Posts Tagged ‘path’

A* path optimization

The A* algorithm, using a straight-line distance heuristic function, is great in terms of performance, but yields a number of cases where the paths produced are not optimal.

For example, here is a path created in ScratchGraph using GraphPaper (the underlying library used for creating the connectors):

A* without path optimization

I suspect the non-optimal result is even more pronounced here given that the path is determined based on specific routing points that exist around the objects (you can spot these as the inflection points in the path), instead of a uniform grid. That said, I don’t want to use a uniform grid; while it’s likely a non-issue with A*, there is also the cost of computing which routing points are accessible vs blocked, and that cost grows quickly as the possible number of routing points grow.

An approach that works well, and doesn’t drastically increase the cost of path computation, is simplifying the generated path by checking if corresponding points in the path are visible to each other. If so, we can remove the intermediate points, and simply connect those 2 points together. Here’s a snipped from the GraphPaper codebase:

/** * * @param {Point[]} _pointsInRoute * @param {Function} _arePointsVisibleToEachOther */ optimize: function(_pointsInRoute, _arePointsVisibleToEachOther) { let start = 0; let end = _pointsInRoute.length - 1; while(true) { if((end-start) <= 1) { start++; end = _pointsInRoute.length - 1; if(start >= _pointsInRoute.length-2) { break; } } if(_arePointsVisibleToEachOther(_pointsInRoute[start], _pointsInRoute[end])) { _pointsInRoute.splice(start + 1, (end-start) - 1); end = _pointsInRoute.length - 1; } else { end--; } } }

The function works as follows:

  • Begin with the points start (first point in the path) and end (last point in the path).
  • Relative to start, check if the other points in the path are visible to it (in the code above, we iterate backwards from the endpoint). If we find that start is visible to another point, we eliminate the intermediate points from the path.
  • Once we get to end being the point after start, update start to the next point in the path and reset end to whatever the last point in the path is.
  • Repeat the latter 2 steps until we’ve checked all corresponding points in the path (start is the point directly preceding end).

Optimizing the path shown above with this method yields an optimal path:

A* with path optimization

In terms of performance, the cost is based on the number of points in the path and the cost of whatever computation the _arePointsVisibleToEachOther() function does. For my use-cases, paths have relatively few points and _arePointsVisibleToEachOther() consists of a number of fairly fast line-line intersection checks, so the method is fairly cheap and there’s no significant decrease in performance when generating paths.

poly2path

I’m working on a little SVG project using Raphaël. Unfortunately, Illustrator exports polygons in its SVG output which is not supported by Raphaël (only paths are supported). So I wrote an app to convert the SVG polygon string to an SVG path string.

Download Here

the conversion…

poly2path conversion

Note that you only input the points data from the polygon (from the points attribute), not the entire polygon element. The result is the path string for the d attribute of the path element.

The conversion is very simple and based upon the fact that a polygon is a path starting with an absolute moveto, linetos to each of the points, and a closepath (this bug report [yes, a bug report!] was pretty helpful).

I actually wanted to render the output, but I was disappointed to discover that Adobe Air doesn’t currently support SVG.

The main reason for not including it was runtime size concerns (adding it would have increased the runtime size by 15 to 20 percent). Initially, the main pain-points regarding AIR were the size of the runtime, integration with the operating system and native APIs, support for the <canvas> tag and new CSS properties, and JavaScript performance. These priorities, coupled with a trend toward reduced interest in SVG graphics, led to SVG support not being included in the current version of Adobe AIR.