Future's Algorithm

.. for calculating Vornoi diagrams.

contrib/voronoi/Doc

@@ -0,0 +1,30 @@
+voronoi - compute Voronoi diagram or Delaunay triangulation
+SYNOPSIS
+	voronoi [-s -t] <pointfile >outputfile
+
+Voronoi reads the standard input 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 this option is not present, the
+Voronoi diagram is produced.  There are four output record types.
+	s a b
+indicates that an input point at coordinates 
+	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.
+
+AUTHOR
+Steve J. Fortune (1987) A Sweepline Algorithm for Voronoi Diagrams,
+Algorithmica 2, 153-174.

contrib/voronoi/Makefile-testing

@@ -0,0 +1,14 @@
+C=edgelist.c geometry.c heap.c main.c memory.c output.c voronoi.c 
+O=edgelist.o geometry.o heap.o main.o memory.o output.o voronoi.o
+
+tt: voronoi t
+	./voronoi <t >tt
+voronoi: $O
+	cc -o voronoi $O -lm
+$O:vdefs.h
+
+voronoi.tar : $C vdefs.h Makefile Doc t
+	tar -cf voronoi.tar $C vdefs.h Makefile Doc t
+
+mailable:	$C vdefs.h Makefile t
+	bundle $C vdefs.h Makefile t > mailable

contrib/voronoi/edgelist.c

@@ -0,0 +1,188 @@
+
+/*** EDGELIST.C ***/
+
+#include "vdefs.h"
+
+int ELhashsize ;
+Site * bottomsite ;
+Freelist hfl ;
+Halfedge * ELleftend, * ELrightend, **ELhash ;
+
+int ntry, totalsearch ;
+
+void
+ELinitialize(void)
+    {
+    int i ;
+
+    freeinit(&hfl, sizeof(Halfedge)) ;
+    ELhashsize = 2 * sqrt_nsites ;
+    ELhash = (Halfedge **)myalloc( sizeof(*ELhash) * ELhashsize) ;
+    for (i = 0  ; i < ELhashsize  ; i++)
+        {
+        ELhash[i] = (Halfedge *)NULL ;
+        }
+    ELleftend = HEcreate((Edge *)NULL, 0) ;
+    ELrightend = HEcreate((Edge *)NULL, 0) ;
+    ELleftend->ELleft = (Halfedge *)NULL ;
+    ELleftend->ELright = ELrightend ;
+    ELrightend->ELleft = ELleftend ;
+    ELrightend->ELright = (Halfedge *)NULL ;
+    ELhash[0] = ELleftend ;
+    ELhash[ELhashsize-1] = ELrightend ;
+    }
+
+Halfedge *
+HEcreate(Edge * e, int pm)
+    {
+    Halfedge * answer ;
+
+    answer = (Halfedge *)getfree(&hfl) ;
+    answer->ELedge = e ;
+    answer->ELpm = pm ;
+    answer->PQnext = (Halfedge *)NULL ;
+    answer->vertex = (Site *)NULL ;
+    answer->ELrefcnt = 0 ;
+    return (answer) ;
+    }
+
+void
+ELinsert(Halfedge * lb, Halfedge * new)
+    {
+    new->ELleft = lb ;
+    new->ELright = lb->ELright ;
+    (lb->ELright)->ELleft = new ;
+    lb->ELright = new ;
+    }
+
+/* Get entry from hash table, pruning any deleted nodes */
+
+Halfedge *
+ELgethash(int b)
+    {
+    Halfedge * he ;
+
+    if ((b < 0) || (b >= ELhashsize))
+        {
+        return ((Halfedge *)NULL) ;
+        }
+    he = ELhash[b] ;
+    if ((he == (Halfedge *)NULL) || (he->ELedge != (Edge *)DELETED))
+        {
+        return (he) ;
+        }
+    /* Hash table points to deleted half edge.  Patch as necessary. */
+    ELhash[b] = (Halfedge *)NULL ;
+    if ((--(he->ELrefcnt)) == 0)
+        {
+        makefree((Freenode *)he, (Freelist *)&hfl) ;
+        }
+    return ((Halfedge *)NULL) ;
+    }
+
+Halfedge *
+ELleftbnd(Point * p)
+    {
+    int i, bucket ;
+    Halfedge * he ;
+
+    /* Use hash table to get close to desired halfedge */
+    bucket = (p->x - xmin) / deltax * ELhashsize ;
+    if (bucket < 0)
+        {
+        bucket = 0 ;
+        }
+    if (bucket >= ELhashsize)
+        {
+        bucket = ELhashsize - 1 ;
+        }
+    he = ELgethash(bucket) ;
+    if  (he == (Halfedge *)NULL)
+        {
+        for (i = 1 ; 1 ; i++)
+            {
+            if ((he = ELgethash(bucket-i)) != (Halfedge *)NULL)
+                {
+                break ;
+                }
+            if ((he = ELgethash(bucket+i)) != (Halfedge *)NULL)
+                {
+                break ;
+                }
+            }
+        totalsearch += i ;
+        }
+    ntry++ ;
+    /* Now search linear list of halfedges for the corect one */
+    if (he == ELleftend || (he != ELrightend && right_of(he,p)))
+        {
+        do  {
+            he = he->ELright ;
+            } while (he != ELrightend && right_of(he,p)) ;
+        he = he->ELleft ;
+        }
+    else
+        {
+        do  {
+            he = he->ELleft ;
+            } while (he != ELleftend && !right_of(he,p)) ;
+        }
+    /*** Update hash table and reference counts ***/
+    if ((bucket > 0) && (bucket < ELhashsize-1))
+        {
+        if (ELhash[bucket] != (Halfedge *)NULL)
+            {
+            (ELhash[bucket]->ELrefcnt)-- ;
+            }
+        ELhash[bucket] = he ;
+        (ELhash[bucket]->ELrefcnt)++ ;
+        }
+    return (he) ;
+    }
+
+/*** This delete routine can't reclaim node, since pointers from hash
+ : table may be present.
+ ***/
+
+void
+ELdelete(Halfedge * he)
+    {
+    (he->ELleft)->ELright = he->ELright ;
+    (he->ELright)->ELleft = he->ELleft ;
+    he->ELedge = (Edge *)DELETED ;
+    }
+
+Halfedge *
+ELright(Halfedge * he)
+    {
+    return (he->ELright) ;
+    }
+
+Halfedge *
+ELleft(Halfedge * he)
+    {
+    return (he->ELleft) ;
+    }
+
+Site *
+leftreg(Halfedge * he)
+    {
+    if (he->ELedge == (Edge *)NULL)
+        {
+        return(bottomsite) ;
+        }
+    return (he->ELpm == le ? he->ELedge->reg[le] :
+        he->ELedge->reg[re]) ;
+    }
+
+Site *
+rightreg(Halfedge * he)
+    {
+    if (he->ELedge == (Edge *)NULL)
+        {
+        return(bottomsite) ;
+        }
+    return (he->ELpm == le ? he->ELedge->reg[re] :
+        he->ELedge->reg[le]) ;
+    }
+

