A javascript function which uses a map to efficiently search for nearby points distributed across a one-dimensional field. There is quite a high up-front cost to initializing the map, but, once that is done, each point-finding operation is extremely cheap.

pointChecker.js

var CheckPoints=function(list, spaceSize, scanSize)
{
    var n,m,map;
    list.sort(
        function(a,b)
        {
            return -(a.x<b.x)+(a.x>b.x);
        }
    );
    map={};
    n=Math.floor(spaceSize/scanSize);
    while(n--)
    {
        map[n*scanSize]=undefined;
    }
    n=list.length;
    while(n--)
    {
        for(m in map)
        {
            if(map[m]===undefined || Math.abs(list[n].x-m)<Math.abs(list[map[m]].x-m))
            {
                map[m]=n;
            }
        }
    }
    return function(x)
    {
        var selected,n,no;
        selected=[];
        n=map[Math.round(x/scanSize)*scanSize];
        while(1)
        {
            no=list[n++];
            if(Math.abs(no.x-x)<scanSize/2+no.r)
            {
                selected.push(no);
            }
            else if(no.x>x)
            {
                break;
            }
        }
        return selected;
    }
};

var Point=function(x)
{
    return {x:x,r:1};
}
var points=[];
var n=1000000;
while(n--)
{
    points[n]=Point(1000*Math.random());
}
var check;

check=CheckPoints(points, 1000, 50);
// Returns the below function after 18.9 seconds. 

var t=Date.now();
check(632);
print(Date.now()-t)
// Returns an array containing every point within a 25 unit radius of a point at 632 after 2 ms.