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Code to generate Voronoi diagrams in PostGIS using Python. Many thanks to everyone who contributed to this code. Original blog post describing the work is here: http://geogeek.garnix.org/2012/04/faster-voronoi-diagrams-in-postgis.html
Raw
voronoi.sql
CREATE OR REPLACE FUNCTION voronoi(table_name text,geom_col text) returns SETOF record as $$
#############################################################################
#
# Voronoi diagram calculator/ Delaunay triangulator
# Translated to Python by Bill Simons
# September, 2005
#
# Additional changes by Carson Farmer added November 2010
#
# Converted to pl/python function by Darrell Fuhriman, April 2012
# based on code from:
# https://svn.osgeo.org/qgis/trunk/qgis/python/plugins/fTools/tools/voronoi.py
#
# Calculate Delaunay triangulation or the Voronoi polygons for a set of
# 2D input points.
#
# Derived from code bearing the following notice:
#
# The author of this software is Steven Fortune. Copyright (c) 1994 by AT&T
# Bell Laboratories.
# Permission to use, copy, modify, and distribute this software for any
# purpose without fee is hereby granted, provided that this entire notice
# is included in all copies of any software which is or includes a copy
# or modification of this software and in all copies of the supporting
# documentation for such software.
# THIS SOFTWARE IS BEING PROVIDED "AS IS", WITHOUT ANY EXPRESS OR IMPLIED
# WARRANTY. IN PARTICULAR, NEITHER THE AUTHORS NOR AT&T MAKE ANY
# REPRESENTATION OR WARRANTY OF ANY KIND CONCERNING THE MERCHANTABILITY
# OF THIS SOFTWARE OR ITS FITNESS FOR ANY PARTICULAR PURPOSE.
#
# Comments were incorporated from Shane O'Sullivan's translation of the
# original code into C++ (http://mapviewer.skynet.ie/voronoi.html)
#
# Steve Fortune's homepage: http://netlib.bell-labs.com/cm/cs/who/sjf/index.html
#
#############################################################################
import math
import sys
import getopt
TOLERANCE = 1e-9
BIG_FLOAT = 1e38
#------------------------------------------------------------------
class Context(object):
def __init__(self):
self.doPrint = 0
self.debug = 0
self.plot = 0
self.triangulate = False
self.vertices = [] # list of vertex 2-tuples: (x,y)
self.lines = [] # equation of line 3-tuple (a b c), for the equation of the line a*x+b*y = c
self.edges = [] # edge 3-tuple: (line index, vertex 1 index, vertex 2 index) if either vertex index is -1, the edge extends to infiinity
self.triangles = [] # 3-tuple of vertex indices
self.polygons = {} # a dict of site:[edges] pairs
def circle(self,x,y,rad):
pass
def clip_line(self,edge):
pass
def line(self,x0,y0,x1,y1):
pass
def outSite(self,s):
if(self.debug):
print "site (%d) at %f %f" % (s.sitenum, s.x, s.y)
elif(self.triangulate):
pass
elif(self.plot):
self.circle (s.x, s.y, cradius)
elif(self.doPrint):
print "s %f %f" % (s.x, s.y)
def outVertex(self,s):
self.vertices.append((s.x,s.y))
if(self.debug):
print "vertex(%d) at %f %f" % (s.sitenum, s.x, s.y)
elif(self.triangulate):
pass
elif(self.doPrint and not self.plot):
print "v %f %f" % (s.x,s.y)
def outTriple(self,s1,s2,s3):
self.triangles.append((s1.sitenum, s2.sitenum, s3.sitenum))
if(self.debug):
print "circle through left=%d right=%d bottom=%d" % (s1.sitenum, s2.sitenum, s3.sitenum)
elif(self.triangulate and self.doPrint and not self.plot):
print "%d %d %d" % (s1.sitenum, s2.sitenum, s3.sitenum)
def outBisector(self,edge):
self.lines.append((edge.a, edge.b, edge.c))
if(self.debug):
print "line(%d) %gx+%gy=%g, bisecting %d %d" % (edge.edgenum, edge.a, edge.b, edge.c, edge.reg[0].sitenum, edge.reg[1].sitenum)
