIDE to do this with no loops at all. It will require being able to create several N2 x NV x NP arrays, where N2=N_ELEMENTS(data2), NV is the number of Voronoi cells, and NP is the maximum number of polygon vertices in a Voronoi cell. Essentially, you add a new dimension of length NV to the existing X1, Y1, X2, Y2 arrays, and then your RET array at the end has a N2 x NV boolean array of which points are in each polygon, which you can just sum up to get what you want. Or, if you're really clever with your histogram magic, you might be able to pull it off making the arrays N2 x NVP instead, where NVP is the total number of polygon vertices for all cells (as long as you still have the connectivity information stored somewhere). But it's probably not worth the pain. -Jeremy.
On Monday, May 4, 2015 at 11:57:42 AM UTC-4, Jeremy Bailin wrote: > On Sunday, May 3, 2015 at 4:49:37 PM UTC-4, Paulo Penteado wrote: >> Hello, >> >> I expect the most efficient solution is dependent on some parameters of your problem, particularly the number of points in data1 and data2, how much overlap there is in the area covered by a polygon surrounding each of them, and how homogeneous/clustered the points are. >> >> Going for a third alternative - not the double loop or the masking method: >> >> Since your polygons are Voronoi cells, each point in data2 will be inside either 0 or 1 polygon in data1. Therefore, I see the point in doing a while loop, to stop searching for a polygon once one is one is found. But calling a function to test a single data point/polygon pair is so inherently inefficient, that I suspect this approach would be better: >> >> 1) Loop over data1's polygons, since there are much fewer polygons than points in data2. For each polygon, call a function that accepts an array of points to test, so that there is only one function call per polygon, testing for all of data2's points. Such as IDLanROI::ContainsPoints (www.exelisvis.com/docs/idlanroi__containspoints.html). >> >> 2) If data2 has many points, and the polygons in data1 cover a large fraction of the area covered by a polygon encircling data2's points, this can be significantly sped up if, after searching for data2's points on each data1 polygon, the matches are removed from data2, since we know a point in data2 cannot be in more than one Voronoi cell. Since data2 will be decreasing in size, the loop iterations will speedup as the code moves through the polygons. >> >> It would be something like >> >> data2_work=data2 >> matches=long64arr(N1) >> foreach roi,rois,iroi do begin >> print,'processing polygon ',iroi >> match=roi.containspoints(data2_work) >> w=where(match eq 1,count,complement=wc,ncomplement=nc) >> matches[iroi]=count >> if (nc gt 0) then data2_work=data2_work[*,wc] else break >> endforeach >> >> Where N1 is the number of polygons in data1, and I am guessing that data2 is a 2xN2 array, with x,y for each of the N2 points. And rois is an array of N1 IDLanROIs, created from the Voronoi cells you have found. >> >> If data2 still has too many points, so that the first loop iterations are taking too long (or, worse, memory fills up), this can be easily parallelized by splitting data2 into smaller chunks. The combined result is just a sum over the matches array produced on testing each chunk of data2. >> >> The code above is only looking for points falling inside each Voronoi polygon. You must also consider that a point can be on the edge or on a vertex of the polygon (in which case ContainsPoints returns 2 or 3), and decide what to do with those, since they do not clearly belong to just one polygon. The way I wrote it, edge and vertex points will not be counted on any polygons. Another possible approach is to count them only in the first polygon where they hit the edge/vertex, which would be done just changing the test to >> >> w=where(match ne 0,count,complement=wc,ncomplement=nc) >> >> Paulo >> >> On Friday, May 1, 2015 at 12:33:04 PM UTC-3, Paula wrote: >>> hey there, >>> i'm looking for ideas on how to best solve this. >>> >>> I have 2 sets of x, y data that I will, non-creatively, call 'data1' and 'data2'. Using data1 I have built Voronoi cells/polygons to represent the x,y space. Now I need to discover how many points from data2 fall in each of the Voronoi cells built from data1. In other words, I need to be able to assign each of the data1's Voronoi cell to all points in data2 falling inside that cell. >>> >>> Firstly I was suggested to use INSIDE function, but