D3JS quadtree nearest neighbor algorithm

This example adapts mbostock's quadtree brushing demo to find the nearest neighbor (shown red) of a new point (shown yellow). Choose a new point to classify by clicking on the diagram. (An alternative approach for nearest neighbors of the mouse position is D3's Voronoi polygons, but the idea here would extend to rapidly classifying many new points against a base collection of points.)

We use a data-dependent order of recursion through the quadtree in order to quickly find a nearby point and then exclude many large rectangles without testing actual points. Green rectangles are visited, with saturation indicating depth in the quadtree. Only the orange points from the base collection are tested for Euclidean distance, other rectangles are excluded with a simple margin test.

I found it helpful to add extent and depth data to the quadtree nodes, maybe a useful general extension?

<!DOCTYPE html>
<meta charset="utf-8">
<title>Quadtree - nearest neighbor</title>
<style>

.point {
  fill: #999;
  stroke: #fff;
}

.point.scanned {
  fill: orange;
  fill-opacity: 1;
  stroke: brown;
}

.point.selected {
  fill: red;
  fill-opacity: 1;
}

.node {
  fill: none;
  stroke: #ccc;
  shape-rendering: crispEdges;
}
  
.brush .extent {
  stroke: #fff;
  fill-opacity: .125;
  shape-rendering: crispEdges;
}

</style>
<body>
<script src="https://d3js.org/d3.v3.min.js"></script>
<script>

var width = 960,
    height = 500;

var data = d3.range(1000).map(function() {
  return [Math.random() * width, Math.random() * height];
});

var quadtree = d3.geom.quadtree()
    .extent([[-1, -1], [width + 1, height + 1]])
    (data);

var color = d3.scale.linear()
    .domain([0, 8])  // max depth of quadtree
    .range(["#efe", "#060"]);
    
var svg = d3.select("body").append("svg")
    .attr("width", width)
    .attr("height", height)
    .on("click", function (d) {
        var xy = d3.mouse(d3.selectAll('svg')[0][0]);
        svg.selectAll("#pt")
            .attr("cx", xy[0])
            .attr("cy", xy[1]);
        clicked();
    });

var point = svg.selectAll(".point")
    .data(data)
  .enter().append("circle")
    .attr("class", "point")
    .attr("cx", function(d) { return d[0]; })
    .attr("cy", function(d) { return d[1]; })
    .attr("r", 3);

svg.append("circle")
    .attr("id", "pt")
    .attr("r", 3)
    .attr("cx", width/2)
    .attr("cy", height/2)
    .style("fill", "yellow");

// PDS Collect a list of nodes to draw rectangles, adding extent and depth data
function nodes(quadtree) {
  var nodes = [];
  quadtree.depth = 0; // root
  quadtree.visit(function(node, x1, y1, x2, y2) {
    node.x1 = x1;
    node.y1 = y1;
    node.x2 = x2;
    node.y2 = y2;
    nodes.push(node);
    for (var i=0; i<4; i++) {
        if (node.nodes[i]) node.nodes[i].depth = node.depth+1;
    }
  });
  return nodes;
}
      
function nearest(x, y, best, node) {
    var x1 = node.x1, y1 = node.y1, x2 = node.x2, y2 = node.y2;
    node.visited = true;
    // exclude node if point is farther away than best distance in either axis
    if (x < x1 - best.d || x > x2 + best.d || y < y1 - best.d || y > y2 + best.d) {
        return best;
    }
    // test point if there is one, potentially updating best
    var p = node.point;
    if (p) {
      p.scanned = true;
      var dx = p[0] - x, dy = p[1] - y, d = Math.sqrt(dx*dx + dy*dy);
      if (d < best.d) {
        best.d = d;
        best.p = p;
      }
    }
    // check if kid is on the right or left, and top or bottom
    // and then recurse on most likely kids first, so we quickly find a 
    // nearby point and then exclude many larger rectangles later
    var kids = node.nodes;
    var rl = (2*x > x1 + x2), bt = (2*y > y1 + y2);
    if (kids[bt*2+rl]) best = nearest(x, y, best, kids[bt*2+rl]);
    if (kids[bt*2+(1-rl)]) best = nearest(x, y, best, kids[bt*2+(1-rl)]);
    if (kids[(1-bt)*2+rl]) best = nearest(x, y, best, kids[(1-bt)*2+rl]);
    if (kids[(1-bt)*2+(1-rl)]) best = nearest(x, y, best, kids[(1-bt)*2+(1-rl)]);
    
    return best;
}

clicked();

</script>

Modified http://d3js.org/d3.v3.min.js to a secure url

https://d3js.org/d3.v3.min.js