elif(self.triangulate):
if(self.plot):
self.line(edge.reg[0].x, edge.reg[0].y, edge.reg[1].x, edge.reg[1].y)
elif(self.doPrint and not self.plot):
print "l %f %f %f" % (edge.a, edge.b, edge.c)
def outEdge(self,edge):
sitenumL = -1
if edge.ep[Edge.LE] is not None:
sitenumL = edge.ep[Edge.LE].sitenum
sitenumR = -1
if edge.ep[Edge.RE] is not None:
sitenumR = edge.ep[Edge.RE].sitenum
if edge.reg[0].sitenum not in self.polygons:
self.polygons[edge.reg[0].sitenum] = []
if edge.reg[1].sitenum not in self.polygons:
self.polygons[edge.reg[1].sitenum] = []
self.polygons[edge.reg[0].sitenum].append((edge.edgenum,sitenumL,sitenumR))
self.polygons[edge.reg[1].sitenum].append((edge.edgenum,sitenumL,sitenumR))
self.edges.append((edge.edgenum,sitenumL,sitenumR))
if(not self.triangulate):
if self.plot:
self.clip_line(edge)
elif(self.doPrint):
print "e %d" % edge.edgenum,
print " %d " % sitenumL,
print "%d" % sitenumR
#------------------------------------------------------------------
def voronoi(siteList,context):
try:
edgeList = EdgeList(siteList.xmin,siteList.xmax,len(siteList))
priorityQ = PriorityQueue(siteList.ymin,siteList.ymax,len(siteList))
siteIter = siteList.iterator()
bottomsite = siteIter.next()
context.outSite(bottomsite)
newsite = siteIter.next()
minpt = Site(-BIG_FLOAT,-BIG_FLOAT)
while True:
if not priorityQ.isEmpty():
minpt = priorityQ.getMinPt()
if (newsite and (priorityQ.isEmpty() or cmp(newsite,minpt) < 0)):
# newsite is smallest - this is a site event
context.outSite(newsite)
# get first Halfedge to the LEFT and RIGHT of the new site
lbnd = edgeList.leftbnd(newsite)
rbnd = lbnd.right
# if this halfedge has no edge, bot = bottom site (whatever that is)
# create a new edge that bisects
bot = lbnd.rightreg(bottomsite)
edge = Edge.bisect(bot,newsite)
context.outBisector(edge)
# create a new Halfedge, setting its pm field to 0 and insert
# this new bisector edge between the left and right vectors in
# a linked list
bisector = Halfedge(edge,Edge.LE)
edgeList.insert(lbnd,bisector)
# if the new bisector intersects with the left edge, remove
# the left edge's vertex, and put in the new one
p = lbnd.intersect(bisector)
if p is not None:
priorityQ.delete(lbnd)
priorityQ.insert(lbnd,p,newsite.distance(p))
# create a new Halfedge, setting its pm field to 1
# insert the new Halfedge to the right of the original bisector
lbnd = bisector
bisector = Halfedge(edge,Edge.RE)
edgeList.insert(lbnd,bisector)
# if this new bisector intersects with the right Halfedge
p = bisector.intersect(rbnd)
if p is not None:
# push the Halfedge into the ordered linked list of vertices
priorityQ.insert(bisector,p,newsite.distance(p))
newsite = siteIter.next()
elif not priorityQ.isEmpty():
# intersection is smallest - this is a vector (circle) event
# pop the Halfedge with the lowest vector off the ordered list of
# vectors. Get the Halfedge to the left and right of the above HE
# and also the Halfedge to the right of the right HE
lbnd = priorityQ.popMinHalfedge()
llbnd = lbnd.left
rbnd = lbnd.right
rrbnd = rbnd.right
# get the Site to the left of the left HE and to the right of
# the right HE which it bisects
bot = lbnd.leftreg(bottomsite)
top = rbnd.rightreg(bottomsite)
# output the triple of sites, stating that a circle goes through them
mid = lbnd.rightreg(bottomsite)
context.outTriple(bot,top,mid)
# get the vertex that caused this event and set the vertex number
# couldn't do this earlier since we didn't know when it would be processed
v = lbnd.vertex
siteList.setSiteNumber(v)
context.outVertex(v)
# set the endpoint of the left and right Halfedge to be this vector
if lbnd.edge.setEndpoint(lbnd.pm,v):
context.outEdge(lbnd.edge)
