在二维点集中寻找孔?

为了简单起见，我用水平线和垂直线来做

I do it by Horizontal and Vertical lines for simplicity

分割输出

只需将同一孔的线组合在一起(相交的线...矢量方法)，也可以在项目符号#4中通过洪水填充(位图方法)来完成

Just group lines of the same hole together (intersecting ones ... vector approach) and also can be done in bullet #4 by flood fill (bitmap approach)

多边形化输出

获取同一孔/组的 H,V 线 的所有边缘点并创建多边形(对它们进行排序，使其连接不会相交).有很多库、算法和源代码.

Take all edge points of H,V lines of the same hole/group and create polygon (sort them so their connection does not intersect anything). There are lot of libs,algorithms and source code about this.

我的这种方法的源代码:

void main_compute(int N)
    {
    // cell storage for density computation
    struct _cell
        {
        double x0,x1,y0,y1; // bounding area of points inside cell
        int cnt;            // points inside cell
        _cell(){}; _cell(_cell& a){ *this=a; }; ~_cell(){}; _cell* operator = (const _cell *a) { *this=*a; return this; }; /*_cell* operator = (const _cell &a) { ...copy... return this; };*/
        };
    // line storage for hole area
    struct _line
        {
        double x0,y0,x1,y1; // line edge points
        int id;             // id of hole for segmentation/polygonize
        int i0,i1,j0,j1;    // index in map[][]
        _line(){}; _line(_line& a){ *this=a; }; ~_line(){}; _line* operator = (const _line *a) { *this=*a; return this; }; /*_line* operator = (const _line &a) { ...copy... return this; };*/
        };

    int i,j,k,M=N*N;        // M = max N^2 but usualy is much much less so dynamic list will be better
    double mx,my;           // scale to map
    _cell *m;               // cell ptr
    glview2D::_pnt *p;      // point ptr
    double x0,x1,y0,y1;     // used area (bounding box)
    _cell **map=NULL;       // cell grid
    _line *lin=NULL;        // temp line list for hole segmentation
    int lins=0;             // actual usage/size of lin[M]

