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Date: Thu, 9 May 2013 07:01:21 +0000 (UTC)
From: "John Berryman (JIRA)" <jira@apache.org>
To: dev@lucene.apache.org
Message-ID: <JIRA.12641676.1365530943467.292699.1368082881844@arcas>
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References: <JIRA.12641676.1365530943467@arcas>
Subject: [jira] [Comment Edited] (LUCENE-4922) A SpatialPrefixTree based on
 the Hilbert Curve and variable grid sizes
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    [ https://issues.apache.org/jira/browse/LUCENE-4922?page=com.atlassian.jira.plugin.system.issuetabpanels:comment-tabpanel&focusedCommentId=13652785#comment-13652785 ] 

John Berryman edited comment on LUCENE-4922 at 5/9/13 7:00 AM:
---------------------------------------------------------------

{{# Converts from an x,y coordinate (vals[0],vals[1]) between min and max values to a point on the Hilbert curve in base4}}
#
def hilbert_point(vals,depth,mins=[],maxs=[]):
    """
    cell_names

    3 2
    0 1

    """
    if(mins):
        # then convert vals to some place in 1-by-1 grid at the origin
        vals[0] = (vals[0]-mins[0])/(maxs[0]-mins[0])
        vals[1] = (vals[1]-mins[1])/(maxs[1]-mins[1])
    
    if(depth == 0):
        return ''

    if( vals[0]<=0.5 and vals[1]<=0.5 ):
        cell_name = '0'
        x = vals[1]*2
        y = vals[0]*2
    elif( vals[0]>=0.5 and vals[1]<=0.5 ):
        cell_name = '1'
        x = (vals[0] - 0.5)*2
        y = vals[1]*2
    elif( vals[0]>=0.5 and vals[1]>=0.5 ):
        cell_name = '2'
        x = (vals[0] - 0.5)*2
        y = (vals[1] - 0.5)*2
    elif( vals[0]<=0.5 and vals[1]>=0.5 ):
        cell_name = '3'
        x = 1 - (vals[1] - 0.5)*2
        y = 1 - vals[0]*2

    return cell_name + hilbert_point([x,y],depth-1)

                
      was (Author: berryman):
    {{
# Converts from an x,y coordinate (vals[0],vals[1]) between min and max values to a point on the Hilbert curve in base4
#
def hilbert_point(vals,depth,mins=[],maxs=[]):
    """
    cell_names

    3 2
    0 1

    """
    if(mins):
        # then convert vals to some place in 1-by-1 grid at the origin
        vals[0] = (vals[0]-mins[0])/(maxs[0]-mins[0])
        vals[1] = (vals[1]-mins[1])/(maxs[1]-mins[1])
    
    if(depth == 0):
        return ''

    if( vals[0]<=0.5 and vals[1]<=0.5 ):
        cell_name = '0'
        x = vals[1]*2
        y = vals[0]*2
    elif( vals[0]>=0.5 and vals[1]<=0.5 ):
        cell_name = '1'
        x = (vals[0] - 0.5)*2
        y = vals[1]*2
    elif( vals[0]>=0.5 and vals[1]>=0.5 ):
        cell_name = '2'
        x = (vals[0] - 0.5)*2
        y = (vals[1] - 0.5)*2
    elif( vals[0]<=0.5 and vals[1]>=0.5 ):
        cell_name = '3'
        x = 1 - (vals[1] - 0.5)*2
        y = 1 - vals[0]*2

    return cell_name + hilbert_point([x,y],depth-1)
}}
                  
> A SpatialPrefixTree based on the Hilbert Curve and variable grid sizes
> ----------------------------------------------------------------------
>
>                 Key: LUCENE-4922
>                 URL: https://issues.apache.org/jira/browse/LUCENE-4922
>             Project: Lucene - Core
>          Issue Type: New Feature
>          Components: modules/spatial
>            Reporter: David Smiley
>            Assignee: David Smiley
>              Labels: gsoc2013, mentor, newdev
>
> My wish-list for an ideal SpatialPrefixTree has these properties:
> * Hilbert Curve ordering
> * Variable grid size per level (ex: 256 at the top, 64 at the bottom, 16 for all in-between)
> * Compact binary encoding (so-called "Morton number")
> * Works for geodetic (i.e. lat & lon) and non-geodetic
> Some bonus wishes for use in geospatial:
> * Use an equal-area projection such that each cell has an equal area to all others at the same level.
> * When advancing a grid level, if a cell's width is less than half its height. then divide it as 4 vertically stacked instead of 2 by 2. The point is to avoid super-skinny cells which occurs towards the poles and degrades performance.
> All of this requires some basic performance benchmarks to measure the effects of these characteristics.

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