if rbnd.edge.setEndpoint(rbnd.pm,v):
context.outEdge(rbnd.edge)
# delete the lowest HE, remove all vertex events to do with the
# right HE and delete the right HE
edgeList.delete(lbnd)
priorityQ.delete(rbnd)
edgeList.delete(rbnd)
# if the site to the left of the event is higher than the Site
# to the right of it, then swap them and set 'pm' to RIGHT
pm = Edge.LE
if bot.y > top.y:
bot,top = top,bot
pm = Edge.RE
# Create an Edge (or line) that is between the two Sites. This
# creates the formula of the line, and assigns a line number to it
edge = Edge.bisect(bot, top)
context.outBisector(edge)
# create a HE from the edge
bisector = Halfedge(edge, pm)
# insert the new bisector to the right of the left HE
# set one endpoint to the new edge to be the vector point 'v'
# If the site to the left of this bisector is higher than the right
# Site, then this endpoint is put in position 0; otherwise in pos 1
edgeList.insert(llbnd, bisector)
if edge.setEndpoint(Edge.RE - pm, v):
context.outEdge(edge)
# if left HE and the new bisector don't intersect, then delete
# the left HE, and reinsert it
p = llbnd.intersect(bisector)
if p is not None:
priorityQ.delete(llbnd);
priorityQ.insert(llbnd, p, bot.distance(p))
# if right HE and the new bisector don't intersect, then reinsert it
p = bisector.intersect(rrbnd)
if p is not None:
priorityQ.insert(bisector, p, bot.distance(p))
else:
break
he = edgeList.leftend.right
while he is not edgeList.rightend:
context.outEdge(he.edge)
he = he.right
Edge.EDGE_NUM = 0
except Exception, err:
print "######################################################"
print str(err)
#------------------------------------------------------------------
def isEqual(a,b,relativeError=TOLERANCE):
# is nearly equal to within the allowed relative error
norm = max(abs(a),abs(b))
return (norm < relativeError) or (abs(a - b) < (relativeError * norm))
#------------------------------------------------------------------
class Site(object):
def __init__(self,x=0.0,y=0.0,sitenum=0):
self.x = x
self.y = y
self.sitenum = sitenum
def dump(self):
print "Site #%d (%g, %g)" % (self.sitenum,self.x,self.y)
def __cmp__(self,other):
if self.y < other.y:
return -1
elif self.y > other.y:
return 1
elif self.x < other.x:
return -1
elif self.x > other.x:
return 1
else:
return 0
def distance(self,other):
dx = self.x - other.x
dy = self.y - other.y
return math.sqrt(dx*dx + dy*dy)
#------------------------------------------------------------------
class Edge(object):
LE = 0
RE = 1
EDGE_NUM = 0
DELETED = {} # marker value
def __init__(self):
self.a = 0.0
self.b = 0.0
self.c = 0.0
self.ep = [None,None]
self.reg = [None,None]
self.edgenum = 0
def dump(self):
print "(#%d a=%g, b=%g, c=%g)" % (self.edgenum,self.a,self.b,self.c)
print "ep",self.ep
print "reg",self.reg
def setEndpoint(self, lrFlag, site):
self.ep[lrFlag] = site
if self.ep[Edge.RE - lrFlag] is None:
return False
return True
@staticmethod
def bisect(s1,s2):
newedge = Edge()
newedge.reg[0] = s1 # store the sites that this edge is bisecting
newedge.reg[1] = s2
# to begin with, there are no endpoints on the bisector - it goes to infinity
# ep[0] and ep[1] are None
# get the difference in x dist between the sites
dx = float(s2.x - s1.x)
dy = float(s2.y - s1.y)
adx = abs(dx) # make sure that the difference in positive
ady = abs(dy)
# get the slope of the line
newedge.c = float(s1.x * dx + s1.y * dy + (dx*dx + dy*dy)*0.5)
if adx > ady :
# set formula of line, with x fixed to 1
newedge.a = 1.0
newedge.b = dy/dx
newedge.c /= dx
else:
# set formula of line, with y fixed to 1
newedge.b = 1.0
newedge.a = dx/dy
newedge.c /= dy
newedge.edgenum = Edge.EDGE_NUM
Edge.EDGE_NUM += 1
