Find intersection of SVG path

Question

Is there a known method for finding the intersect of an SVG path with itself? Take the ampersand for example, &, it's one line that intersects itself at two points.

I have come across an intersection library but it seems to talk of two shapes intersecting, rather than one intersecting itself.

I'm familiar with d3 so any javascript based answer would be great, but also happy to hear what mathematical approach could be used.

Thanks

Answer 1

You are right - the library from Kevin Lindsey (@thelonious) seems to do the job here.

You tell the library to look for intersections between two instances of the same shape, strip out Vector2D objects, and what is left are 2 sets of the same intersection points (Point2D type objects in his library).

This is the main part:

var pathEl = path.node();
var intersections = [];

// Kevin Lindsey's library
var shape1 = new Path(pathEl);
var overlays = Intersection.intersectShapes(shape1, shape1);

for (i in overlays.points) {
    if (overlays.points[i].getName() == "Point2D") {
       intersections.push(overlays.points[i]);   
    }
}

Full embedded example below:

var ampersand = "M 72.184621,99.39089 C 68.398038,95.61996 48.405425,73.700329 50.716835,49.985704 C 52.990823,26.655017 76.884556,12.578576 98.97427,11.448114 C 119.34404,10.405671 142.83345,16.156173 152.28457,35.843184 C 162.40413,56.922579 150.99532,81.842705 134.24772,94.48352 C 128.42088,98.881524 127.0609,99.082849 118.46055,102.84216 C 106.06795,108.25911 93.590914,113.54803 80.869078,118.1294 C 54.582831,127.59557 34.539139,149.03858 35.259701,178.23878 C 35.916374,204.84994 59.631137,225.67546 85.210802,229.70364 C 112.43115,233.99018 134.41358,229.54707 153.1347,208.67628 C 161.17912,199.70814 177.58763,184.99294 185.76751,176.14503 C 200.25035,160.47941 207.7442,147.82465 213.06419,126.69158 C 216.66826,112.37483 192.54569,115.67347 196.78314,103.62942 C 222.23036,100.69638 247.81229,99.84462 273.34564,97.96536 C 277.34887,109.81154 263.97786,106.33066 246.61613,121.01207 C 227.0104,137.59107 217.88679,151.73768 201.01195,170.86236 L 189.11358,184.34708 C 181.10521,193.42317 167.95634,207.85044 159.78314,216.77784 C 142.32024,235.85217 126.21297,247.41796 100.27427,252.39343 C 72.543606,257.71262 39.651129,254.69839 20.122962,231.94973 C -0.62641014,207.77846 -4.0848351,167.90434 18.462826,143.66847 C 33.171306,127.85873 41.031184,120.17885 60.724466,112.09432 C 76.147466,105.76283 100.05575,99.431353 112.29677,94.160526 C 139.69178,82.364582 140.40896,53.478721 127.50818,32.380115 C 116.44184,14.281646 83.908653,15.752833 77.904904,37.000557 C 72.689417,55.458561 80.089538,67.982449 91.37226,80.93907 L 187.58994,191.43156 C 199.42503,205.63979 217.24414,228.88851 237.39579,232.51125 C 250.72342,234.90721 267.9319,228.93995 277.27793,220.4821 C 282.25334,229.49138 275.03265,236.84049 269.43939,242.49659 C 251.14471,260.99681 219.58458,257.23653 199.30993,242.48439 C 187.00911,233.53413 178.95611,227.18492 167.95716,215.15746 L 72.184621,99.39089 z ";

var svg = d3.select("body").append("svg")
    .attr("width", 300)
    .attr("height", 300);

var path = svg.append("svg:path")
            .attr("d",ampersand)
            .style("stroke-width", 2)
            .style("stroke", "steelblue")
            .style("fill", "none");

// Taken from https://stackoverflow.com/questions/332422/how-do-i-get-the-name-of-an-objects-type-in-javascript
Object.prototype.getName = function() { 
   var funcNameRegex = /function (.{1,})\(/;
   var results = (funcNameRegex).exec((this).constructor.toString());
   return (results && results.length > 1) ? results[1] : "";
};

// Taken from https://stackoverflow.com/questions/9229645/remove-duplicates-from-javascript-array
function uniq(a) {
    var prims = {"boolean":{}, "number":{}, "string":{}}, objs = [];

    return a.filter(function(item) {
        var type = typeof item;
        if(type in prims)
            return prims[type].hasOwnProperty(item) ? false : (prims[type][item] = true);
        else
            return objs.indexOf(item) >= 0 ? false : objs.push(item);
    });
}

var pathEl = path.node();
var intersections = [];

// Kevin Lindsey's library
var shape1 = new Path(pathEl);
var overlays = Intersection.intersectShapes(shape1, shape1);

for (i in overlays.points) {
   if (overlays.points[i].constructor.name == "Point2D") {
      intersections.push(overlays.points[i]);   
   }
}

// The path will record 2 points for each intersection, so deduping is necessary
var deduped_intersections = uniq(intersections);

var circles = svg.selectAll("circle")
                 .data(deduped_intersections)
                .enter()
                 .append("circle");

var circleAttributes = circles
                       .attr("cx", function (d) { return d.x; })
                       .attr("cy", function (d) { return d.y; })
                       .attr("r", "3")
                       .style("fill", "red");

<script src="https://cdnjs.cloudflare.com/ajax/libs/d3/3.4.11/d3.min.js"></script>
<script src="http://www.kevlindev.com/gui/2D.js"></script>