    // scan point cloud for bounding box (if it is known then skip it)
    p=&view.pnt[0];
    x0=p->p[0]; x1=x0;
    y0=p->p[1]; y1=y0;
    for (i=0;i<view.pnt.num;i++)
        {
        p=&view.pnt[i];
        if (x0>p->p[0]) x0=p->p[0];
        if (x1<p->p[0]) x1=p->p[0];
        if (y0>p->p[1]) y0=p->p[1];
        if (y1<p->p[1]) y1=p->p[1];
        }
    // compute scale for coordinate to map index conversion
    mx=double(N)/(x1-x0);   // add avoidance of division by zero if empty point cloud !!!
    my=double(N)/(y1-y0);
    // dynamic allocation of map[N][N],lin[M]
    lin=new _line[M];
    map=new _cell*[N];
    for (i=0;i<N;i++) map[i]=new _cell[N];
    // reset map[N][N]
    for (i=0;i<N;i++)
     for (j=0;j<N;j++)
      map[i][j].cnt=0;
    // compute point cloud density
    for (k=0;k<view.pnt.num;k++)
        {
        p=&view.pnt[k];
        i=double((p->p[0]-x0)*mx); if (i<0) i=0; if (i>=N) i=N-1;
        j=double((p->p[1]-y0)*my); if (j<0) j=0; if (j>=N) j=N-1;
        m=&map[i][j];
        if (!m->cnt)
            {
            m->x0=p->p[0];
            m->x1=p->p[0];
            m->y0=p->p[1];
            m->y1=p->p[1];
            }
        if (m->cnt<0x7FFFFFFF) m->cnt++;    // avoid overflow
        if (m->x0>p->p[0]) m->x0=p->p[0];
        if (m->x1<p->p[0]) m->x1=p->p[0];
        if (m->y0>p->p[1]) m->y0=p->p[1];
        if (m->y1<p->p[1]) m->y1=p->p[1];
        }
    // find holes (map[i][j].cnt==0) or (map[i][j].cnt<=treshold)
    // and create lin[] list of H,V lines covering holes
    for (j=0;j<N;j++) // search lines
        {
        for (i=0;i<N;)
            {
            int i0,i1;
            for (;i<N;i++) if (map[i][j].cnt==0) break; i0=i-1; // find start of hole
            for (;i<N;i++) if (map[i][j].cnt!=0) break; i1=i;   // find end of hole
            if (i0< 0) continue;                // skip bad circumstances (edges or no hole found)
            if (i1>=N) continue;
            if (map[i0][j].cnt==0) continue;
            if (map[i1][j].cnt==0) continue;
            _line l;
            l.i0=i0; l.x0=map[i0][j].x1;
            l.i1=i1; l.x1=map[i1][j].x0;
            l.j0=j ; l.y0=0.25*(map[i0][j].y0+map[i0][j].y1+map[i1][j].y0+map[i1][j].y1);
            l.j1=j ; l.y1=l.y0;
            lin[lins]=l; lins++;
            }
        }
    for (i=0;i<N;i++) // search columns
        {
        for (j=0;j<N;)
            {
            int j0,j1;
            for (;j<N;j++) if (map[i][j].cnt==0) break; j0=j-1; // find start of hole
            for (;j<N;j++) if (map[i][j].cnt!=0) break; j1=j;   // find end of hole
            if (j0< 0) continue;                // skip bad circumstances (edges or no hole found)
            if (j1>=N) continue;
            if (map[i][j0].cnt==0) continue;
            if (map[i][j1].cnt==0) continue;
            _line l;
            l.i0=i ; l.y0=map[i][j0].y1;
            l.i1=i ; l.y1=map[i][j1].y0;
            l.j0=j0; l.x0=0.25*(map[i][j0].x0+map[i][j0].x1+map[i][j1].x0+map[i][j1].x1);
            l.j1=j1; l.x1=l.x0;
            lin[lins]=l; lins++;
            }
        }
    // segmentate lin[] ... group lines of the same hole together by lin[].id
    // segmentation based on vector lines data
    // you can also segmentate the map[][] directly as bitmap during hole detection
    for (i=0;i<lins;i++) lin[i].id=i;   // all lines are separate
    for (;;)                            // join what you can
        {
        int e=0,i0,i1;
        _line *a,*b;
        for (a=lin,i=0;i<lins;i++,a++)
            {
            for (b=a,j=i;j<lins;j++,b++)
             if (a->id!=b->id)
                {
                // do 2D lines a,b intersect ?
                double xx0,yy0,xx1,yy1;
                double kx0,ky0,dx0,dy0,t0;
                double kx1,ky1,dx1,dy1,t1;
                double x0=a->x0,y0=a->y0;
                double x1=a->x1,y1=a->y1;
                double x2=b->x0,y2=b->y0;
                double x3=b->x1,y3=b->y1;
                // discart lines with non intersecting bound rectangles
                double a0,a1,b0,b1;
                if (x0<x1) { a0=x0; a1=x1; } else { a0=x1; a1=x0; }
                if (x2<x3) { b0=x2; b1=x3; } else { b0=x3; b1=x2; }
                if (a1<b0) continue;
                if (a0>b1) continue;
                if (y0<y1) { a0=y0; a1=y1; } else { a0=y1; a1=y0; }
                if (y2<y3) { b0=y2; b1=y3; } else { b0=y3; b1=y2; }
                if (a1<b0) continue;
                if (a0>b1) continue;
                // compute intersection
                kx0=x0; ky0=y0; dx0=x1-x0; dy0=y1-y0;
                kx1=x2; ky1=y2; dx1=x3-x2; dy1=y3-y2;
                t1=divide(dx0*(ky0-ky1)+dy0*(kx1-kx0),(dx0*dy1)-(dx1*dy0));
                xx1=kx1+(dx1*t1);
                yy1=ky1+(dy1*t1);
                if (fabs(dx0)>=fabs(dy0)) t0=divide(kx1-kx0+(dx1*t1),dx0);
                else                      t0=divide(ky1-ky0+(dy1*t1),dy0);
                xx0=kx0+(dx0*t0);
                yy0=ky0+(dy0*t0);
                // check if intersection exists
                if (fabs(xx1-xx0)>1e-6) continue;
                if (fabs(yy1-yy0)>1e-6) continue;
                if ((t0<0.0)||(t0>1.0)) continue;
                if ((t1<0.0)||(t1>1.0)) continue;
                // if yes ... intersection point = xx0,yy0
                e=1; break;
                }
            if (e) break;                       // join found ... stop searching
            }
        if (!e) break;                          // no join found ... stop segmentation
        i0=a->id;                               // joid ids ... rename i1 to i0
        i1=b->id;
        for (a=lin,i=0;i<lins;i++,a++)
         if (a->id==i1)
          a->id=i0;
        }

