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https://issues.apache.org/jira/browse/LUCENE-7229?page=com.atlassian.jira.plugin.system.issuetabpanels:comment-tabpanel&focusedCommentId=15246486#comment-15246486
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Nicholas Knize commented on LUCENE-7229:
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That's what I'm talking about.
{noformat}
return lineCrossesLine(aX1, aY1, aX2, aY2, rMinX, rMinY, rMaxX, rMaxY)
|| lineCrossesLine(aX1, aY1, aX2, aY2, rMaxX, rMinY, rMinX, rMaxY);
{noformat}
It's checking if the line crosses either diagonal of the candidate rectangle.
First (the short-circuit check) checks if either line endpoint falls inside the
candidate rectangle (to test extruding polygons). If not, it then checks if the
poly line crosses either diagonal.
This works well for rasterization because the cells are small enough that
earth's curvature doesn't matter and lines are "straight". It could fail for
large inner BKD nodes though when curvature does have an effect.
> Improve Polygon.relate
> ----------------------
>
> Key: LUCENE-7229
> URL: https://issues.apache.org/jira/browse/LUCENE-7229
> Project: Lucene - Core
> Issue Type: Improvement
> Reporter: Robert Muir
> Attachments: LUCENE-7229.patch, LUCENE-7229.patch
>
>
> This method is currently quite slow and in many cases does more work than is
> required. The speed actually directly impacts queries (tree traversal) and
> bounds grid size to something tiny making it less effective.
> I think we should replace it line intersections based on orientation methods
> described here http://www.cs.berkeley.edu/~jrs/meshpapers/robnotes.pdf and
> https://www.cs.cmu.edu/~quake/robust.html
> For one, a naive implementation is considerably faster than the method today:
> both because it reduces the cost of BKD tree traversals and also because it
> makes grid construction cheaper. This means we can increase its level of
> detail with similar or lower startup cost. Now its more like a Mario Brothers
> 2 picture of your polygon instead of Space Invaders.
> Synthetic polygons from luceneUtil
> ||vertices||old QPS||new QPS||old startup cost||new startup cost||
> |50|20.4|21.7|1ms|1ms|
> |500|11.2|14.4|5ms|4ms|
> |1000|7.4|10.0|9ms|8ms|
> Real polygons (33 london districts:
> http://data.london.gov.uk/2011-boundary-files)
> ||vertices||old QPS||new QPS||old startup cost||new startup cost||
> |avg 5.6k|4.9|8.6|94ms|85ms|
> But I also like using this method because its possible to extend it to remove
> floating point error completely in the future with techniques described in
> those links. This may be necessary if we want to do smarter things (e.g. not
> linear time).
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