void space_partion_rec(point ps[], int count, int l, int r) { if (r > l + 1) { int rp = rand() % (r - l - 1) + l + 1; point f = ps[l]; point s = r == count ? ps[0] : ps[r]; point rps = random_point_on_segment(f, s); point rpe = ps[rp]; swap(ps, l + 1, rp); int i = l + 2; int j = r - 1; bool l_dir = to_left(rps, rpe, ps[l]); while (i <= j) { while (i < r && to_left(rps, rpe, ps[i]) == l_dir) i++; while (j > l + 1 && to_left(rps, rpe, ps[j]) != l_dir) j--; if (i <= j) { swap(ps, i, j); i++; j--; } } swap(ps, l + 1, j); space_partion_rec(ps, count, l, j); space_partion_rec(ps, count, j, r); } }
bool in_triangle(const point &p, const point &q, const point &r, const point &k) { bool pq_left = to_left(p, q, k); bool qr_left = to_left(q, r, k); bool rp_left = to_left(r, p, k); return (pq_left == qr_left) && (qr_left == rp_left); }
void split_route(vector<Segment> &vs,VR &nodes,int idx, int n1, int n2){ ParamEdge e=vs[idx].edge; debugline(e.from(),e.to(),255,0,0,true); double minp=DBL_MAX; int minidx=-1; for (int j=0,n=nodes.size();j<n;j++){ if (j==n1 || j==n2) continue; if (e.cross(nodes[j])){ if (nodes[j].contains(e.from())) continue; if (nodes[j].contains(e.to())) continue; double p=e.cross_param_smallest(nodes[j]); if (p<minp){ minp=p; minidx=j; } } } if (minidx<0) return ; Point dc=e.dist_vec(nodes[minidx].center()); if (dc.is_null()){ dc=to_left(e.unit(),PI/2); // minidxust choose a side } VP pts; Point r=e.dist_vec(nodes[minidx].TL()); if (scalar(r,dc)<0) pts.push_back(nodes[minidx].TL()); r=e.dist_vec(nodes[minidx].TR()); if (scalar(r,dc)<0) pts.push_back(nodes[minidx].TR()); r=e.dist_vec(nodes[minidx].BL()); if (scalar(r,dc)<0) pts.push_back(nodes[minidx].BL()); r=e.dist_vec(nodes[minidx].BR()); if (scalar(r,dc)<0) pts.push_back(nodes[minidx].BR()); if (pts.size()==0) { printf("Ups, no points on smaller side of edge/node cut area"); return; } if (pts.size()>2 ) throw "expected 1 or 2 points"; vector<Segment> vsnew; int idxlast=idx+1; if (pts.size()==1){ vsnew.push_back(Segment(ParamEdge(e.from(),pts[0]),vs[idx].first,false)); vsnew.push_back(Segment(ParamEdge(pts[0],e.to()),false,vs[idx].last)); } else if (pts.size()==2) { if (norm(pts[0]-e.from())>norm(pts[1]-e.from())){ // do nearest point first swap(pts[0],pts[1]); } vsnew.push_back(Segment(ParamEdge(e.from(),pts[0]),vs[idx].first,false)); vsnew.push_back(Segment(ParamEdge(pts[0],pts[1]),false,false)); vsnew.push_back(Segment(ParamEdge(pts[1],e.to()),false,vs[idx].last)); idxlast++; } vs.erase(vs.begin()+idx); vs.insert(vs.begin()+idx,vsnew.begin(),vsnew.end()); split_route(vs,nodes,idxlast,minidx,n2); split_route(vs,nodes,idx,n1,minidx); // new overlaps could be introduced after makeing a kink into the line }
//Space Partitioning algorithm from "Heuristics for the Generation of Random Polygons, T. Auer & M. Held" // The worst case is O(n^2) // The best case is O(nlgn) void space_partition(point ps[], int count) { int first = 0; int second = rand() % (count - 1) + 1; point f = ps[first]; point s = ps[second]; swap(ps, 1, second); int i = 2; int j = count - 1; while (i <= j) { while (i < count && to_left(f, s, ps[i])) i++; while (j > 1 && !to_left(f, s, ps[j])) j--; if (i <= j) { swap(ps, i, j); i++; j--; } } swap(ps, 1, j); space_partion_rec(ps, count, 0, j); space_partion_rec(ps, count, j, count); }