contrib/voronoi/geometry.c

@@ -0,0 +1,221 @@
+
+/*** GEOMETRY.C ***/
+
+#include <math.h>
+#include "vdefs.h"
+
+float deltax, deltay ;
+int nedges, sqrt_nsites, nvertices ;
+Freelist efl ;
+
+void
+geominit(void)
+    {
+    freeinit(&efl, sizeof(Edge)) ;
+    nvertices = nedges = 0 ;
+    sqrt_nsites = sqrt(nsites+4) ;
+    deltay = ymax - ymin ;
+    deltax = xmax - xmin ;
+    }
+
+Edge *
+bisect(Site * s1, Site * s2)
+    {
+    float dx, dy, adx, ady ;
+    Edge * newedge ;
+
+    newedge = (Edge *)getfree(&efl) ;
+    newedge->reg[0] = s1 ;
+    newedge->reg[1] = s2 ;
+    ref(s1) ;
+    ref(s2) ;
+    newedge->ep[0] = newedge->ep[1] = (Site *)NULL ;
+    dx = s2->coord.x - s1->coord.x ;
+    dy = s2->coord.y - s1->coord.y ;
+    adx = dx>0 ? dx : -dx ;
+    ady = dy>0 ? dy : -dy ;
+    newedge->c = s1->coord.x * dx + s1->coord.y * dy + (dx*dx +
+dy*dy) * 0.5 ;
+    if (adx > ady)
+        {
+        newedge->a = 1.0 ;
+        newedge->b = dy/dx ;
+        newedge->c /= dx ;
+        }
+    else
+        {
+        newedge->b = 1.0 ;
+        newedge->a = dx/dy ;
+        newedge->c /= dy ;
+        }
+    newedge->edgenbr = nedges ;
+    out_bisector(newedge) ;
+    nedges++ ;
+    return (newedge) ;
+    }
+
+Site *
+intersect(Halfedge * el1, Halfedge * el2)
+    {
+    Edge * e1, * e2, * e ;
+    Halfedge * el ;
+    float d, xint, yint ;
+    int right_of_site ;
+    Site * v ;
+
+    e1 = el1->ELedge ;
+    e2 = el2->ELedge ;
+    if ((e1 == (Edge*)NULL) || (e2 == (Edge*)NULL))
+        {
+        return ((Site *)NULL) ;
+        }
+    if (e1->reg[1] == e2->reg[1])
+        {
+        return ((Site *)NULL) ;
+        }
+    d = (e1->a * e2->b) - (e1->b * e2->a) ;
+    if ((-1.0e-10 < d) && (d < 1.0e-10))
+        {
+        return ((Site *)NULL) ;
+        }
+    xint = (e1->c * e2->b - e2->c * e1->b) / d ;
+    yint = (e2->c * e1->a - e1->c * e2->a) / d ;
+    if ((e1->reg[1]->coord.y < e2->reg[1]->coord.y) ||
+        (e1->reg[1]->coord.y == e2->reg[1]->coord.y &&
+        e1->reg[1]->coord.x < e2->reg[1]->coord.x))
+        {
+        el = el1 ;
+        e = e1 ;
+        }
+    else
+        {
+        el = el2 ;
+        e = e2 ;
+        }
+    right_of_site = (xint >= e->reg[1]->coord.x) ;
+    if ((right_of_site && (el->ELpm == le)) ||
+       (!right_of_site && (el->ELpm == re)))
+        {
+        return ((Site *)NULL) ;
+        }
+    v = (Site *)getfree(&sfl) ;
+    v->refcnt = 0 ;
+    v->coord.x = xint ;
+    v->coord.y = yint ;
+    return (v) ;
+    }
+
+/*** returns 1 if p is to right of halfedge e ***/
+
+int
+right_of(Halfedge * el, Point * p)
+    {
+    Edge * e ;
+    Site * topsite ;
+    int right_of_site, above, fast ;
+    float dxp, dyp, dxs, t1, t2, t3, yl ;
+
+    e = el->ELedge ;
+    topsite = e->reg[1] ;
+    right_of_site = (p->x > topsite->coord.x) ;
+    if (right_of_site && (el->ELpm == le))
+        {
+        return (1) ;
+        }
+    if(!right_of_site && (el->ELpm == re))
+        {
+        return (0) ;
+        }
+    if (e->a == 1.0)
+        {
+        dyp = p->y - topsite->coord.y ;
+        dxp = p->x - topsite->coord.x ;
+        fast = 0 ;
+        if ((!right_of_site & (e->b < 0.0)) ||
+         (right_of_site & (e->b >= 0.0)))
+            {
+            fast = above = (dyp >= e->b*dxp) ;
+            }
+        else
+            {
+            above = ((p->x + p->y * e->b) > (e->c)) ;
+            if (e->b < 0.0)
+                {
+                above = !above ;
+                }
+            if (!above)
+                {
+                fast = 1 ;
+                }
+            }
+        if (!fast)
+            {
+            dxs = topsite->coord.x - (e->reg[0])->coord.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 = !above ;
+                }
+            }
+        }
+    else  /*** e->b == 1.0 ***/
+        {
+        yl = e->c - e->a * p->x ;
+        t1 = p->y - yl ;
+        t2 = p->x - topsite->coord.x ;
+        t3 = yl - topsite->coord.y ;
+        above = ((t1*t1) > ((t2 * t2) + (t3 * t3))) ;
+        }
+    return (el->ELpm == le ? above : !above) ;
+    }
+
+void
+endpoint(Edge * e, int lr, Site * s)
+    {
+    e->ep[lr] = s ;
+    ref(s) ;
+    if (e->ep[re-lr] == (Site *)NULL)
+        {
+        return ;
+        }
+    out_ep(e) ;
+    deref(e->reg[le]) ;
+    deref(e->reg[re]) ;
+    makefree((Freenode *)e, (Freelist *) &efl) ;
+    }
+
+float
+dist(Site * s, Site * t)
+    {
+    float dx,dy ;
+
+    dx = s->coord.x - t->coord.x ;
+    dy = s->coord.y - t->coord.y ;
+    return (sqrt(dx*dx + dy*dy)) ;
+    }
+
+void
+makevertex(Site * v)
+    {
+    v->sitenbr = nvertices++ ;
+    out_vertex(v) ;
+    }
+
+void
+deref(Site * v)
+    {
+    if (--(v->refcnt) == 0 )
+        {
+        makefree((Freenode *)v, (Freelist *)&sfl) ;
+        }
+    }
+
+void
+ref(Site * v)
+    {
+    ++(v->refcnt) ;
+    }
+