    // visualize lin[]
    for (i=0;i<lins;i++)
        {
        glview2D::_lin l;
        l.p0.p[0]=lin[i].x0;
        l.p0.p[1]=lin[i].y0;
        l.p1.p[0]=lin[i].x1;
        l.p1.p[1]=lin[i].y1;
//      l.col=0x0000FF00;
        l.col=(lin[i].id*0x00D00C10A)+0x00800000;   // color is any function of ID
        view.lin.add(l);
        }

    // dynamic deallocation of map[N][N],lin[M]
    for (i=0;i<N;i++) delete[] map[i];
    delete[] map;
    delete[] lin;
    }
//---------------------------------------------------------------------------

忽略我的 glview2D 东西(它是我的几何图形 gfx 渲染引擎)

Just ignore my glview2D stuff (it is my gfx render engine for geometry)

• view.pnt[] 是你点的动态列表(随机生成)
• view.lin[] 是动态列表输出H,V 线 仅用于可视化
• lin[] 是你的行输出

• view.pnt[] is dynamic list of your points (generated by random)
• view.lin[] is dynamic list output H,V lines for visualization only
• lin[] is your lines output

这是输出:

我现在懒得添加多边形化，你可以看到分割工作(着色).如果您还需要多边形化方面的帮助，请评论我，但我认为这不应该有任何问题.

I am too lazy to add polygonize for now you can see that segmentation works (coloring). If you need also help with polygonize then comment me but I think that should not be any problem.

复杂度估计取决于整体孔覆盖率

Complexity estimation depends on the overall hole coverage

但对于大多数代码，它是 O(N) 并且对于孔搜索/分割 ~O((M^2)+(U^2))其中:

but for most of the code it is O(N) and for hole search/segmentation ~O((M^2)+(U^2)) where:

• N 是点数
• M 是地图网格大小
• U 是 H,V 线 计数取决于孔...
• <代码>M <<

• N is point count
• M is map grid size
• U is H,V lines count dependent on holes ...
• M << N, U << M*M

正如您在上图中看到的 3783 点 30x30 网格在我的设置中花费了几乎 9ms

as you can see for 3783 points 30x30 grid on the image above it took almost 9ms on my setup

[Edit1] 使用矢量多边形化一点

对于简单的洞很好，但对于更复杂的洞，还有一些小问题

for simple holes is fine but for more complicated ones there are some hick-ups yet

[Edit2] 终于有一点时间了，所以这里是:

这是一个简单的孔/多边形搜索类，以更愉快/易于管理的形式:

This is simple class for hole/polygon search in more pleasant/manageable form:

//---------------------------------------------------------------------------
class holes
    {
public:
    int xs,ys,n;            // cell grid x,y - size  and points count
    int **map;              // points density map[xs][ys]
                            // i=(x-x0)*g2l;    x=x0+(i*l2g);
                            // j=(y-y0)*g2l;    y=y0+(j*l2g);
    double mg2l,ml2g;       // scale to/from global/map space   (x,y) <-> map[i][j]
    double x0,x1,y0,y1;     // used area (bounding box)

    struct _line
        {
        int id;             // id of hole for segmentation/polygonize
        int i0,i1,j0,j1;    // index in map[][]
        _line(){}; _line(_line& a){ *this=a; }; ~_line(){}; _line* operator = (const _line *a) { *this=*a; return this; }; /*_line* operator = (const _line &a) { ...copy... return this; };*/
        };
    List<_line> lin;
    int lin_i0;             // start index for perimeter lines (smaller indexes are the H,V lines inside hole)

    struct _point
        {
        int i,j;            // index in map[][]
        int p0,p1;          // previous next point
        int used;
        _point(){}; _point(_point& a){ *this=a; }; ~_point(){}; _point* operator = (const _point *a) { *this=*a; return this; }; /*_point* operator = (const _point &a) { ...copy... return this; };*/
        };
    List<_point> pnt;