void route_edges(Layouter &state,plugin& pg, double scale, int iter, double temp, int debug){ int n=state.nw.nodes.size(); int i,j,k; vector<NodeLinePair> gs; Rect bb=state.nw.getBB(); bb.extend(state.avgsize/10); Network nv; vector<VI> nodemap(n); vector<vector<VI> > edge_crossings(n+4,vector<VI>(n+4)); // this stores for each voronoi line between node i and j the crosspoints; includes 4 virtual nodes printf("finding Voronoi separator lines\n"); for (i=0;i<n;i++){ gs.clear(); double x=state.nw.nodes[i].x; double y=state.nw.nodes[i].y; double w=state.nw.nodes[i].width; double h=state.nw.nodes[i].height; Rect ri=state.nw.nodes[i].rect(); //if (i==iter) debugrect(ri,0,0,255); gs.push_back(NodeLinePair(n,ParamEdge(Point(x,bb.ymin),bb.TL()))); // boundary lines (should point to left); adds virtual nodes n ... n+3 gs.push_back(NodeLinePair(n+1,ParamEdge(Point(bb.xmin,y),bb.BL()))); gs.push_back(NodeLinePair(n+2,ParamEdge(Point(x,bb.ymax),bb.BR()))); gs.push_back(NodeLinePair(n+3,ParamEdge(Point(bb.xmax,y),bb.TR()))); double dclosest=DBL_MAX; int iclosest; for (j=0;j<n;j++){ if (i==j) continue; double x2=state.nw.nodes[j].x; double y2=state.nw.nodes[j].y; double w2=state.nw.nodes[j].width; double h2=state.nw.nodes[j].height; double dx=x2-x; double dy=y2-y; double mx=(dx>0 ? (x+w/2+x2-w2/2)/2 : (x-w/2+x2+w2/2)/2); // point thru which separation line should go (in the middle between the two nodes) double my=(dy>0 ? (y+h/2+y2-h2/2)/2 : (y-h/2+y2+h2/2)/2); if (my<min(y,y2)) my=min(y,y2); // if nodes "overlap" in one direction, these limits need to be applied if (mx<min(x,x2)) mx=min(x,x2); if (my>max(y,y2)) my=max(y,y2); if (mx>max(x,x2)) mx=max(x,x2); Point m(mx,my); double gx=dy; // line sould point perpendicular to distance vector; points to left double gy=-dx; //if (i==iter) debugline(m.x,m.y,m.x+gx,m.y+gy,200,100,100,true); // if (i==iter) debugline(x,y,x2,y2,100,100,200,true); double ord_angles[4]; double &alpha=ord_angles[0]; alpha=angle(Point(gx,gy)); // find suitable 0, 45 and 90° lines and sort them by proximity to (gx,gy) line double &nearest=ord_angles[1]; // just references to iterate through candidates later on double &second=ord_angles[2]; double &third=ord_angles[3]; nearest=PI/4*round(4*alpha/PI); double left=PI/2*floor(2*alpha/PI); double right=PI/2*ceil(2*alpha/PI); // find second nearest second=PI/4*floor(4*alpha/PI); if (second==nearest) second=PI/4*ceil(4*alpha/PI); // find third nearest if (nearest==left){ third=right; } else if (nearest==right){ third=left; } else if (second==left){ third=right; } else { third=left; } /* for (k=0;k<3;k++){ if (i==1) debugline(m.x,m.y,m.x+100*Point(ord_angles[k]).x,m.y+100*Point(ord_angles[k]).y,100,100,200,true); }*/ // check candidates in the defined order whether they collide with one of the two nodes (i or j) Rect rj=state.nw.nodes[j].rect(); Point g(0,0); bool found=false; for (k=0;k<4;k++){ g=Point(ord_angles[k]); if (prod(g,rj.TL()-m)>0 && prod(g,rj.TR()-m)>0 && prod(g,rj.BR()-m)>0 && prod(g,rj.BL()-m)>0 && prod(g,ri.TL()-m)<0 && prod(g,ri.TR()-m)<0 && prod(g,ri.BR()-m)<0 && prod(g,ri.BL()-m)<0) { // node j completely right of g && i completely left found=true; break; } } if (!found) g=Point(ord_angles[0]); // ups? do nodes overlap? // generate the line and save it ParamEdge ge(m,m+g); // the voronoi line separating node i from node j Point pclosest=ge.dist_vec(state.nw.nodes[i]); // closest point on line to node i ge.re_ref(state.nw.nodes[i]+pclosest); // reference point of line needs to be the closest point to node i gs.push_back(NodeLinePair(j,ge)); if (norm(pclosest)<dclosest){ // find closest line to node i on the fly dclosest=norm(pclosest); iclosest=gs.size()-1; } //if (i==iter) debugline(ge.from(),ge.p(state.avgsize*4),100,100,100,true); } //find set of voronoi lines which minimally surround node i int curidx=iclosest; int minidx; int lastidx=-1; bool first=true; int gl=gs.size(); VI used(gl,0); while (first || curidx!=iclosest){ ParamEdge &cur=gs[curidx].line; double minc=DBL_MAX; for (j=0;j<gl;j++){ // find the nearest crosspoint of one of all voronoi lines; searching to the left from last cross point if (j==curidx) continue; if (used[j]) continue; if (j==lastidx) continue; // finds the last voronoi line again; should not happen as this line should be in used[] already; except for iclosest double c=cur.cross_param(gs[j].line); if (c==0) { // special case, check whether new line points inwards Point ctr90=to_left(Point(x,y)-cur.p(c),PI); Point cln90=to_left(cur.unit(),PI); Point dirj=gs[j].line.unit(); if (!((scalar(ctr90,dirj)<0) && (scalar(cln90,dirj)>0))){ // new line not between center line and current line continue; } } if (c>=0 && c<minc){ minc=c; minidx=j; //if (i==iter) debugpoint(cur.p(c),state.avgsize/10,0,0,255); } } used[minidx]=1; Point cp=cur.cross_point(gs[minidx].line); //if (i==iter) debugpoint(cp,state.avgsize/10,0,255,0); gs[minidx].line.re_ref(cp); // setting ref point of next line to the current cross point //if (i==iter) debugline(gs[minidx].line.from(),gs[minidx].line.p(state.avgsize),255,0,255); int newnode=nv.nodes.size(); nv.addNode(newnode,other,"",1,1,cp.x,cp.y,0); edge_crossings[min(i,gs[curidx].node)][max(i,gs[curidx].node)].push_back(newnode); // add the new node to the two veronoi lines it belongs to edge_crossings[min(i,gs[minidx].node)][max(i,gs[minidx].node)].push_back(newnode); //nodemap[i].push_back(newnode); lastidx=curidx; curidx=minidx; first=false; //if (i==iter) debugline(cur.from(),cp,0,0,0); } } printf("finding relevant cross points on seperator lines and building network\n"); // go through all voronoi lines and connect all registered cross points CmpCrossPoints ccp(nv); for (i=0;i<n+4;i++){ // includes 4 virtual nodes for (j=i+1;j<n+4;j++){ if (edge_crossings[i][j].size() ==0 ) continue; sort(edge_crossings[i][j].begin(),edge_crossings[i][j].end(),ccp); // sort cross points on line for (k=0;k<(int)edge_crossings[i][j].size();k++){ int n1=edge_crossings[i][j][k]; if (i<n) nodemap[i].push_back(n1); // register voronoi node to be adjacent to original node i (if not virtual node) if (j<n) nodemap[j].push_back(n1); if (k==((int)edge_crossings[i][j].size())-1) break; // for the last crosspoint