The next measurement done was after implementing the Douglas-Peucker algorithm for filtering the line string. The principle behind this algorithm is pretty simple: after choosing an epsilon value, the smaller the epsilon the higher the precision and the lower the compression, you apply the following steps:
1) find the farthest point from the segment determined by the first and the last point, let it have the index X
2) if this just found greatest distance is smaller than epsilon, then return the line string formed from the first and the last node.
3) now, we now that X has a distance greater than epsilon, so we solve recursively for [start…X] and for [X…end], and then join the solutions obtained from these two.
The average case complexity of the algorithm is O(N log N), but its worst case is O(N^2).
Determining the epsilon according to the current detail level was pretty fun, since I had to test all kinds of formulas. Right now it looks like this (still provisional 🙂 ):
335 qreal GeoDataLineString::epsilonFromDetailLevel( int detailLevel ) const
337 if ( p()->m_vector.size() < 30 )
338 return 0;
340 if ( detailLevel <= 1 )
341 return 50000;
342 if ( detailLevel == 2 )
343 return 20000;
344 if ( detailLevel > 2 && detailLevel <= 8 )
345 return 17500 – 2500 * ( detailLevel – 2 );
346 if ( detailLevel > 8 && detailLevel <= 11 )
347 return 2500 – 700 * ( detailLevel – 8 );
349 return 400 / ( 1 << ( detailLevel – 12 ) );
As a start, I implemented the “zoom-caching” version of Douglas-Peucker, and it has one major advantage and one major disadvantage:
- the disadvantage is that the creation of the cache lasts between 1 and 3 seconds ( less for lower detail levels ) – and it becomes annoying because it happens at each zoom change
- the advantage is that the time for creating polygons is 1-2 ms for each detail level smaller than 10 ( Atlas map has 8 detail levels, OSM is the only one with more, 18 to be precise )
Right now, I am working on a method to use Douglas-Peucker with no cache rebuilding at zooming, by mixing this method and the last one presented in the previous post.
Here are some pictures of the line string on different zoom levels, with / without filtering:
Level 2, Filtered – built with 44 nodes (out of the total of 624072)
Level 2, Unfiltered
Level 3, Filtered – built with 71 nodes (out of the total of 624072)
Level 3, Unfiltered
Level 5, Filtered – built with 134 nodes (out of the total of 624072)
Level 5, Unfiltered
Level 7, Filtered – built with 296 nodes (out of the total of 624072)
Level 7, Unfiltered
Level 9, Filtered – built with 848 nodes (out of the total of 624072)
Level 9, Unfiltered
Seeing this pictures, I realize that I could use more some nodes for levels >= 7, what do you think?