that doesn't look good to me because it involves going through a double loop: for every x,y point in data2, test each of the voronoi polygons until I discover a match. That FOR+WHILE structure will be slow, specially given that data2 is much larger than the number of Voronoi polygons (I'm "FOR-looping" through the largest of the data arrays, besides I know IDL "hates" loops :)). >>> >>> I'm wondering how I can build an algorithm differently... if I think about the two datasets as if they were 2D images, I could FOR-loop through the Voronoi cells (the smallest dataset) and use them as a mask. It would be something like: >>> >>> 1) build a 2D image from data2 >>> 2) FOR loop: for each voronoi polygon, make a 2D image where the inside of the loop polygon equals to 1, everything else equals to 0 >>> 3) multiply the "voronoi mask" in step 2) by the image built in step 1) >>> The non-zero results of the multiplication in step above are exactly the points in data2 that I'm looking for (in true, I only need the total number of points, so i don't even need to track back to the original x,y data2 values). >>> 4) Write out the number of non-zero points, close the FOR loop. >>> Done! (done in only 1 FOR loop, looping through the smallest dataset) >>> >>> Does that reasoning make sense? >>> How can I efficiently build an image from a) a set of x,y points and b) a polygon? >>> If I don't find a way to efficiently built the images, better to stick to the inefficient loop over the larger x,y array using INSIDE I guess... (or not?) >>> >>> thanks, >>> Paula > > Paolo's solution is definitely going to be the easiest to code, but if memory isn't outrageous then I think you can modify INSIDE to do this with no loops at all. It will require being able to create several N2 x NV x NP arrays, where N2=N_ELEMENTS(data2), NV is the number of Voronoi cells, and NP is the maximum number of polygon vertices in a Voronoi cell. Essentially, you add a new dimension of length NV to the existing X1, Y1, X2, Y2 arrays, and then your RET array at the end has a N2 x NV boolean array of which points are in each polygon, which you can just sum up to get what you want. > > Or, if you're really clever with your histogram magic, you might be able to pull it off making the arrays N2 x NVP instead, where NVP is the total number of polygon vertices for all cells (as long as you still have the connectivity information stored somewhere). But it's probably not worth the pain. > > -Jeremy. Here is code based heavily on INSIDE that does it without loops: seed = 2L npts = 10 ; polygons are a grid of squares, for convenience ; they must be closed, so add the extra vertex on the end if they aren't polygons = [ $ [ [0,0], [0,1], [1,1], [1,0], [0,0] ], $ ; square 1 [ [1,0], [1,1], [2,1], [2,0], [1,0] ], $ ; square 2 [ [0,1], [0,2], [1,2], [1,1], [0,1] ], $ ; square 3 [ [1,1], [1,2], [2,2], [2,1], [1,1] ] ] ; square 4 polysize = size(polygons, /dimen) npoly = polysize[2] nvert_per_poly = polysize[1] ; make some random data datapts = 2*randomu(seed, [2,npts]) ; plot it up so we can see the expected result. For this seed, there should be ; 5 points in the first polygon, then 1, then 3, then 1 cgplot, psym=4, datapts[0,*], datapts[1,*], xrange=[-0.5, 2.5], yrange=[-0.5, 2.5] for i=0,npoly-1 do begin for j=0l,nvert_per_poly-2 do cgplot, /over, [polygons[0,j,i], polygons[0,j+1,i]], $ [polygons[1,j,i], polygons[1,j+1,i]] endfor ; do the same calculation as in INSIDE.PRO but add in a middle dimension that runs through ; each polygon x1 = rebin(reform(polygons[0,0:nvert_per_poly-2,*], [nvert_per_poly-1,npoly]), [nvert_per_poly-1,npoly,npts], /sample) - $ rebin(reform(datapts[0,*], [1,1,npts]), [nvert_per_poly-1,npoly,npts], /sample) y1 = rebin(reform(polygons[1,0:nvert_per_poly-2,*], [nvert_per_poly-1,npoly]), [nvert_per_poly-1,npoly,npts], /sample) - $ rebin(reform(datapts[1,*], [1,1,npts]), [nvert_per_poly-1,npoly,npts], /sample) x2 = rebin(reform(polygons[0,1:nvert_per_poly-1,*], [nvert_per_poly-1,npoly]), [nvert_per_poly-1,npoly,npts], /sample) - $ rebin(reform(datapts[0,*], [1,1,npts]), [nvert_per_poly-1,npoly,npts], /sample) y2 = rebin(reform(polygons[1,1:nvert_per_poly-1,*], [nvert_per_poly-1,npoly]), [nvert_per_poly-1,npoly,npts], /sample) - $ rebin(reform(datapts[1,*], [1,1,npts]), [nvert_per_poly-1,npoly,npts], /sample) dp = x2*x1 + y1*y2 ; dot product cp = x1*y2 - y1*x2 ; cross product theta = atan(cp, dp) ; boolean n_poly x npts array of wheather a given point is inside a given polygon insidep = abs(total(theta,1)) gt 0.01 ; add up how many are in each polygon n_inside_each_polygon = total(insidep, 2, /int) print, n_inside_each_polygon end
