/*
* Copyright (C) 2011 The Android Open Source Project
*
* Licensed under the Apache License, Version 2.0 (the "License");
* you may not use this file except in compliance with the License.
* You may obtain a copy of the License at
*
* http://www.apache.org/licenses/LICENSE-2.0
*
* Unless required by applicable law or agreed to in writing, software
* distributed under the License is distributed on an "AS IS" BASIS,
* WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
* See the License for the specific language governing permissions and
* limitations under the License.
*/
// Delaunay.cpp
// $Id: Delaunay.cpp,v 1.10 2011/06/17 13:35:48 mbansal Exp $
#include <stdio.h>
#include <stdlib.h>
#include <memory.h>
#include "Delaunay.h"
#define QQ 9 // Optimal value as determined by testing
#define DM 38 // 2^(1+DM/2) element sort capability. DM=38 for >10^6 elements
#define NYL -1
#define valid(l) ccw(orig(basel), dest(l), dest(basel))
CDelaunay::CDelaunay()
{
}
CDelaunay::~CDelaunay()
{
}
// Allocate storage, construct triangulation, compute voronoi corners
int CDelaunay::triangulate(SEdgeVector **edges, int n_sites, int width, int height)
{
EdgePointer cep;
deleteAllEdges();
buildTriangulation(n_sites);
cep = consolidateEdges();
*edges = ev;
// Note: construction_list will change ev
return constructList(cep, width, height);
}
// builds delaunay triangulation
void CDelaunay::buildTriangulation(int size)
{
int i, rows;
EdgePointer lefte, righte;
rows = (int)( 0.5 + sqrt( (double) size / log( (double) size )));
// Sort the pointers by x-coordinate of site
for ( i=0 ; i < size ; i++ ) {
sp[i] = (SitePointer) i;
}
spsortx( sp, 0, size-1 );
build( 0, size-1, &lefte, &righte, rows );
oneBndryEdge = lefte;
}
// Recursive Delaunay Triangulation Procedure
// Contains modifications for axis-switching division.
void CDelaunay::build(int lo, int hi, EdgePointer *le, EdgePointer *re, int rows)
{
EdgePointer a, b, c, ldo, rdi, ldi, rdo, maxx, minx;
int split, lowrows;
int low, high;
SitePointer s1, s2, s3;
low = lo;
high = hi;
if ( low < (high-2) ) {
// more than three elements; do recursion
minx = sp[low];
maxx = sp[high];
if (rows == 1) { // time to switch axis of division
spsorty( sp, low, high);
rows = 65536;
}
lowrows = rows/2;
split = low - 1 + (int)
(0.5 + ((double)(high-low+1) * ((double)lowrows / (double)rows)));
build( low, split, &ldo, &ldi, lowrows );
build( split+1, high, &rdi, &rdo, (rows-lowrows) );
doMerge(&ldo, ldi, rdi, &rdo);
while (orig(ldo) != minx) {
ldo = rprev(ldo);
}
while (orig(rdo) != maxx) {
rdo = (SitePointer) lprev(rdo);
}
*le = ldo;
*re = rdo;
}
else if (low >= (high - 1)) { // two or one points
a = makeEdge(sp[low], sp[high]);
*le = a;
*re = (EdgePointer) sym(a);
} else { // three points
// 3 cases: triangles of 2 orientations, and 3 points on a line
a = makeEdge((s1 = sp[low]), (s2 = sp[low+1]));
b = makeEdge(s2, (s3 = sp[high]));
splice((EdgePointer) sym(a), b);
if (ccw(s1, s3, s2)) {
c = connectLeft(b, a);
*le = (EdgePointer) sym(c);
*re = c;
} else {
*le = a;
*re = (EdgePointer) sym(b);
if (ccw(s1, s2, s3)) {