contrib/voronoi/heap.c

@@ -0,0 +1,118 @@
+
+/*** HEAP.C ***/
+
+
+#include "vdefs.h"
+
+int PQmin, PQcount, PQhashsize ;
+Halfedge * PQhash ;
+
+void
+PQinsert(Halfedge * he, Site * v, float offset)
+    {
+    Halfedge * last, * next ;
+
+    he->vertex = v ;
+    ref(v) ;
+    he->ystar = v->coord.y + offset ;
+    last = &PQhash[ PQbucket(he)] ;
+    while ((next = last->PQnext) != (Halfedge *)NULL &&
+      (he->ystar  > next->ystar  ||
+      (he->ystar == next->ystar &&
+      v->coord.x > next->vertex->coord.x)))
+        {
+        last = next ;
+        }
+    he->PQnext = last->PQnext ;
+    last->PQnext = he ;
+    PQcount++ ;
+    }
+
+void
+PQdelete(Halfedge * he)
+    {
+    Halfedge * last;
+
+    if(he ->  vertex != (Site *) NULL)
+        {
+        last = &PQhash[PQbucket(he)] ;
+        while (last -> PQnext != he)
+            {
+            last = last->PQnext ;
+            }
+        last->PQnext = he->PQnext;
+        PQcount-- ;
+        deref(he->vertex) ;
+        he->vertex = (Site *)NULL ;
+        }
+    }
+
+int
+PQbucket(Halfedge * he)
+    {
+    int bucket ;
+
+
+    if	    (he->ystar < ymin)  bucket = 0;
+    else if (he->ystar >= ymax) bucket = PQhashsize-1;
+    else 			bucket = (he->ystar - ymin)/deltay * PQhashsize;
+    if (bucket < 0)
+        {
+        bucket = 0 ;
+        }
+    if (bucket >= PQhashsize)
+        {
+        bucket = PQhashsize-1 ;
+        }
+    if (bucket < PQmin)
+        {
+        PQmin = bucket ;
+        }
+    return (bucket);
+    }
+
+int
+PQempty(void)
+    {
+    return (PQcount == 0) ;
+    }
+
+
+Point
+PQ_min(void)
+    {
+    Point answer ;
+
+    while (PQhash[PQmin].PQnext == (Halfedge *)NULL)
+        {
+        ++PQmin ;
+        }
+    answer.x = PQhash[PQmin].PQnext->vertex->coord.x ;
+    answer.y = PQhash[PQmin].PQnext->ystar ;
+    return (answer) ;
+    }
+
+Halfedge *
+PQextractmin(void)
+    {
+    Halfedge * curr ;
+
+    curr = PQhash[PQmin].PQnext ;
+    PQhash[PQmin].PQnext = curr->PQnext ;
+    PQcount-- ;
+    return (curr) ;
+    }
+
+void
+PQinitialize(void)
+    {
+    int i ;
+
+    PQcount = PQmin = 0 ;
+    PQhashsize = 4 * sqrt_nsites ;
+    PQhash = (Halfedge *)myalloc(PQhashsize * sizeof *PQhash) ;
+    for (i = 0 ; i < PQhashsize; i++)
+        {
+        PQhash[i].PQnext = (Halfedge *)NULL ;
+        }
+    }

contrib/voronoi/main.c

@@ -0,0 +1,161 @@
+/*** MAIN.C ***/
+
+#include <stdio.h>
+#include <stdlib.h>  /* realloc(), qsort() */
+
+#include "vdefs.h"
+
+Site * readone(void), * nextone(void) ;
+void readsites(void) ;
+
+int sorted, triangulate, plot, debug, nsites, siteidx ;
+float xmin, xmax, ymin, ymax ;
+Site * sites ;
+Freelist sfl ;
+
+int
+main(int argc, char *argv[])
+    {
+    int c ;
+    Site *(*next)() ;
+
+    sorted = triangulate = plot = debug = 0 ;