we do not create an edge int n2=edge_crossings[i][j][k+1]; nv.addEdge(n1,n2,undirected); if (iter<=1) debugline(nv.nodes[n1].x,nv.nodes[n1].y,nv.nodes[n2].x,nv.nodes[n2].y,0,0,0,true); } } } printf("finding shortest path through network for each original edge\n"); if (iter>=1){ // this is just for showing 1 step show only veronoi lines, 2nd show splines nv.calcEdgeLengths(); int m=state.nw.edges.size(); for (i=0;i<m;i++){ printf(".");fflush(stdout); Edge &e=state.nw.edges[i]; int n1=e.from; int n2=e.to; BFS bfs(nv,nodemap[n1]); int nn=bfs.next(); while (nn>=0 && find(nodemap[n2].begin(),nodemap[n2].end(),nn)==nodemap[n2].end()){ nn=bfs.next(); } if (nn<0) printf("Ups, no route for edge\n"); VI path=bfs.path(); smooth_path(nv,path,state.avgsize/4); e.splinepoints.clear(); e.splinehandles.clear(); double beta; Point vec; double dd1=(path.size()>1 ? (norm(nv.nodes[path[0]]-state.nw.nodes[n1])-max(state.nw.nodes[n1].width,state.nw.nodes[n1].height)/2)/2 : (norm(state.nw.nodes[n2]-state.nw.nodes[n1])-max(state.nw.nodes[n1].width,state.nw.nodes[n1].height)/2-max(state.nw.nodes[n2].width,state.nw.nodes[n2].height)/2)/2); dd1=min(dd1,state.avgsize/2); double d1=max(state.nw.nodes[n1].width,state.nw.nodes[n1].height)/2+dd1; double dd2=(path.size()>1 ? (norm(nv.nodes[path.back()]-state.nw.nodes[n2])-max(state.nw.nodes[n2].width,state.nw.nodes[n2].height)/2)/2 : (norm(state.nw.nodes[n2]-state.nw.nodes[n1])-max(state.nw.nodes[n1].width,state.nw.nodes[n1].height)/2-max(state.nw.nodes[n2].width,state.nw.nodes[n2].height)/2)/2); dd2=min(dd2,state.avgsize/2); double d2=max(state.nw.nodes[n2].width,state.nw.nodes[n2].height)/2+state.avgsize/2; Point sp1,sp2; switch(e.type){ case substrate: reverse(path.begin(),path.end()); swap(n1,n2); swap(d1,d2); sp1=(path.size()>1 ? nv.nodes[path[0]] : state.nw.nodes[n2]); e.splinehandles.push_back(unit(sp1-state.nw.nodes[n1])*d1); e.splinehandles.push_back(Point(state.nw.nodes[n2].dir+PI/2)*d2); break; case product: e.splinehandles.push_back(Point(state.nw.nodes[n1].dir-PI/2)*d1); sp2=(path.size()>1 ? nv.nodes[path.back()] : state.nw.nodes[n1]); e.splinehandles.push_back(unit(sp2-state.nw.nodes[n2])*d2); break; case activator: case inhibitor: case catalyst: reverse(path.begin(),path.end()); swap(n1,n2); swap(d1,d2); vec=state.nw.nodes[n1]-state.nw.nodes[n2]; // vector pointing from n2 (reaction) to n1 (catalyst,etc) beta=0; if (scalar(vec,Point(state.nw.nodes[n2].dir+PI))>scalar(vec,Point(state.nw.nodes[n2].dir))) beta=PI; sp1=(path.size()>1 ? nv.nodes[path[0]] : state.nw.nodes[n2]); e.splinehandles.push_back(unit(sp1-state.nw.nodes[n1])*d1); e.splinehandles.push_back(Point(state.nw.nodes[n2].dir+beta)*d2); break; default: sp1=(path.size()>1 ? nv.nodes[path[0]] : state.nw.nodes[n2]); e.splinehandles.push_back(unit(sp1-state.nw.nodes[n1])*d1); sp2=(path.size()>1 ? nv.nodes[path.back()] : state.nw.nodes[n1]); e.splinehandles.push_back(unit(sp2-state.nw.nodes[n2])*d2); } if (path.size()>1){ //debugline(state.nw.nodes[n1].x,state.nw.nodes[n1].y,nv.nodes[path.front()].x,nv.nodes[path.front()].y,255,100,100); for (j=0;j<(int)path.size();j++){ Point before=(j==0 ? state.nw.nodes[n1] : nv.nodes[path[j-1]]); Point &after=(j==((int)path.size())-1 ? state.nw.nodes[n2] : nv.nodes[path[j+1]]); Point &cur=nv.nodes[path[j]]; if (after==cur) continue; if (before==cur) { if (j-1<0) continue; before=(j-1==0 ? state.nw.nodes[n1] : nv.nodes[path[j-2]]); } Point d=unit(before-cur)+unit(after-cur); if (d.is_null()) continue; d=unit(d)*min(min(norm(before-cur),norm(after-cur))/2,state.avgsize/2); e.splinehandles.insert(--e.splinehandles.end(),to_left(d,PI/2)*sign(scalar(to_left(d,PI/2),before-cur))); e.splinepoints.push_back(cur+d); //debugline(cur+d,cur+d+to_left(d,PI/2)*sign(scalar(to_left(d,PI/2),before-cur)),0,0,255,true); //if (j<path.size()-1) debugline(nv.nodes[path[j]].x,nv.nodes[path[j]].y,nv.nodes[path[j+1]].x,nv.nodes[path[j+1]].y,255,100,100); } //debugline(nv.nodes[path.back()].x,nv.nodes[path.back()].y,state.nw.nodes[n2].x,state.nw.nodes[n2].y,255,100,100); } } } /* NetDisplay nd(nv); nd.waitKeyPress=true; nd.show();*/ }
void route_edges2(Layouter &state,plugin& pg, double scale, int iter, double temp, int debug){ VR nodes; double d=state.avgsize/5; int n=state.nw.nodes.size(); for (int i=0;i<n;i++){ nodes.push_back(state.nw.nodes[i].rect()); nodes.back().extend(d); //debugrect(nodes.back(),0,0,255); } for (int i=0,m=state.nw.edges.size();i<m;i++){ //if (i!=iter) continue; Edge &e=state.nw.edges[i]; e.splinehandles.clear(); e.splinepoints.clear(); int n1=e.from; int n2=e.to; Point vec,p1,p2; double dir; switch(e.type){ case substrate: dir=lim(state.nw.nodes[n1].dir+PI/2); vec=Point(dir); swap(n1,n2); p1=state.nw.nodes[n1]; vec=state.nw.nodes[n2].rect().border_vec(vec); p2=state.nw.nodes[n2]+vec; break; case product: dir=lim(state.nw.nodes[n1].dir-PI/2); vec=Point(dir); vec=state.nw.nodes[n1].rect().border_vec(vec); p1=state.nw.nodes[n1]+vec; p2=state.nw.nodes[n2]; break; case activator: case inhibitor: case catalyst: swap(n1,n2); default: p1=state.nw.nodes[n1]; p2=state.nw.nodes[n2]; } vector<Segment> vs; vs.push_back(Segment(ParamEdge(p1,p2),true,true)); split_route(vs,nodes,0,n1,n2); Point vec1=state.nw.nodes[n1].rect().border_vec(vs.front().edge.to()-vs.front().edge.from()); Point vec2=state.nw.nodes[n2].rect().border_vec(vs.back().edge.from()-vs.back().edge.to()); switch(e.type){ case activator: case inhibitor: case catalyst: dir=lim(state.nw.nodes[n2].dir); if (scalar(Point(dir),vs.back().edge.from()-vs.back().edge.to())<0) dir=lim(dir+PI); vec=Point(dir); vec=state.nw.nodes[n2].rect().border_vec(vec); p2=state.nw.nodes[n2]+vec; case substrate: e.splinehandles.push_back(vec1+d); e.splinehandles.push_back(vec+d); break; case product: e.splinehandles.push_back(vec+d); e.splinehandles.push_back(vec2+d); break; default: e.splinehandles.push_back(vec1+d); e.splinehandles.push_back(vec2+d); } for (int j=1,s=vs.size();j<s;j++){ Point before=vs[j-1].edge.from(); Point cur=vs[j-1].edge.to(); //if (cur!=vs[j].edge.from()) throw "ups: edge segments not continious"; Point after=vs[j].edge.to(); Point dv=unit(before-cur)*d+unit(after-cur)*d; debugline(cur,cur+dv,0,255,0,true); e.splinehandles.insert(--e.splinehandles.end(),unit(to_left(dv,PI/2))*sign(scalar(to_left(dv,PI/2),before-cur))*d); e.splinepoints.push_back(cur+dv); } } }