// not colinear
c = connectLeft(b, a);
}
}
}
}
// Quad-edge manipulation primitives
EdgePointer CDelaunay::makeEdge(SitePointer origin, SitePointer destination)
{
EdgePointer temp, ans;
temp = allocEdge();
ans = temp;
onext(temp) = ans;
orig(temp) = origin;
onext(++temp) = (EdgePointer) (ans + 3);
onext(++temp) = (EdgePointer) (ans + 2);
orig(temp) = destination;
onext(++temp) = (EdgePointer) (ans + 1);
return(ans);
}
void CDelaunay::splice(EdgePointer a, EdgePointer b)
{
EdgePointer alpha, beta, temp;
alpha = (EdgePointer) rot(onext(a));
beta = (EdgePointer) rot(onext(b));
temp = onext(alpha);
onext(alpha) = onext(beta);
onext(beta) = temp;
temp = onext(a);
onext(a) = onext(b);
onext(b) = temp;
}
EdgePointer CDelaunay::connectLeft(EdgePointer a, EdgePointer b)
{
EdgePointer ans;
ans = makeEdge(dest(a), orig(b));
splice(ans, (EdgePointer) lnext(a));
splice((EdgePointer) sym(ans), b);
return(ans);
}
EdgePointer CDelaunay::connectRight(EdgePointer a, EdgePointer b)
{
EdgePointer ans;
ans = makeEdge(dest(a), orig(b));
splice(ans, (EdgePointer) sym(a));
splice((EdgePointer) sym(ans), (EdgePointer) oprev(b));
return(ans);
}
// disconnects e from the rest of the structure and destroys it
void CDelaunay::deleteEdge(EdgePointer e)
{
splice(e, (EdgePointer) oprev(e));
splice((EdgePointer) sym(e), (EdgePointer) oprev(sym(e)));
freeEdge(e);
}
//
// Overall storage allocation
//
// Quad-edge storage allocation
CSite *CDelaunay::allocMemory(int n)
{
unsigned int size;
size = ((sizeof(CSite) + sizeof(SitePointer)) * n +
(sizeof(SitePointer) + sizeof(EdgePointer)) * 12
) * n;
if (!(sa = (CSite*) malloc(size))) {
return NULL;
}
sp = (SitePointer *) (sa + n);
ev = (SEdgeVector *) (org = sp + n);
next = (EdgePointer *) (org + 12 * n);
ei = (struct EDGE_INFO *) (next + 12 * n);
return sa;
}
void CDelaunay::freeMemory()
{
if (sa) {
free(sa);
sa = (CSite*)NULL;
}
}
//
// Edge storage management
//
void CDelaunay::deleteAllEdges()
{
nextEdge = 0;
availEdge = NYL;
}
EdgePointer CDelaunay::allocEdge()
{
EdgePointer ans;
if (availEdge == NYL) {
ans = nextEdge, nextEdge += 4;
} else {
ans = availEdge, availEdge = onext(availEdge);
}
return(ans);
}
void CDelaunay::freeEdge(EdgePointer e)
{
e ^= e & 3;
onext(e) = availEdge;
availEdge = e;
}
EdgePointer CDelaunay::consolidateEdges()
{
EdgePointer e;
int i,j;
while (availEdge != NYL) {
nextEdge -= 4; e = availEdge; availEdge = onext(availEdge);
if (e==nextEdge) {
continue; // the one deleted was the last one anyway
}
if ((oneBndryEdge&~3) == nextEdge) {
oneBndryEdge = (EdgePointer) (e | (oneBndryEdge&3));
}
for (i=0,j=3; i<4; i++,j=rot(j)) {
onext(e+i) = onext(nextEdge+i);
onext(rot(onext(e+i))) = (EdgePointer) (e+j);
}
}
return nextEdge;
}
//
// Sorting Routines
//
int CDelaunay::xcmpsp(int i, int j)
{
double d = sa[(i>=0)?sp[i]:sp1].X() - sa[(j>=0)?sp[j]:sp1].X();
if ( d > 0. ) {
return 1;
}
if ( d < 0. ) {
return -1;
}
d = sa[(i>=0)?sp[i]:sp1].Y() - sa[(j>=0)?sp[j]:sp1].Y();
if ( d > 0. ) {
return 1;
}
if ( d < 0. ) {
return -1;
}
return 0;
}
int CDelaunay::ycmpsp(int i, int j)
{
double d = sa[(i>=0)?sp[i]:sp1].Y() - sa[(j>=0)?sp[j]:sp1].Y();