+    while ((c = getopt(argc, argv, "dpst")) != EOF)
+        {
+        switch(c)
+            {
+            case 'd':
+                debug = 1 ;
+                break ;
+            case 's':
+                sorted = 1 ;
+                break ;
+            case 't':
+                triangulate = 1 ;
+                break ;
+            case 'p':
+                plot = 1 ;
+                break ;
+            }
+        }
+
+    freeinit(&sfl, sizeof(Site)) ;
+    if (sorted)
+        {
+        scanf("%d %f %f %f %f", &nsites, &xmin, &xmax, &ymin, &ymax) ;
+        next = readone ;
+        }
+    else
+        {
+        readsites() ;
+        next = nextone ;
+        }
+    siteidx = 0 ;
+    geominit() ;
+    if (plot)
+        {
+        plotinit() ;
+        }
+    voronoi(next) ;
+    return (0) ;
+    }
+
+/*** sort sites on y, then x, coord ***/
+
+int
+scomp(const void * vs1, const void * vs2)
+    {
+    Point * s1 = (Point *)vs1 ;
+    Point * s2 = (Point *)vs2 ;
+
+    if (s1->y < s2->y)
+        {
+        return (-1) ;
+        }
+    if (s1->y > s2->y)
+        {
+        return (1) ;
+        }
+    if (s1->x < s2->x)
+        {
+        return (-1) ;
+        }
+    if (s1->x > s2->x)
+        {
+        return (1) ;
+        }
+    return (0) ;
+    }
+
+/*** return a single in-storage site ***/
+
+Site *
+nextone(void)
+    {
+    Site * s ;
+
+    if (siteidx < nsites)
+        {
+        s = &sites[siteidx++];
+        return (s) ;
+        }
+    else
+        {
+        return ((Site *)NULL) ;
+        }
+    }
+
+/*** read all sites, sort, and compute xmin, xmax, ymin, ymax ***/
+
+void
+readsites(void)
+    {
+    int i ;
+
+    nsites = 0 ;
+    sites = (Site *) myalloc(4000 * sizeof(Site));
+    while (scanf("%f %f", &sites[nsites].coord.x,
+&sites[nsites].coord.y) !=EOF)
+        {
+        sites[nsites].sitenbr = nsites ;
+        sites[nsites++].refcnt = 0 ;
+        if (nsites % 4000 == 0)
+            sites = (Site *)
+realloc(sites,(nsites+4000)*sizeof(Site));
+        }
+
+    qsort((void *)sites, nsites, sizeof(Site), scomp) ;
+    xmin = sites[0].coord.x ;
+    xmax = sites[0].coord.x ;
+    for (i = 1 ; i < nsites ; ++i)
+        {
+        if(sites[i].coord.x < xmin)
+            {
+            xmin = sites[i].coord.x ;
+            }
+        if (sites[i].coord.x > xmax)
+            {
+            xmax = sites[i].coord.x ;
+            }
+        }
+    ymin = sites[0].coord.y ;
+    ymax = sites[nsites-1].coord.y ;
+    }
+
+/*** read one site ***/
+
+Site *
+readone(void)
+    {
+    Site * s ;
+
+    s = (Site *)getfree(&sfl) ;
+    s->refcnt = 0 ;
+    s->sitenbr = siteidx++ ;
+    if (scanf("%f %f", &(s->coord.x), &(s->coord.y)) == EOF)
+        {
+        return ((Site *)NULL ) ;
+        }
+    return (s) ;
+    }
+

