How to shrink polygon on two sides?

Question

I have a polygon which I know is a rectangle, although it may be at any orientation:

I want to shrink this polygon by a third of the width from two sides, so that I just get the strip in the middle - ending up with a result like the red area in this image:

I can't think how to go about doing this easily. If I try and negatively buffer the polygon then it will be shrunk on all sides. I have many tens of thousands of these polygons to do - so obviously can't do them manually.

Any ideas? I have access to ArcGIS, QGIS and am relatively experienced at Python programming - if that helps.

Answer 1

Here's some R code that does the job, the caveat being we are in cartesian coordinates. The input matrix coords is a 5x2 matrix of x,y columns, with the last point being coincident with the first point. This is what you get out of spatial objects in R when you read a shapefile, for example.

thinrect <- function(coords, factor=1/3){
    dx = diff(coords[,1])
    dy = diff(coords[,2])
    ## test if slope(1-2) is > slope(2-3)
    w = diff(atan2(abs(dx[1:2]), abs(dy[1:2])) %% pi) > 0
    ## if it is, then wrap it round so the first side is the steepest
    if(w){
        coords = rbind(coords[-1,], coords[1,])
        dx = c(dx[-1],dx[1])
        dy = c(dy[-1],dy[1])
    }
    ## now its just four points offset from corners 1 and 3
    dxy = c(dx[1],dy[1])
    p1 = coords[1,] + factor*dxy
    p2 = coords[1,] + (0.5+factor/2)*dxy
    p3 = coords[3,] - (factor)*dxy
    p4 = coords[3,] - (0.5+factor/2)*dxy

    rbind(p1, p2, p3, p4, p1)
}

Here's the output on a rectangle under various rotations. Note how the selected rectangle changes to stay parallel to the steepest side.

Simple usage, creating a 5x2 matrix of a unit square:

> coords=matrix(c(0,0,0,1,1,1,1,0,0,0),ncol=2,byrow=TRUE)
> coords
     [,1] [,2]
[1,]    0    0
[2,]    0    1
[3,]    1    1
[4,]    1    0
[5,]    0    0
> thinrect(coords)
        [,1] [,2]
p1 0.3333333    1
p2 0.6666667    1
p3 0.6666667    0
p4 0.3333333    0
p1 0.3333333    1
> plot(coords)
> polygon(thinrect(coords))

Looping this over a shapefile is pretty trivial.

The algorithm could be ported to Python pretty simply too.

Answer 2

This can be solved with a model but there are 4 caveats:

• You need an Advance (ArcInfo) license
• This model assumes your rectangle is a rectangle so the 2 vertical sides are longer
• Your rectangle is constructed from 4 vertices only
• If you want to automate this then all your rectangles must have the same dimensions

So after running this model you you are left with the remaining centre rectangle as shown in this image:

You would need to wrap this up with an iterator and adjust the various parameters as you require.

Answer 3

I created an ArcGIS Create Custom Grid tool that could be useful for this. However, it might have trouble if any of the rectangles are oriented like a diamond shape.

You would set the vertical division to 3 and leave the horizontal to 0.

After the tool is ran you need to use the Split Polygons tool in the Advanced Editing toolbar.

If you use it, let me know if you have any problems.

You can download the toolbox at the top of the page here:

http://ianbroad.com/creating-quarter-quarter-section-grid-python/