if ( d > 0. ) {
return 1;
}
if ( d < 0. ) {
return -1;
}
d = sa[(i>=0)?sp[i]:sp1].X() - sa[(j>=0)?sp[j]:sp1].X();
if ( d > 0. ) {
return 1;
}
if ( d < 0. ) {
return -1;
}
return 0;
}
int CDelaunay::cmpev(int i, int j)
{
return (ev[i].first - ev[j].first);
}
void CDelaunay::swapsp(int i, int j)
{
int t;
t = (i>=0) ? sp[i] : sp1;
if (i>=0) {
sp[i] = (j>=0)?sp[j]:sp1;
} else {
sp1 = (j>=0)?sp[j]:sp1;
}
if (j>=0) {
sp[j] = (SitePointer) t;
} else {
sp1 = (SitePointer) t;
}
}
void CDelaunay::swapev(int i, int j)
{
SEdgeVector temp;
temp = ev[i];
ev[i] = ev[j];
ev[j] = temp;
}
void CDelaunay::copysp(int i, int j)
{
if (j>=0) {
sp[j] = (i>=0)?sp[i]:sp1;
} else {
sp1 = (i>=0)?sp[i]:sp1;
}
}
void CDelaunay::copyev(int i, int j)
{
ev[j] = ev[i];
}
void CDelaunay::spsortx(SitePointer *sp_in, int low, int high)
{
sp = sp_in;
rcssort(low,high,-1,&CDelaunay::xcmpsp,&CDelaunay::swapsp,&CDelaunay::copysp);
}
void CDelaunay::spsorty(SitePointer *sp_in, int low, int high )
{
sp = sp_in;
rcssort(low,high,-1,&CDelaunay::ycmpsp,&CDelaunay::swapsp,&CDelaunay::copysp);
}
void CDelaunay::rcssort(int lowelt, int highelt, int temp,
int (CDelaunay::*comparison)(int,int),
void (CDelaunay::*swap)(int,int),
void (CDelaunay::*copy)(int,int))
{
int m,sij,si,sj,sL,sk;
int stack[DM];
if (highelt-lowelt<=1) {
return;
}
if (highelt-lowelt>QQ) {
m = 0;
si = lowelt; sj = highelt;
for (;;) { // partition [si,sj] about median-of-3.
sij = (sj+si) >> 1;
// Now to sort elements si,sij,sj into order & set temp=their median
if ( (this->*comparison)( si,sij ) > 0 ) {
(this->*swap)( si,sij );
}
if ( (this->*comparison)( sij,sj ) > 0 ) {
(this->*swap)( sj,sij );
if ( (this->*comparison)( si,sij ) > 0 ) {
(this->*swap)( si,sij );
}
}
(this->*copy)( sij,temp );
// Now to partition into elements <=temp, >=temp, and ==temp.
sk = si; sL = sj;
do {
do {
sL--;
} while( (this->*comparison)( sL,temp ) > 0 );
do {
sk++;
} while( (this->*comparison)( temp,sk ) > 0 );
if ( sk < sL ) {
(this->*swap)( sL,sk );
}
} while(sk <= sL);
// Now to recurse on shorter partition, store longer partition on stack
if ( sL-si > sj-sk ) {
if ( sL-si < QQ ) {
if( m==0 ) {
break; // empty stack && both partitions < QQ so break
} else {
sj = stack[--m];
si = stack[--m];
}
}
else {
if ( sj-sk < QQ ) {
sj = sL;
} else {
stack[m++] = si;
stack[m++] = sL;
si = sk;
}
}
}
else {
if ( sj-sk < QQ ) {
if ( m==0 ) {
break; // empty stack && both partitions < QQ so break
} else {
sj = stack[--m];
si = stack[--m];
}
}
else {
if ( sL-si < QQ ) {
si = sk;
} else {
stack[m++] = sk;
stack[m++] = sj;
sj = sL;
}
}
}
}
}
// Now for 0 or Data bounded "straight insertion" sort of [0,nels-1]; if it is
// known that el[-1] = -INF, then can omit the "sk>=0" test and save time.
for (si=lowelt; si<highelt; si++) {
if ( (this->*comparison)( si,si+1 ) > 0 ) {
(this->*copy)( si+1,temp );
sj = sk = si;
sj++;
do {
(this->*copy)( sk,sj );
sj = sk;
sk--;
} while ( (this->*comparison)( sk,temp ) > 0 && sk>=lowelt );
(this->*copy)( temp,sj );
}
}
}
//
// Geometric primitives
//
// incircle, as in the Guibas-Stolfi paper.