contrib/voronoi/memory.c

@@ -0,0 +1,57 @@
+
+/*** MEMORY.C ***/
+
+#include <stdio.h>
+#include <stdlib.h>  /* malloc(), exit() */
+
+#include "vdefs.h"
+
+extern int sqrt_nsites, siteidx ;
+
+void
+freeinit(Freelist * fl, int size)
+    {
+    fl->head = (Freenode *)NULL ;
+    fl->nodesize = size ;
+    }
+
+char *
+getfree(Freelist * fl)
+    {
+    int i ;
+    Freenode * t ;
+    if (fl->head == (Freenode *)NULL)
+        {
+        t =  (Freenode *) myalloc(sqrt_nsites * fl->nodesize) ;
+        for(i = 0 ; i < sqrt_nsites ; i++)
+            {
+            makefree((Freenode *)((char *)t+i*fl->nodesize), fl) ;
+            }
+        }
+    t = fl->head ;
+    fl->head = (fl->head)->nextfree ;
+    return ((char *)t) ;
+    }
+
+void
+makefree(Freenode * curr, Freelist * fl)
+    {
+    curr->nextfree = fl->head ;
+    fl->head = curr ;
+    }
+
+int total_alloc ;
+
+char *
+myalloc(unsigned n)
+    {
+    char * t ;
+    if ((t=malloc(n)) == (char *) 0)
+        {
+        fprintf(stderr,"Insufficient memory processing site %d (%d bytes in use)\n",
+        siteidx, total_alloc) ;
+        return(0) ; // was exit(0) in original source, we aint having that here !!!
+        }
+    total_alloc += n ;
+    return (t) ;
+    }