On Monday, May 4, 2015 at 2:22:11 PM UTC-4, Jeremy Bailin wrote: > On Monday, May 4, 2015 at 11:57:42 AM UTC-4, Jeremy Bailin wrote: >> On Sunday, May 3, 2015 at 4:49:37 PM UTC-4, Paulo Penteado wrote: >>> Hello, >>> >>> I expect the most efficient solution is dependent on some parameters of your problem, particularly the number of points in data1 and data2, how much overlap there is in the area covered by a polygon surrounding each of them, and how homogeneous/clustered the points are. >>> >>> Going for a third alternative - not the double loop or the masking method: >>> >>> Since your polygons are Voronoi cells, each point in data2 will be inside either 0 or 1 polygon in data1. Therefore, I see the point in doing a while loop, to stop searching for a polygon once one is one is found. But calling a function to test a single data point/polygon pair is so inherently inefficient, that I suspect this approach would be better: >>> >>> 1) Loop over data1's polygons, since there are much fewer polygons than points in data2. For each polygon, call a function that accepts an array of points to test, so that there is only one function call per polygon, testing for all of data2's points. Such as IDLanROI::ContainsPoints (www.exelisvis.com/docs/idlanroi__containspoints.html). >>> >>> 2) If data2 has many points, and the polygons in data1 cover a large fraction of the area covered by a polygon encircling data2's points, this can be significantly sped up if, after searching for data2's points on each data1 polygon, the matches are removed from data2, since we know a point in data2 cannot be in more than one Voronoi cell. Since data2 will be decreasing in size, the loop iterations will speedup as the code moves through the polygons. >>> >>> It would be something like >>> >>> data2_work=data2 >>> matches=long64arr(N1) >>> foreach roi,rois,iroi do begin >>> print,'processing polygon ',iroi >>> match=roi.containspoints(data2_work) >>> w=where(match eq 1,count,complement=wc,ncomplement=nc) >>> matches[iroi]=count >>> if (nc gt 0) then data2_work=data2_work[*,wc] else break >>> endforeach >>> >>> Where N1 is the number of polygons in data1, and I am guessing that data2 is a 2xN2 array, with x,y for each of the N2 points. And rois is an array of N1 IDLanROIs, created from the Voronoi cells you have found. >>> >>> If data2 still has too many points, so that the first loop iterations are taking too long (or, worse, memory fills up), this can be easily parallelized by splitting data2 into smaller chunks. The combined result is just a sum over the matches array produced on testing each chunk of data2. >>> >>> The code above is only looking for points falling inside each Voronoi polygon. You must also consider that a point can be on the edge or on a vertex of the polygon (in which case ContainsPoints returns 2 or 3), and decide what to do with those, since they do not clearly belong to just one polygon. The way I wrote it, edge and vertex points will not be counted on any polygons. Another possible approach is to count them only in the first polygon where they hit the edge/vertex, which would be done just changing the test to >>> >>> w=where(match ne 0,count,complement=wc,ncomplement=nc) >>> >>> Paulo >>> >>> On Friday, May 1, 2015 at 12:33:04 PM UTC-3, Paula wrote: >>>> hey there, >>>> i'm looking for ideas on how to best solve this. >>>> >>>> I have 2 sets of x, y data that I will, non-creatively, call 'data1' and 'data2'. Using data1 I have built Voronoi cells/polygons to represent the x,y space. Now I need to discover how many points from data2 fall in each of the Voronoi cells built from data1. In other words, I need to be able to assign each of the data1's Voronoi cell to all points in data2 falling inside that cell. >>>> >>>> Firstly I was suggested to use INSIDE function, but that doesn't look good to me because it involves going through a double loop: for every x,y point in data2, test each of the voronoi polygons until I discover a match. That FOR+WHILE structure will be slow, specially given that data2 is much larger than the number of Voronoi polygons (I'm "FOR-looping" through the largest of the data arrays, besides I know IDL "hates" loops :)). >>>> >>>> I'm wondering how I can build an algorithm differently... if I think about the two datasets as if they