return newedge
#------------------------------------------------------------------
class Halfedge(object):
def __init__(self,edge=None,pm=Edge.LE):
self.left = None # left Halfedge in the edge list
self.right = None # right Halfedge in the edge list
self.qnext = None # priority queue linked list pointer
self.edge = edge # edge list Edge
self.pm = pm
self.vertex = None # Site()
self.ystar = BIG_FLOAT
def dump(self):
print "Halfedge--------------------------"
print "left: ", self.left
print "right: ", self.right
print "edge: ", self.edge
print "pm: ", self.pm
print "vertex: ",
if self.vertex: self.vertex.dump()
else: print "None"
print "ystar: ", self.ystar
def __cmp__(self,other):
if self.ystar > other.ystar:
return 1
elif self.ystar < other.ystar:
return -1
elif self.vertex.x > other.vertex.x:
return 1
elif self.vertex.x < other.vertex.x:
return -1
else:
return 0
def leftreg(self,default):
if not self.edge:
return default
elif self.pm == Edge.LE:
return self.edge.reg[Edge.LE]
else:
return self.edge.reg[Edge.RE]
def rightreg(self,default):
if not self.edge:
return default
elif self.pm == Edge.LE:
return self.edge.reg[Edge.RE]
else:
return self.edge.reg[Edge.LE]
# returns True if p is to right of halfedge self
def isPointRightOf(self,pt):
e = self.edge
topsite = e.reg[1]
right_of_site = pt.x > topsite.x
if(right_of_site and self.pm == Edge.LE):
return True
if(not right_of_site and self.pm == Edge.RE):
return False
if(e.a == 1.0):
dyp = pt.y - topsite.y
dxp = pt.x - topsite.x
fast = 0;
if ((not right_of_site and e.b < 0.0) or (right_of_site and e.b >= 0.0)):
above = dyp >= e.b * dxp
fast = above
else:
above = pt.x + pt.y * e.b > e.c
if(e.b < 0.0):
above = not above
if (not above):
fast = 1
if (not fast):
dxs = topsite.x - (e.reg[0]).x
above = e.b * (dxp*dxp - dyp*dyp) < dxs*dyp*(1.0+2.0*dxp/dxs + e.b*e.b)
if(e.b < 0.0):
above = not above
else: # e.b == 1.0
yl = e.c - e.a * pt.x
t1 = pt.y - yl
t2 = pt.x - topsite.x
t3 = yl - topsite.y
above = t1*t1 > t2*t2 + t3*t3
if(self.pm==Edge.LE):
return above
else:
return not above
#--------------------------
# create a new site where the Halfedges el1 and el2 intersect
def intersect(self,other):
e1 = self.edge
e2 = other.edge
if (e1 is None) or (e2 is None):
return None
# if the two edges bisect the same parent return None
if e1.reg[1] is e2.reg[1]:
return None
d = e1.a * e2.b - e1.b * e2.a
if isEqual(d,0.0):
return None
xint = (e1.c*e2.b - e2.c*e1.b) / d
yint = (e2.c*e1.a - e1.c*e2.a) / d
if(cmp(e1.reg[1],e2.reg[1]) < 0):
he = self
e = e1
else:
he = other
e = e2
rightOfSite = xint >= e.reg[1].x
if((rightOfSite and he.pm == Edge.LE) or
(not rightOfSite and he.pm == Edge.RE)):
return None
# create a new site at the point of intersection - this is a new
# vector event waiting to happen
return Site(xint,yint)
#------------------------------------------------------------------
class EdgeList(object):
def __init__(self,xmin,xmax,nsites):
if xmin > xmax: xmin,xmax = xmax,xmin
self.hashsize = int(2*math.sqrt(nsites+4))
self.xmin = xmin
self.deltax = float(xmax - xmin)
self.hash = [None]*self.hashsize
self.leftend = Halfedge()
self.rightend = Halfedge()
self.leftend.right = self.rightend
self.rightend.left = self.leftend
self.hash[0] = self.leftend
self.hash[-1] = self.rightend
def insert(self,left,he):
he.left = left
he.right = left.right
left.right.left = he
left.right = he
def delete(self,he):
he.left.right = he.right
he.right.left = he.left
he.edge = Edge.DELETED
# Get entry from hash table, pruning any deleted nodes
def gethash(self,b):
if(b < 0 or b >= self.hashsize):
return None
he = self.hash[b]
if he is None or he.edge is not Edge.DELETED:
return he
# Hash table points to deleted half edge. Patch as necessary.
self.hash[b] = None
return None
def leftbnd(self,pt):
# Use hash table to get close to desired halfedge
bucket = int(((pt.x - self.xmin)/self.deltax * self.hashsize))
if(bucket < 0):
bucket =0;
if(bucket >=self.hashsize):
bucket = self.hashsize-1
he = self.gethash(bucket)
if(he is None):
i = 1
while True:
he = self.gethash(bucket-i)
if (he is not None): break;
he = self.gethash(bucket+i)
if (he is not None): break;
i += 1
# Now search linear list of halfedges for the corect one
if (he is self.leftend) or (he is not self.rightend and he.isPointRightOf(pt)):
he = he.right
while he is not self.rightend and he.isPointRightOf(pt):
he = he.right
he = he.left;
else:
he = he.left
while (he is not self.leftend and not he.isPointRightOf(pt)):
he = he.left
# Update hash table and reference counts
if(bucket > 0 and bucket < self.hashsize-1):
self.hash[bucket] = he
return he
#------------------------------------------------------------------
class PriorityQueue(object):
def __init__(self,ymin,ymax,nsites):
self.ymin = ymin
self.deltay = ymax - ymin
self.hashsize = int(4 * math.sqrt(nsites))
self.count = 0
self.minidx = 0
self.hash = []
for i in range(self.hashsize):
self.hash.append(Halfedge())
def __len__(self):
return self.count
def isEmpty(self):
return self.count == 0
def insert(self,he,site,offset):
he.vertex = site
he.ystar = site.y + offset
last = self.hash[self.getBucket(he)]
next = last.qnext
while((next is not None) and cmp(he,next) > 0):
last = next
next = last.qnext
he.qnext = last.qnext
last.qnext = he
self.count += 1
def delete(self,he):
if (he.vertex is not None):
last = self.hash[self.getBucket(he)]
while last.qnext is not he:
last = last.qnext
last.qnext = he.qnext
self.count -= 1
he.vertex = None
def getBucket(self,he):
bucket = int(((he.ystar - self.ymin) / self.deltay) * self.hashsize)
if bucket < 0: bucket = 0
if bucket >= self.hashsize: bucket = self.hashsize-1
if bucket < self.minidx: self.minidx = bucket
return bucket
def getMinPt(self):
while(self.hash[self.minidx].qnext is None):
self.minidx += 1
he = self.hash[self.minidx].qnext
x = he.vertex.x
y = he.ystar
return Site(x,y)
def popMinHalfedge(self):
curr = self.hash[self.minidx].qnext
self.hash[self.minidx].qnext = curr.qnext
self.count -= 1
return curr
#------------------------------------------------------------------
class SiteList(object):
def __init__(self,pointList):
self.__sites = []
self.__sitenum = 0
self.__xmin = pointList[0].x
self.__ymin = pointList[0].y
self.__xmax = pointList[0].x
self.__ymax = pointList[0].y
for i,pt in enumerate(pointList):
self.__sites.append(Site(pt.x,pt.y,i))
if pt.x < self.__xmin: self.__xmin = pt.x
if pt.y < self.__ymin: self.__ymin = pt.y
if pt.x > self.__xmax: self.__xmax = pt.x
if pt.y > self.__ymax: self.__ymax = pt.y
self.__sites.sort()
def setSiteNumber(self,site):
site.sitenum = self.__sitenum