contrib/voronoi/output.c

@@ -0,0 +1,244 @@
+
+/*** OUTPUT.C ***/
+
+
+#include <stdio.h>
+
+#include "vdefs.h"
+
+extern int triangulate, plot, debug ;
+extern float ymax, ymin, xmax, xmin ;
+
+float pxmin, pxmax, pymin, pymax, cradius;
+
+void
+openpl(void)
+    {
+    }
+
+#pragma argsused
+void
+line(float ax, float ay, float bx, float by)
+    {
+    }
+
+#pragma argsused
+void
+circle(float ax, float ay, float radius)
+    {
+    }
+
+#pragma argsused
+void
+range(float pxmin, float pxmax, float pymin, float pymax)
+    {
+    }
+
+void
+out_bisector(Edge * e)
+    {
+    if (triangulate && plot && !debug)
+        {
+        line(e->reg[0]->coord.x, e->reg[0]->coord.y,
+             e->reg[1]->coord.x, e->reg[1]->coord.y) ;
+        }
+    if (!triangulate && !plot && !debug)
+        {
+        printf("l %f %f %f\n", e->a, e->b, e->c) ;
+        }
+    if (debug)
+        {
+        printf("line(%d) %gx+%gy=%g, bisecting %d %d\n", e->edgenbr,
+        e->a, e->b, e->c, e->reg[le]->sitenbr, e->reg[re]->sitenbr) ;
+        }
+    }
+
+void
+out_ep(Edge * e)
+    {
+    if (!triangulate && plot)
+        {
+        clip_line(e) ;
+        }
+    if (!triangulate && !plot)
+        {
+        printf("e %d", e->edgenbr);
+        printf(" %d ", e->ep[le] != (Site *)NULL ? e->ep[le]->sitenbr : -1) ;
+        printf("%d\n", e->ep[re] != (Site *)NULL ? e->ep[re]->sitenbr : -1) ;
+        }
+    }
+
+void
+out_vertex(Site * v)
+    {
+    if (!triangulate && !plot && !debug)
+        {
+        printf ("v %f %f\n", v->coord.x, v->coord.y) ;
+        }
+    if (debug)
+        {
+        printf("vertex(%d) at %f %f\n", v->sitenbr, v->coord.x, v->coord.y) ;
+        }
+    }
+
+void
+out_site(Site * s)
+    {
+    if (!triangulate && plot && !debug)
+        {
+        circle (s->coord.x, s->coord.y, cradius) ;
+        }
+    if (!triangulate && !plot && !debug)
+        {
+        printf("s %f %f\n", s->coord.x, s->coord.y) ;
+        }
+    if (debug)
+        {
+        printf("site (%d) at %f %f\n", s->sitenbr, s->coord.x, s->coord.y) ;
+        }
+    }
+
+void
+out_triple(Site * s1, Site * s2, Site * s3)
+    {
+    if (triangulate && !plot && !debug)
+        {
+        printf("%d %d %d\n", s1->sitenbr, s2->sitenbr, s3->sitenbr) ;
+        }
+    if (debug)
+        {
+        printf("circle through left=%d right=%d bottom=%d\n",
+        s1->sitenbr, s2->sitenbr, s3->sitenbr) ;
+        }
+    }
+
+void
+plotinit(void)
+    {
+    float dx, dy, d ;
+
+    dy = ymax - ymin ;
+    dx = xmax - xmin ;
+    d = ( dx > dy ? dx : dy) * 1.1 ;
+    pxmin = xmin - (d-dx) / 2.0 ;
+    pxmax = xmax + (d-dx) / 2.0 ;
+    pymin = ymin - (d-dy) / 2.0 ;
+    pymax = ymax + (d-dy) / 2.0 ;
+    cradius = (pxmax - pxmin) / 350.0 ;
+    openpl() ;
+    range(pxmin, pymin, pxmax, pymax) ;
+    }
+
+void
+clip_line(Edge * e)
+    {
+    Site * s1, * s2 ;
+    float x1, x2, y1, y2 ;
+
+    if (e->a == 1.0 && e->b >= 0.0)
+        {
+        s1 = e->ep[1] ;
+        s2 = e->ep[0] ;
+        }
+    else
+        {
+        s1 = e->ep[0] ;
+        s2 = e->ep[1] ;
+        }
+    if (e->a == 1.0)
+        {
+        y1 = pymin ;
+        if (s1 != (Site *)NULL && s1->coord.y > pymin)
+            {
+             y1 = s1->coord.y ;
+             }
+        if (y1 > pymax)
+            {
+            return ;
+            }
+        x1 = e->c - e->b * y1 ;
+        y2 = pymax ;
+        if (s2 != (Site *)NULL && s2->coord.y < pymax)
+            {
+            y2 = s2->coord.y ;
+            }
+        if (y2 < pymin)
+            {
+            return ;
+            }
+        x2 = e->c - e->b * y2 ;
+        if (((x1 > pxmax) && (x2 > pxmax)) || ((x1 < pxmin) && (x2 < pxmin)))
+            {
+            return ;
+            }
+        if (x1 > pxmax)
+            {
+            x1 = pxmax ;
+            y1 = (e->c - x1) / e->b ;
+            }
+        if (x1 < pxmin)
+            {
+            x1 = pxmin ;
+            y1 = (e->c - x1) / e->b ;
+            }
+        if (x2 > pxmax)
+            {
+            x2 = pxmax ;
+            y2 = (e->c - x2) / e->b ;
+            }
+        if (x2 < pxmin)
+            {
+            x2 = pxmin ;
+            y2 = (e->c - x2) / e->b ;
+            }
+        }
+    else
+        {
+        x1 = pxmin ;
+        if (s1 != (Site *)NULL && s1->coord.x > pxmin)
+            {
+            x1 = s1->coord.x ;
+            }
+        if (x1 > pxmax)
+            {
+            return ;
+            }
+        y1 = e->c - e->a * x1 ;
+        x2 = pxmax ;
+        if (s2 != (Site *)NULL && s2->coord.x < pxmax)
+            {
+            x2 = s2->coord.x ;
+            }
+        if (x2 < pxmin)
+            {
+            return ;
+            }
+        y2 = e->c - e->a * x2 ;
+        if (((y1 > pymax) && (y2 > pymax)) || ((y1 < pymin) && (y2 <pymin)))
+            {
+            return ;
+            }
+        if (y1> pymax)
+            {
+            y1 = pymax ;
+            x1 = (e->c - y1) / e->a ;
+            }
+        if (y1 < pymin)
+            {
+            y1 = pymin ;
+            x1 = (e->c - y1) / e->a ;
+            }
+        if (y2 > pymax)
+            {
+            y2 = pymax ;
+            x2 = (e->c - y2) / e->a ;
+            }
+        if (y2 < pymin)
+            {
+            y2 = pymin ;
+            x2 = (e->c - y2) / e->a ;
+            }
+        }
+    line(x1,y1,x2,y2);
+    }
+