were 2D images, I could FOR-loop through the Voronoi cells (the smallest dataset) and use them as a mask. It would be something like: >>>> >>>> 1) build a 2D image from data2 >>>> 2) FOR loop: for each voronoi polygon, make a 2D image where the inside of the loop polygon equals to 1, everything else equals to 0 >>>> 3) multiply the "voronoi mask" in step 2) by the image built in step 1) >>>> The non-zero results of the multiplication in step above are exactly the points in data2 that I'm looking for (in true, I only need the total number of points, so i don't even need to track back to the original x,y data2 values). >>>> 4) Write out the number of non-zero points, close the FOR loop. >>>> Done! (done in only 1 FOR loop, looping through the smallest dataset) >>>> >>>> Does that reasoning make sense? >>>> How can I efficiently build an image from a) a set of x,y points and b) a polygon? >>>> If I don't find a way to efficiently built the images, better to stick to the inefficient loop over the larger x,y array using INSIDE I guess... (or not?) >>>> >>>> thanks, >>>> Paula >> >> Paolo's solution is definitely going to be the easiest to code, but if memory isn't outrageous then I think you can modify INSIDE to do this with no loops at all. It will require being able to create several N2 x NV x NP arrays, where N2=N_ELEMENTS(data2), NV is the number of Voronoi cells, and NP is the maximum number of polygon vertices in a Voronoi cell. Essentially, you add a new dimension of length NV to the existing X1, Y1, X2, Y2 arrays, and then your RET array at the end has a N2 x NV boolean array of which points are in each polygon, which you can just sum up to get what you want. >> >> Or, if you're really clever with your histogram magic, you might be able to pull it off making the arrays N2 x NVP instead, where NVP is the total number of polygon vertices for all cells (as long as you still have the connectivity information stored somewhere). But it's probably not worth the pain. >> >> -Jeremy. > > Here is code based heavily on INSIDE that does it without loops: > > seed = 2L > npts = 10 > ; polygons are a grid of squares, for convenience > ; they must be closed, so add the extra vertex on the end if they aren't > polygons = [ $ > [ [0,0], [0,1], [1,1], [1,0], [0,0] ], $ ; square 1 > [ [1,0], [1,1], [2,1], [2,0], [1,0] ], $ ; square 2 > [ [0,1], [0,2], [1,2], [1,1], [0,1] ], $ ; square 3 > [ [1,1], [1,2], [2,2], [2,1], [1,1] ] ] ; square 4 > polysize = size(polygons, /dimen) > npoly = polysize[2] > nvert_per_poly = polysize[1] > > ; make some random data > datapts = 2*randomu(seed, [2,npts]) > > ; plot it up so we can see the expected result. For this seed, there should be > ; 5 points in the first polygon, then 1, then 3, then 1 > cgplot, psym=4, datapts[0,*], datapts[1,*], xrange=[-0.5, 2.5], yrange=[-0.5, 2.5] > for i=0,npoly-1 do begin > for j=0l,nvert_per_poly-2 do cgplot, /over, [polygons[0,j,i], polygons[0,j+1,i]], $ > [polygons[1,j,i], polygons[1,j+1,i]] > endfor > > ; do the same calculation as in INSIDE.PRO but add in a middle dimension that runs through > ; each polygon > x1 = rebin(reform(polygons[0,0:nvert_per_poly-2,*], [nvert_per_poly-1,npoly]), [nvert_per_poly-1,npoly,npts], /sample) - $ > rebin(reform(datapts[0,*], [1,1,npts]), [nvert_per_poly-1,npoly,npts], /sample) > y1 = rebin(reform(polygons[1,0:nvert_per_poly-2,*], [nvert_per_poly-1,npoly]), [nvert_per_poly-1,npoly,npts], /sample) - $ > rebin(reform(datapts[1,*], [1,1,npts]), [nvert_per_poly-1,npoly,npts], /sample) > x2 = rebin(reform(polygons[0,1:nvert_per_poly-1,*], [nvert_per_poly-1,npoly]), [nvert_per_poly-1,npoly,npts], /sample) - $ > rebin(reform(datapts[0,*], [1,1,npts]), [nvert_per_poly-1,npoly,npts], /sample) > y2 = rebin(reform(polygons[1,1:nvert_per_poly-1,*], [nvert_per_poly-1,npoly]), [nvert_per_poly-1,npoly,npts], /sample) - $ > rebin(reform(datapts[1,*], [1,1,npts]), [nvert_per_poly-1,npoly,npts], /sample) > > dp = x2*x1 + y1*y2 ; dot product > cp = x1*y2 - y1*x2 ; cross product > theta = atan(cp, dp) > > ; boolean n_poly x npts array of wheather a given point is inside a given polygon > insidep = abs(total(theta,1)) gt 0.01 > > ; add up how many are in each polygon > n_inside_each_polygon = total(insidep, 2, /int) > > print, n_inside_each_polygon > end Also note that, as Paulo says, in this method you can also break up your data2 into big chunks, work on them independently, and just add up the results at the end if you have memory problems. -Jeremy.