/* * 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(); } } }