contrib/voronoi/t

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contrib/voronoi/vdefs.h

@@ -0,0 +1,135 @@
+#ifndef __VDEFS_H
+#define __VDEFS_H
+
+#ifndef NULL
+#define NULL 0
+#endif
+
+#define DELETED -2
+
+typedef struct tagFreenode
+    {
+    struct tagFreenode * nextfree;
+    } Freenode ;
+
+
+typedef struct tagFreelist
+    {
+    Freenode * head;
+    int nodesize;
+    } Freelist ;
+
+typedef struct tagPoint
+    {
+    float x ;
+    float y ;
+    } Point ;
+
+/* structure used both for sites and for vertices */
+
+typedef struct tagSite
+    {
+    Point coord ;
+    int sitenbr ;
+    int refcnt ;
+    } Site ;
+
+
+typedef struct tagEdge
+    {
+    float a, b, c ;
+    Site * ep[2] ;
+    Site * reg[2] ;
+    int edgenbr ;
+    } Edge ;
+
+#define le 0
+#define re 1
+
+typedef struct tagHalfedge
+    {
+    struct tagHalfedge * ELleft ;
+    struct tagHalfedge * ELright ;
+    Edge * ELedge ;
+    int ELrefcnt ;
+    char ELpm ;
+    Site * vertex ;
+    float ystar ;
+    struct tagHalfedge * PQnext ;
+    } Halfedge ;
+
+/* edgelist.c */
+void ELinitialize(void) ;
+Halfedge * HEcreate(Edge *, int) ;
+void ELinsert(Halfedge *, Halfedge *) ;
+Halfedge * ELgethash(int) ;
+Halfedge * ELleftbnd(Point *) ;
+void ELdelete(Halfedge *) ;
+Halfedge * ELright(Halfedge *) ;
+Halfedge * ELleft(Halfedge *) ;
+Site * leftreg(Halfedge *) ;
+Site * rightreg(Halfedge *) ;
+extern int ELhashsize ;
+extern Site * bottomsite ;
+extern Freelist hfl ;
+extern Halfedge * ELleftend, * ELrightend, **ELhash ;
+
+/* geometry.c */
+void geominit(void) ;
+Edge * bisect(Site *, Site *) ;
+Site * intersect(Halfedge *, Halfedge *) ;
+int right_of(Halfedge *, Point *) ;
+void endpoint(Edge *, int, Site *) ;
+float dist(Site *, Site *) ;
+void makevertex(Site *) ;
+void deref(Site *) ;
+void ref(Site *) ;
+extern float deltax, deltay ;
+extern int nsites, nedges, sqrt_nsites, nvertices ;
+extern Freelist sfl, efl ;
+
+/* heap.c */
+void PQinsert(Halfedge *, Site *, float) ;
+void PQdelete(Halfedge *) ;
+int PQbucket(Halfedge *) ;
+int PQempty(void) ;
+Point PQ_min(void) ;
+Halfedge * PQextractmin(void) ;
+void PQinitialize(void) ;
+extern int PQmin, PQcount, PQhashsize ;
+extern Halfedge * PQhash ;
+
+/* main.c */
+extern int sorted, triangulate, plot, debug, nsites, siteidx ;
+extern float xmin, xmax, ymin, ymax ;
+extern Site * sites ;
+extern Freelist sfl ;
+
+/* getopt.c */
+extern int getopt(int, char *const *, const char *);
+
+/* memory.c */
+void freeinit(Freelist *, int) ;
+char *getfree(Freelist *) ;
+void makefree(Freenode *, Freelist *) ;
+char *myalloc(unsigned) ;
+
+/* output.c */
+void openpl(void) ;
+void line(float, float, float, float) ;
+void circle(float, float, float) ;
+void range(float, float, float, float) ;
+void out_bisector(Edge *) ;
+void out_ep(Edge *) ;
+void out_vertex(Site *) ;
+void out_site(Site *) ;
+void out_triple(Site *, Site *, Site *) ;
+void plotinit(void) ;
+void clip_line(Edge *) ;
+
+/* voronoi.c */
+void voronoi(Site *(*)()) ;
+
+#endif  
+
+

