voronoi.py 26.8 KB
Newer Older
1
#!/usr/bin/env python
2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31
#############################################################################
#
# Voronoi diagram calculator/ Delaunay triangulator
# Translated to Python by Bill Simons
# September, 2005
#
# 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
#
#############################################################################

Thomas Holder's avatar
Thomas Holder committed
32 33
from __future__ import print_function

34
def usage():
Thomas Holder's avatar
Thomas Holder committed
35
    print("""
36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71
voronoi - compute Voronoi diagram or Delaunay triangulation

voronoi [-t -p -d]  [filename]

Voronoi reads from filename (or standard input if no filename given) for a set 
of points in the plane and writes either the Voronoi diagram or the Delaunay 
triangulation to the standard output.  Each input line should consist of two 
real numbers, separated by white space.

If option -t is present, the Delaunay triangulation is produced. 
Each output line is a triple i j k, which are the indices of the three points
in a Delaunay triangle. Points are numbered starting at 0.

If option -t is not present, the Voronoi diagram is produced.  
There are four output record types.

s a b      indicates that an input point at coordinates a b was seen.
l a b c    indicates a line with equation ax + by = c.
v a b      indicates a vertex at a b.
e l v1 v2  indicates a Voronoi segment which is a subsegment of line number l
           with endpoints numbered v1 and v2.  If v1 or v2 is -1, the line 
           extends to infinity.

Other options include:

d    Print debugging info

p    Produce output suitable for input to plot (1), rather than the forms 
     described above.

On unsorted data uniformly distributed in the unit square, voronoi uses about 
20n+140 bytes of storage.

AUTHOR
Steve J. Fortune (1987) A Sweepline Algorithm for Voronoi Diagrams,
Algorithmica 2, 153-174.
Thomas Holder's avatar
Thomas Holder committed
72
""")
73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127

#############################################################################
#
# For programmatic use two functions are available:
#
#   computeVoronoiDiagram(points)
#
#        Takes a list of point objects (which must have x and y fields).
#        Returns a 3-tuple of:
#
#           (1) a list of 2-tuples, which are the x,y coordinates of the 
#               Voronoi diagram vertices
#           (2) a list of 3-tuples (a,b,c) which are the equations of the
#               lines in the Voronoi diagram: a*x + b*y = c
#           (3) a list of 3-tuples, (l, v1, v2) representing edges of the 
#               Voronoi diagram.  l is the index of the line, v1 and v2 are
#               the indices of the vetices at the end of the edge.  If 
#               v1 or v2 is -1, the line extends to infinity.
#
#   computeDelaunayTriangulation(points):
#
#        Takes a list of point objects (which must have x and y fields).
#        Returns a list of 3-tuples: the indices of the points that form a
#        Delaunay triangle.
#
#############################################################################
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

    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):
Thomas Holder's avatar
Thomas Holder committed
128
            print("site (%d) at %f %f" % (s.sitenum, s.x, s.y))
129 130 131 132 133
        elif(self.triangulate):
            pass
        elif(self.plot):
            self.circle (s.x, s.y, cradius)
        elif(self.doPrint):
Thomas Holder's avatar
Thomas Holder committed
134
            print("s %f %f" % (s.x, s.y))
135 136 137 138

    def outVertex(self,s):
        self.vertices.append((s.x,s.y))
        if(self.debug):
Thomas Holder's avatar
Thomas Holder committed
139
            print("vertex(%d) at %f %f" % (s.sitenum, s.x, s.y))
140 141 142
        elif(self.triangulate):
            pass
        elif(self.doPrint and not self.plot):
Thomas Holder's avatar
Thomas Holder committed
143
            print("v %f %f" % (s.x,s.y))
144 145 146 147

