Calculating the percent overlap of two polygons in JavaScript

Question

Here's the problem: I have geoJSON and topoJSON files that give me the polygons for Census block groups and voting precincts. I'm trying to see by how much a given Census block group overlaps with a given precinct.

I've seen a couple examples of what I'm after in other languages—i.e. R and in some GIS tools—but I'm trying to write this as a Node.js script. A few questions:

1. Is there an NPM module (I've done a fair amount of Googling, but I haven't found one) that can spit out the percent overlap?
2. Is there an algorithm, or an exmaple written in another language, that I should know about (I've looked, but I haven't the foggiest where to begin) and that I could port to JavaScript?
3. Failing these, can someone explain to me how I would go about thinking about creating an algorithm for this?

In the end, the final product would look something like this—imagining that I have arrays of precincts and blockgroups, and each one is an object with a geometry property that contains the polygon data for the precinct or block group, and also imagining that I have a function called overlap that, when passed two polygons spits out the percent overlap:

// Iterate over each precinct.
_.each( precincts, function ( precinct ) {

    // Iterate over each blockgroup.
    _.each( blockgroups, function ( blockgroup ) {

        // Get the overlap for the current precinct and blockgroup.
        var o = overlap( precinct.geometry, blockgroup.geometry );

        // If they overlap at all...
        if ( o > 0 ) {

            // ...Add information about the overlap to the precinct.
            precinct.overlaps.push({
                blockgroup: blockgroup.id,
                overlap: o
            });

        }

    }

}

(I've seen this module, but that only gives if the polygons overlap, not by how much they do.)

Answer 1

To compute the overlapping percentage

1. Compute the intersection of the two polygons

   Intersection = intersect(Precinct, Block)
   

2. Divide the area of Intersection by the area of the parent polygon of interest.

   Overlap = area(Intersection) / area(Parent)
   

3. It is a little unclear what you mean by the percent overlap. The parent polygon could be one of several possibilities

   a) area(Intersection) / area(Precinct)
   
   b) area(Intersection) / area(Block)
   
   c) area(Intersection) / area(Precinct union Block)
   

As for a javascript library, this one seems to have what you need Intersection.js

There's also the JSTS Topology Suite which can do geospatial processing in JavaScript. See Node.js examples here.