contrib/voronoi/voronoi.c

@@ -0,0 +1,120 @@
+
+/*** VORONOI.C ***/
+
+#include "vdefs.h"
+
+extern Site * bottomsite ;
+extern Halfedge * ELleftend, * ELrightend ;
+
+/*** implicit parameters: nsites, sqrt_nsites, xmin, xmax, ymin, ymax,
+ : deltax, deltay (can all be estimates).
+ : Performance suffers if they are wrong; better to make nsites,
+ : deltax, and deltay too big than too small.  (?)
+ ***/
+
+void
+voronoi(Site *(*nextsite)(void))
+    {
+    Site * newsite, * bot, * top, * temp, * p, * v ;
+    Point newintstar ;
+    int pm ;
+    Halfedge * lbnd, * rbnd, * llbnd, * rrbnd, * bisector ;
+    Edge * e ;
+
+    PQinitialize() ;
+    bottomsite = (*nextsite)() ;
+    out_site(bottomsite) ;
+    ELinitialize() ;
+    newsite = (*nextsite)() ;
+    while (1)
+        {
+        if(!PQempty())
+            {
+            newintstar = PQ_min() ;
+            }
+        if (newsite != (Site *)NULL && (PQempty()
+            || newsite -> coord.y < newintstar.y
+            || (newsite->coord.y == newintstar.y
+            && newsite->coord.x < newintstar.x))) {/* new site is
+smallest */
+            {
+            out_site(newsite) ;
+            }
+        lbnd = ELleftbnd(&(newsite->coord)) ;
+        rbnd = ELright(lbnd) ;
+        bot = rightreg(lbnd) ;
+        e = bisect(bot, newsite) ;
+        bisector = HEcreate(e, le) ;
+        ELinsert(lbnd, bisector) ;
+        p = intersect(lbnd, bisector) ;
+        if (p != (Site *)NULL)
+            {
+            PQdelete(lbnd) ;
+            PQinsert(lbnd, p, dist(p,newsite)) ;
+            }
+        lbnd = bisector ;
+        bisector = HEcreate(e, re) ;
+        ELinsert(lbnd, bisector) ;
+        p = intersect(bisector, rbnd) ;
+        if (p != (Site *)NULL)
+            {
+            PQinsert(bisector, p, dist(p,newsite)) ;
+            }
+        newsite = (*nextsite)() ;
+        }
+    else if (!PQempty())   /* intersection is smallest */
+            {
+            lbnd = PQextractmin() ;
+            llbnd = ELleft(lbnd) ;
+            rbnd = ELright(lbnd) ;
+            rrbnd = ELright(rbnd) ;
+            bot = leftreg(lbnd) ;
+            top = rightreg(rbnd) ;
+            out_triple(bot, top, rightreg(lbnd)) ;
+            v = lbnd->vertex ;
+            makevertex(v) ;
+            endpoint(lbnd->ELedge, lbnd->ELpm, v);
+            endpoint(rbnd->ELedge, rbnd->ELpm, v) ;
+            ELdelete(lbnd) ;
+            PQdelete(rbnd) ;
+            ELdelete(rbnd) ;
+            pm = le ;
+            if (bot->coord.y > top->coord.y)
+                {
+                temp = bot ;
+                bot = top ;
+                top = temp ;
+                pm = re ;
+                }
+            e = bisect(bot, top) ;
+            bisector = HEcreate(e, pm) ;
+            ELinsert(llbnd, bisector) ;
+            endpoint(e, re-pm, v) ;
+            deref(v) ;
+            p = intersect(llbnd, bisector) ;
+            if (p  != (Site *) NULL)
+                {
+                PQdelete(llbnd) ;
+                PQinsert(llbnd, p, dist(p,bot)) ;
+                }
+            p = intersect(bisector, rrbnd) ;
+            if (p != (Site *) NULL)
+                {
+                PQinsert(bisector, p, dist(p,bot)) ;
+                }
+            }
+        else
+            {
+            break ;
+            }
+        }
+
+    for( lbnd = ELright(ELleftend) ;
+         lbnd != ELrightend ;
+         lbnd = ELright(lbnd))
+        {
+        e = lbnd->ELedge ;
+        out_ep(e) ;
+        }
+    }
+

src/src.pro

@@ -756,6 +756,7 @@ HEADERS += ../contrib/qtsolutions/codeeditor/codeeditor.h ../contrib/qtsolutions
            ../contrib/boost/GeometricTools_BSplineCurve.h \
            ../contrib/kmeans/kmeans_dataset.h ../contrib/kmeans/kmeans_general_functions.h ../contrib/kmeans/hamerly_kmeans.h \
            ../contrib/kmeans/kmeans.h ../contrib/kmeans/original_space_kmeans.h ../contrib/kmeans/triangle_inequality_base_kmeans.h
+           ../contrib/voronoi/vdefs.h
 
 
 # Train View
@@ -865,7 +866,9 @@ SOURCES += ../contrib/qtsolutions/codeeditor/codeeditor.cpp ../contrib/qtsolutio
            ../contrib/levmar/Axb_core.c ../contrib/levmar/lm.c ../contrib/levmar/lmbc.c ../contrib/levmar/lmblec.c ../contrib/levmar/lmbleic.c \
            ../contrib/levmar/lmlec_core.c ../contrib/levmar/misc_core.c \
            ../contrib/kmeans/kmeans_dataset.cpp ../contrib/kmeans/kmeans_general_functions.cpp ../contrib/kmeans/hamerly_kmeans.cpp \
-           ../contrib/kmeans/kmeans.cpp ../contrib/kmeans/original_space_kmeans.cpp ../contrib/kmeans/triangle_inequality_base_kmeans.cpp
+           ../contrib/kmeans/kmeans.cpp ../contrib/kmeans/original_space_kmeans.cpp ../contrib/kmeans/triangle_inequality_base_kmeans.cpp \
+           ../contrib/voronoi/edgelist.c ../contrib/voronoi/geometry.c ../contrib/voronoi/heap.c \
+           ../contrib/voronoi/memory.c ../contrib/voronoi/output.c ../contrib/voronoi/voronoi.c
 
 
 ## Train View Components