Monday 28 January 2019

Hilbert and Morton Curves in JTS

I just landed a JTS pull request for Hilbert and Morton (Z-order) codes and curves.
Hilbert Curve of level 3
Morton Curve of level 3

Apart from pretty pictures of fractals, the goal is to support experimenting with Packed Hilbert R-trees, as an alternative to the current Sort-Tile-Recursive packing strategy (implemented as STRtree in JTS).  STRtrees are heavily used to speed up spatial algorithms inside JTS (and externally as per recent report). So if Hilbert curve-based packing provides better performance that would be a big win.

Thursday 17 January 2019

Fun wit JEQL: Hilbert Curves

Hilbert Curve of order 4:

Hilbert Curve of order 6:
Code is in the JEQL script repo.

import jeql.std.function.HashFunction;

hilbertOrder = 6;
side = Val.toInt( Math.pow(2, hilbertOrder) );
count = side * side;

t = select * from Generate.sequence( 0, count-2 );

t = select i, geom: Geom.buffer(hilbertEdge, 0.4)
let
hilbertPt1 = HashFunction.hilbertPoint(hilbertOrder, i),
hilbertPt2 = HashFunction.hilbertPoint(hilbertOrder, i+1),
hilbertEdge = Geom.createLineFromPoints( hilbertPt1, hilbertPt2 )
from t;

t1 = select *,
styleFill: clr, styleStroke: clr, styleStrokeWidth: 1
let
clr = Color.toRGBfromHSV(Val.toDouble(i) / count, 1, 1)
from t;
Mem t1;

The function hilbertPoint uses the efficient algorithm from http://threadlocalmutex.com/.  Code is on Github.