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Future's Algorithm

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.. for calculating Vornoi diagrams.
This commit is contained in:
Mark Liversedge
2021-09-28 19:28:42 +01:00
parent 4c720884b6
commit 53ee8f358c
14 changed files with 2251 additions and 1 deletions
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30
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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.

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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

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/*** 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]) ;
}

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/*** 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) ;
}

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/*** 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 ;
}
}

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/*** 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) ;
}

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/*** 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) ;
}

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/*** 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);
}

100
contrib/voronoi/t Normal file
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135
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#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

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120
contrib/voronoi/voronoi.c Normal file
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/*** 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) ;
}
}