self.__sitenum += 1
class Iterator(object):
def __init__(this,lst): this.generator = (s for s in lst)
def __iter__(this): return this
def next(this):
try:
return this.generator.next()
except StopIteration:
return None
def iterator(self):
return SiteList.Iterator(self.__sites)
def __iter__(self):
return SiteList.Iterator(self.__sites)
def __len__(self):
return len(self.__sites)
def _getxmin(self): return self.__xmin
def _getymin(self): return self.__ymin
def _getxmax(self): return self.__xmax
def _getymax(self): return self.__ymax
xmin = property(_getxmin)
ymin = property(_getymin)
xmax = property(_getxmax)
ymax = property(_getymax)
def clip_voronoi( edges, c, width, height, extent, exX, exY ):
""" Clip voronoi function based on code written for Inkscape
Copyright (C) 2010 Alvin Penner, penner@vaxxine.com
"""
def clip_line( x1, y1, x2, y2, w, h, x, y ):
if x1 < 0 - x and x2 < 0 - x:
return [ 0, 0, 0, 0 ]
if x1 > w + x and x2 > w + x:
return [ 0, 0, 0, 0 ]
if x1 < 0 - x:
y1 = ( y1 * x2 - y2 * x1 ) / ( x2 - x1 )
x1 = 0 - x
if x2 < 0 - x:
y2 = ( y1 * x2 - y2 * x1 ) / ( x2 - x1 )
x2 = 0 - x
if x1 > w + x:
y1 = y1 + ( w + x - x1 ) * ( y2 - y1 ) / ( x2 - x1 )
x1 = w + x
if x2 > w + x:
y2 = y1 + ( w + x - x1 ) *( y2 - y1 ) / ( x2 - x1 )
x2 = w + x
if y1 < 0 - y and y2 < 0 - y:
return [ 0, 0, 0, 0 ]
if y1 > h + y and y2 > h + y:
return [ 0, 0, 0, 0 ]
if x1 == x2 and y1 == y2:
return [ 0, 0, 0, 0 ]
if y1 < 0 - y:
x1 = ( x1 * y2 - x2 * y1 ) / ( y2 - y1 )
y1 = 0 - y
if y2 < 0 - y:
x2 = ( x1 * y2 - x2 * y1 ) / ( y2 - y1 )
y2 = 0 - y
if y1 > h + y:
x1 = x1 + ( h + y - y1 ) * ( x2 - x1 ) / ( y2 - y1 )
y1 = h + y
if y2 > h + y:
x2 = x1 + ( h + y - y1) * ( x2 - x1 ) / ( y2 - y1 )
y2 = h + y
return [ x1, y1, x2, y2 ]
# 'lines' is a list of all points coordinate pairs of all edges
lines = []
hasXMin = False
hasYMin = False
hasXMax = False
hasYMax = False
for edge in edges:
if edge[ 1 ] >= 0 and edge[ 2 ] >= 0: # two vertices
[ x1, y1, x2, y2 ] = clip_line( c.vertices[ edge[ 1 ] ][ 0 ], c.vertices[ edge[ 1 ] ][ 1 ], c.vertices[ edge[ 2 ] ][ 0 ], c.vertices[ edge[ 2 ] ][ 1 ], width, height, exX, exY )
elif edge[ 1 ] >= 0: # only one vertex
if c.lines[ edge[ 0 ] ][ 1 ] == 0: # vertical line
xtemp = c.lines[ edge[ 0 ] ][ 2 ] / c.lines[ edge[ 0 ] ][ 0 ]
if c.vertices[ edge[ 1 ] ][ 1 ] > ( height + exY ) / 2:
ytemp = height + exY
else:
ytemp = 0 - exX
else:
xtemp = width + exX
ytemp = ( c.lines[ edge[ 0 ] ][ 2 ] - ( width + exX ) * c.lines[ edge[ 0 ] ][ 0 ] ) / c.lines[ edge[ 0 ] ][ 1 ]
[ x1, y1, x2, y2 ] = clip_line( c.vertices[ edge[ 1 ] ][ 0 ], c.vertices[ edge[ 1 ] ][ 1 ], xtemp, ytemp, width, height, exX, exY )
elif edge[ 2 ] >= 0: # only one vertex
if c.lines[ edge[ 0 ] ][ 1 ] == 0: # vertical line
xtemp = c.lines[ edge[ 0 ] ][ 2 ] / c.lines[ edge[ 0 ] ][ 0 ]
if c.vertices[ edge[ 2 ] ][ 1 ] > ( height + exY ) / 2:
ytemp = height + exY
else:
ytemp = 0.0 - exY
else:
xtemp = 0.0 - exX