int CDelaunay::incircle(SitePointer a, SitePointer b, SitePointer c, SitePointer d)
{
double adx, ady, bdx, bdy, cdx, cdy, dx, dy, nad, nbd, ncd;
dx = sa[d].X();
dy = sa[d].Y();
adx = sa[a].X() - dx;
ady = sa[a].Y() - dy;
bdx = sa[b].X() - dx;
bdy = sa[b].Y() - dy;
cdx = sa[c].X() - dx;
cdy = sa[c].Y() - dy;
nad = adx*adx+ady*ady;
nbd = bdx*bdx+bdy*bdy;
ncd = cdx*cdx+cdy*cdy;
return( (0.0 < (nad * (bdx * cdy - bdy * cdx)
+ nbd * (cdx * ady - cdy * adx)
+ ncd * (adx * bdy - ady * bdx))) ? TRUE : FALSE );
}
// TRUE iff A, B, C form a counterclockwise oriented triangle
int CDelaunay::ccw(SitePointer a, SitePointer b, SitePointer c)
{
int result;
double ax = sa[a].X();
double bx = sa[b].X();
double cx = sa[c].X();
double ay = sa[a].Y();
double by = sa[b].Y();
double cy = sa[c].Y();
double val = (ax - cx)*(by - cy) - (bx - cx)*(ay - cy);
if ( val > 0.0) {
return true;
}
return false;
}
//
// The Merge Procedure.
//
void CDelaunay::doMerge(EdgePointer *ldo, EdgePointer ldi, EdgePointer rdi, EdgePointer *rdo)
{
int rvalid, lvalid;
EdgePointer basel,lcand,rcand,t;
for (;;) {
while (ccw(orig(ldi), dest(ldi), orig(rdi))) {
ldi = (EdgePointer) lnext(ldi);
}
if (ccw(dest(rdi), orig(rdi), orig(ldi))) {
rdi = (EdgePointer)rprev(rdi);
} else {
break;
}
}
basel = connectLeft((EdgePointer) sym(rdi), ldi);
lcand = rprev(basel);
rcand = (EdgePointer) oprev(basel);
if (orig(basel) == orig(*rdo)) {
*rdo = basel;
}
if (dest(basel) == orig(*ldo)) {
*ldo = (EdgePointer) sym(basel);
}
for (;;) {
#if 1
if (valid(t=onext(lcand))) {
#else
t = (EdgePointer)onext(lcand);
if (valid(basel, t)) {
#endif
while (incircle(dest(lcand), dest(t), orig(lcand), orig(basel))) {
deleteEdge(lcand);
lcand = t;
t = onext(lcand);
}
}
#if 1
if (valid(t=(EdgePointer)oprev(rcand))) {
#else
t = (EdgePointer)oprev(rcand);
if (valid(basel, t)) {
#endif
while (incircle(dest(t), dest(rcand), orig(rcand), dest(basel))) {
deleteEdge(rcand);
rcand = t;
t = (EdgePointer)oprev(rcand);
}
}
#if 1
lvalid = valid(lcand);
rvalid = valid(rcand);
#else
lvalid = valid(basel, lcand);
rvalid = valid(basel, rcand);
#endif
if ((! lvalid) && (! rvalid)) {
return;
}
if (!lvalid ||
(rvalid && incircle(dest(lcand), orig(lcand), orig(rcand), dest(rcand)))) {
basel = connectLeft(rcand, (EdgePointer) sym(basel));
rcand = (EdgePointer) lnext(sym(basel));
} else {
basel = (EdgePointer) sym(connectRight(lcand, basel));
lcand = rprev(basel);
}
}
}
int CDelaunay::constructList(EdgePointer last, int width, int height)
{
int c, i;
EdgePointer curr, src, nex;
SEdgeVector *currv, *prevv;
c = (int) ((curr = (EdgePointer) ((last & ~3))) >> 1);
for (last -= 4; last >= 0; last -= 4) {
src = orig(last);
nex = dest(last);
orig(--curr) = src;
orig(--curr) = nex;
orig(--curr) = nex;
orig(--curr) = src;
}
rcssort(0, c - 1, -1, &CDelaunay::cmpev, &CDelaunay::swapev, &CDelaunay::copyev);
// Throw out any edges that are too far apart
currv = prevv = ev;
for (i = c; i--; currv++) {
if ((int) fabs(sa[currv->first].getVCenter().x - sa[currv->second].getVCenter().x) <= width &&
(int) fabs(sa[currv->first].getVCenter().y - sa[currv->second].getVCenter().y) <= height) {
*(prevv++) = *currv;
} else {
c--;
}
}
return c;
}
// Fill in site neighbor information
void CDelaunay::linkNeighbors(SEdgeVector *edge, int nedge, int nsite)
{
int i;
for (i = 0; i < nsite; i++) {
sa[i].setNeighbor(edge);
sa[i].setNumNeighbors(0);
for (; edge->first == i && nedge; edge++, nedge--) {
sa[i].incrNumNeighbors();
}
}
}