    def outTriple(self,s1,s2,s3):
        self.triangles.append((s1.sitenum, s2.sitenum, s3.sitenum))
        if(self.debug):
Thomas Holder's avatar
Thomas Holder committed
148
            print("circle through left=%d right=%d bottom=%d" % (s1.sitenum, s2.sitenum, s3.sitenum))
149
        elif(self.triangulate and self.doPrint and not self.plot):
Thomas Holder's avatar
Thomas Holder committed
150
            print("%d %d %d" % (s1.sitenum, s2.sitenum, s3.sitenum))
151 152 153 154

    def outBisector(self,edge):
        self.lines.append((edge.a, edge.b, edge.c))
        if(self.debug):
Thomas Holder's avatar
Thomas Holder committed
155
            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))
156 157 158 159
        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):
Thomas Holder's avatar
Thomas Holder committed
160
            print("l %f %f %f" % (edge.a, edge.b, edge.c))
161 162 163 164 165 166 167 168 169 170 171 172 173

    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
        self.edges.append((edge.edgenum,sitenumL,sitenumR))
        if(not self.triangulate):
            if self.plot:
                self.clip_line(edge)
            elif(self.doPrint): 
Thomas Holder's avatar
Thomas Holder committed
174 175 176
                print("e %d" % edge.edgenum, end=' ')
                print(" %d " % sitenumL, end=' ')
                print("%d" % sitenumR)
177 178 179 180 181 182 183 184 185 186 187 188 189 190 191

#------------------------------------------------------------------
def voronoi(siteList,context):
    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()

192
        if (newsite and (priorityQ.isEmpty() or newsite < minpt)):
193 194 195 196 197 198 199 200 201 202 203 204 205 206 207 208 209 210 211 212 213 214 215 216 217 218 219 220 221 222 223 224 225 226 227 228 229 230 231 232 233 234 235 236 237 238 239 240 241 242 243 244 245 246 247 248 249 250 251 252 253 254 255 256 257 258 259 260 261 262 263 264 265 266 267 268 269 270 271 272 273 274 275 276 277 278 279 280 281 282 283 284 285 286 287 288 289 290 291 292 293 294 295 296 297 298 299 300 301 302 303 304 305 306 307 308 309 310 311 312 313 314 315 316 317 318 319 320 321 322 323 324 325 326 327 328 329
            # 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

#------------------------------------------------------------------
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):
Thomas Holder's avatar
Thomas Holder committed
330
        print("Site #%d (%g, %g)" % (self.sitenum,self.x,self.y))
331 332 333 334 335 336 337 338 339 340 341 342 343

    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

344 345 346
    def __lt__(self, other):
        return self.__cmp__(other) < 0

347 348 349 350 351 352 353 354 355 356 357 358 359 360 361 362 363 364 365 366 367
    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):
Thomas Holder's avatar
Thomas Holder committed
368 369 370
        print("(#%d a=%g, b=%g, c=%g)" % (self.edgenum,self.a,self.b,self.c))
        print("ep",self.ep)
        print("reg",self.reg)
371 372 373 374 375 376 377 378 379 380 381 382 383 384 385 386 387 388 389 390 391 392 393 394 395 396 397 398 399 400 401 402

    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
403 404
            if dy <= 0:
                dy = 0.01
405 406 407 408 409 410 411 412 413 414 415 416 417 418 419 420 421 422 423 424
            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):
Thomas Holder's avatar
Thomas Holder committed
425 426 427 428 429 430
        print("Halfedge--------------------------")
        print("left: ",    self.left)
        print("right: ",   self.right)
        print("edge: ",    self.edge)
        print("pm: ",      self.pm)
        print("vertex: ", end=' ')
431
        if self.vertex: self.vertex.dump()
Thomas Holder's avatar
Thomas Holder committed
432 433
        else: print("None")
        print("ystar: ",   self.ystar)
434 435 436 437 438 439 440 441 442 443 444 445 446 447


