Find polygon perimeter of points quickly in Javascript

问题

I'm making a terrain editor and I need to find the perimeter polygon of a set of points. If I just needed a convex hull then the speed would be no issue. To make a concave hull, I must go through a few hoops. I've figured out that I can triangulate the points and then throw away any triangles with a side longer than the known distance between the points.

The next step is the problem: Combining the triangles (as mini polygons) into one large polygon using the JSTS geometry library (http://github.com/bjornharrtell/jsts) is really slow.

See the full code: http://codepen.io/anon/pen/oCfDh

I've got an array (polys) that gets merged to form the final polygon. The problem is that with 552 points (I want to support 15k+), it takes ~3500ms to run. Look at the console in the codepen link for your speed.

  var reader = new jsts.io.WKTReader(),
      merged = reader.read(polys[0]).union(reader.read(polys[1]));
  console.time('jsts mergization');
  for(var i = 2; i<polys.length; i++){
    try{
      merged = merged.union(reader.read(polys[i]));
    }catch(err){
      console.log('Error triangulating points!');
    };
  };
  console.timeEnd('jsts mergization');

Does anybody know of any faster way to either merge triangles into a polygon or to go even wider and build a concave polygon from a set a points in a whole different way?

回答1:

Thanks simonzack!

I've rewritten the algorithm using your suggestion and it's much faster!

Reworked codepen: http://codepen.io/anon/pen/Btdyj

The same example now runs in ~15ms!

function pointsToPolygon(points, triangles, maxEdgeLength){
  console.time('homebrewed mergization');
  var dist = function(a, b){
    if(typeof a === "number"){
      a = points[a];
    };
    if(typeof b === "number"){
      b = points[b];
    };
    return Math.sqrt(Math.pow(a[0] - b[0], 2) + 
            Math.pow(a[1] - b[1], 2));
  };
  if(!points.length){
    return undefined;
  };
  var pointFreq = [];
  points.forEach(function(v){
    pointFreq.push(0);
  });
  for(var i = triangles.length; i; i-=3){
    if(dist(triangles[i-1], triangles[i-2]) < maxEdgeLength &&
       dist(triangles[i-3], triangles[i-2]) < maxEdgeLength &&
       dist(triangles[i-1], triangles[i-3]) < maxEdgeLength){
      pointFreq[triangles[i-1]]++;
      pointFreq[triangles[i-2]]++;
      pointFreq[triangles[i-3]]++;
    };
  };

  // Keep points that are used in 3 or fewer triangles
  var output =[];
  pointFreq.forEach(function(freq, i){
    if(freq<4){
      output.push(points[i]);
    };
  });

  // Sort points by looping around by each next closest point
  var sorted = [];
  while(output.length>0){
    sorted.push(output.pop());
    output=output.sort(function(a,b){
      var distA =dist(sorted[sorted.length-1], a),
          distB =dist(sorted[sorted.length-1], b);
      if(distA < distB){
        return 1;
      }else if(distA === distB){
        return 0;
      };
      return -1;
    });
  };

  sorted=simplifyPath(sorted,0.1);

  console.timeEnd('homebrewed mergization');
  return sorted;

};

I can find the boundary by filtering the points that are used in 3 or fewer triangles then sort points by looping around by each next closest point from any arbitrary point.

Maybe not 100% as accurate due to the Douglas-Peucker simplification algorithm (adapted from https://gist.github.com/adammiller/826148) but it seems good enough for me.

来源：https://stackoverflow.com/questions/25521146/find-polygon-perimeter-of-points-quickly-in-javascript