ytemp = c.lines[ edge[ 0 ] ][ 2 ] / c.lines[ edge[ 0 ] ][ 1 ]
[ x1, y1, x2, y2 ] = clip_line( xtemp, ytemp, c.vertices[ edge[ 2 ] ][ 0 ], c.vertices[ edge[ 2 ] ][ 1 ], width, height, exX, exY )
if x1 or x2 or y1 or y2:
lines.append( ( x1 + extent["xmin"], y1 + extent["ymin"] ) )
lines.append( ( x2 + extent["xmin"], y2 + extent["ymin"] ) )
if 0 - exX in ( x1, x2 ):
hasXMin = True
if 0 - exY in ( y1, y2 ):
hasYMin = True
if height + exY in ( y1, y2 ):
hasYMax = True
if width + exX in ( x1, x2 ):
hasXMax = True
if hasXMin:
if hasYMax:
lines.append( ( extent["xmin"] - exX, height + extent["ymin"] + exY ) )
if hasYMin:
lines.append( ( extent["xmin"] - exX, extent["ymin"] - exY ) )
if hasXMax:
if hasYMax:
lines.append( ( width + extent["xmin"] + exX, height + extent["ymin"] + exY ) )
if hasYMin:
lines.append( ( width + extent["xmin"] + exX, extent["ymin"] - exY ) )
return lines
def lines_as_wkt(lines):
if lines:
multipoint_wkt = ''
for line in lines:
multipoint_wkt += '%s %s,' % (line[0],line[1])
return "MULTIPOINT(%s)" % multipoint_wkt[:-1]
else:
return None
pts = []
c=Context()
# table_name text,table_key text,geom_col text)
rv = plpy.execute("SELECT ST_SRID(%s) as srid FROM %s" % (geom_col, table_name), 1)
srid = rv[0]['srid']
if srid <= 0:
srid = -1
# calculate extent
extent = {}
rv = plpy.execute("SELECT ST_SetSRID(ST_extent(%s), %i) as extent FROM %s" % (geom_col, srid, table_name), 1)
extentWKB = rv[0]['extent']
rv = plpy.execute("SELECT ST_XMin('%s'::geometry), ST_XMax('%s'::geometry), ST_YMin('%s'::geometry), ST_YMax('%s'::geometry)" % (extentWKB,extentWKB,extentWKB,extentWKB))
extent["xmin"] = rv[0]["st_xmin"]
extent["xmax"] = rv[0]["st_xmax"]
extent["ymin"] = rv[0]["st_ymin"]
extent["ymax"] = rv[0]["st_ymax"]
width = extent["xmax"] - extent["xmin"]
height = extent["ymax"] - extent["ymin"]
plpy.debug("got srid: %i" % srid)
plpy.debug("got extent: %s" % extent)
plpy.debug("got width: %s" % width)
plpy.debug("got height: %s" % height)
# we need to use distinct, because the code barfs if we have duplicate points
for row in plpy.execute("SELECT DISTINCT st_x(%s) as x, st_y(%s) as y FROM %s" % (geom_col, geom_col, table_name)):
pts.append(Site(row["x"] - extent["xmin"],row["y"] - extent["ymin"])) # note reative coordinates
# do the real work
sl = SiteList(pts)
voronoi(sl,c)
for site, edges in c.polygons.iteritems():
# trim the extracted polygons to the extent of the input points
lines = clip_voronoi( edges, c, width, height, extent, 0, 0 )
lines_wkt = lines_as_wkt(lines)
if lines_wkt is not None:
rv = plpy.execute("SELECT ST_ConvexHull(ST_MPointFromText('%s',%i)) AS the_geom" % (lines_wkt,srid))
yield (site+1, rv[0]['the_geom'])
$$ LANGUAGE plpythonu;
CREATE OR REPLACE FUNCTION voronoi(table_name text) returns SETOF record as $$
SELECT * from voronoi($1, 'the_geom') as (id integer,the_geom geometry);
$$ LANGUAGE SQL;
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