    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

448 449 450
    def __lt__(self, other):
        return self.__cmp__(other) < 0

451 452 453 454 455 456 457 458 459 460 461 462 463 464 465 466 467 468 469 470 471 472 473 474 475 476 477 478 479 480 481 482 483 484 485 486 487 488 489 490 491 492 493 494 495 496 497 498 499 500 501 502 503 504 505 506 507 508 509 510 511 512 513 514 515 516 517 518 519 520 521 522 523 524 525 526 527
    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
528
        if e1.reg[1] < e2.reg[1]:
529 530 531 532 533 534 535 536 537 538 539 540 541 542 543 544 545 546 547 548 549 550 551 552 553 554 555 556 557 558 559 560 561 562 563 564 565 566 567 568 569 570 571 572 573 574 575 576 577 578 579 580 581 582 583 584 585 586 587 588 589 590 591 592 593 594 595 596 597 598 599 600 601 602 603 604 605 606 607 608 609 610 611 612 613 614 615 616 617 618 619 620 621 622 623 624 625 626 627 628 629 630 631 632 633 634 635 636 637 638 639 640 641 642 643 644 645
            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
646
        while((next is not None) and he > next):
647 648 649 650 651 652 653 654 655 656 657 658 659 660 661 662 663 664 665 666 667 668 669 670 671 672 673 674 675 676 677 678 679 680 681 682 683 684 685 686 687 688 689 690 691 692 693 694 695 696 697 698 699 700 701 702 703 704 705 706 707 708 709 710
            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:
711
                return next(this.generator)
712 713 714 715 716 717 718 719 720 721 722 723 724 725 726 727 728 729 730 731 732 733 734 735 736 737 738 739 740 741 742 743 744 745 746 747 748 749 750 751 752 753 754 755 756 757 758 759 760
            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 computeVoronoiDiagram(points):
    """ Takes a list of point objects (which must have x and y fields).
        Returns a 3-tuple of:

           (1) a list of 2-tuples, which are the x,y coordinates of the 
               Voronoi diagram vertices
           (2) a list of 3-tuples (a,b,c) which are the equations of the
               lines in the Voronoi diagram: a*x + b*y = c
           (3) a list of 3-tuples, (l, v1, v2) representing edges of the 
               Voronoi diagram.  l is the index of the line, v1 and v2 are
               the indices of the vetices at the end of the edge.  If 
               v1 or v2 is -1, the line extends to infinity.
    """
    siteList = SiteList(points)
    context  = Context()
    voronoi(siteList,context)
    return (context.vertices,context.lines,context.edges)

#------------------------------------------------------------------
def computeDelaunayTriangulation(points):
    """ Takes a list of point objects (which must have x and y fields).
        Returns a list of 3-tuples: the indices of the points that form a
        Delaunay triangle.
    """
    siteList = SiteList(points)
    context  = Context()
761
    context.triangulate = True
762 763 764 765 766 767 768 769 770 771 772 773 774 775 776 777 778 779 780 781 782 783 784 785 786 787 788 789 790 791 792 793 794 795 796 797 798 799 800
    voronoi(siteList,context)
    return context.triangles

#-----------------------------------------------------------------------------
if __name__=="__main__":
    try:
        optlist,args = getopt.getopt(sys.argv[1:],"thdp")
    except getopt.GetoptError:
        usage()
        sys.exit(2)
      
    doHelp = 0
    c = Context()
    c.doPrint = 1
    for opt in optlist:
        if opt[0] == "-d":  c.debug = 1
        if opt[0] == "-p":  c.plot  = 1
        if opt[0] == "-t":  c.triangulate = 1
        if opt[0] == "-h":  doHelp = 1

    if not doHelp:
        pts = []
        fp = sys.stdin
        if len(args) > 0:
            fp = open(args[0],'r')
        for line in fp:
            fld = line.split()
            x = float(fld[0])
            y = float(fld[1])
            pts.append(Site(x,y))
        if len(args) > 0: fp.close()

    if doHelp or len(pts) == 0:
        usage()
        sys.exit(2)

    sl = SiteList(pts)
    voronoi(sl,c)