    // class init and internal stuff
    holes()  { xs=0; ys=0; n=0; map=NULL; mg2l=1.0; ml2g=1.0;  x0=0.0; y0=0.0; x1=0.0; y1=0.0; lin_i0=0; };
    holes(holes& a){ *this=a; };
    ~holes() { _free(); };
    holes* operator = (const holes *a) { *this=*a; return this; };
    holes* operator = (const holes &a)
        {
        xs=0; ys=0; n=a.n; map=NULL;
        mg2l=a.mg2l; x0=a.x0; x1=a.x1;
        ml2g=a.ml2g; y0=a.y0; y1=a.y1;
        _alloc(a.xs,a.ys);
        for (int i=0;i<xs;i++)
        for (int j=0;j<ys;j++) map[i][j]=a.map[i][j];
        return this;
        }
    void _free() { if (map) { for (int i=0;i<xs;i++) if (map[i]) delete[] map[i]; delete[] map; } xs=0; ys=0; }
    void _alloc(int _xs,int _ys) { int i=0; _free(); xs=_xs; ys=_ys; map=new int*[xs]; if (map) for (i=0;i<xs;i++) { map[i]=new int[ys]; if (map[i]==NULL) { i=-1; break; } } else i=-1; if (i<0) _free(); }

    // scann boundary box interface
    void scann_beg();
    void scann_pnt(double x,double y);
    void scann_end();

    // dynamic allocations
    void cell_size(double sz);      // compute/allocate grid from grid cell size = sz x sz

    // scann holes interface
    void holes_beg();
    void holes_pnt(double x,double y);
    void holes_end();

    // global(x,y) <- local map[i][j] + half cell offset
    inline void l2g(double &x,double &y,int i,int j) { x=x0+((double(i)+0.5)*ml2g); y=y0+((double(j)+0.5)*ml2g); }
    // local map[i][j] <- global(x,y)
    inline void g2l(int &i,int &j,double x,double y) { i=     double((x-x0) *mg2l); j=     double((y-y0) *mg2l); }
    };
//---------------------------------------------------------------------------
void holes::scann_beg()
    {
    x0=0.0; y0=0.0; x1=0.0; y1=0.0; n=0;
    }
//---------------------------------------------------------------------------
void holes::scann_pnt(double x,double y)
    {
    if (!n) { x0=x; y0=y; x1=x; y1=y; }
    if (n<0x7FFFFFFF) n++;  // avoid overflow
    if (x0>x) x0=x; if (x1<x) x1=x;
    if (y0>y) y0=y; if (y1<y) y1=y;
    }
//---------------------------------------------------------------------------
void holes::scann_end()
    {
    }
//---------------------------------------------------------------------------
void holes::cell_size(double sz)
    {
    int x,y;
    if (sz<1e-6) sz=1e-6;
    x=ceil((x1-x0)/sz);
    y=ceil((y1-y0)/sz);
    _alloc(x,y);
    ml2g=sz; mg2l=1.0/sz;
    }
//---------------------------------------------------------------------------
void holes::holes_beg()
    {
    int i,j;
    for (i=0;i<xs;i++)
     for (j=0;j<ys;j++)
      map[i][j]=0;
    }
//---------------------------------------------------------------------------
void holes::holes_pnt(double x,double y)
    {
    int i,j;
    g2l(i,j,x,y);
    if ((i>=0)&&(i<xs))
     if ((j>=0)&&(j<ys))
      if (map[i][j]<0x7FFFFFFF) map[i][j]++;    // avoid overflow
    }
//---------------------------------------------------------------------------
void holes::holes_end()
    {
    int i,j,e,i0,i1;
    List<int> ix;       // hole lines start/stop indexes for speed up the polygonization
    _line *a,*b,l;
    _point *aa,*bb,p;
    lin.num=0; lin_i0=0;// clear lines
    ix.num=0;           // clear indexes

    // find holes (map[i][j].cnt==0) or (map[i][j].cnt<=treshold)
    // and create lin[] list of H,V lines covering holes
    for (j=0;j<ys;j++) // search lines
     for (i=0;i<xs;)
        {
        int i0,i1;
        for (;i<xs;i++) if (map[i][j]==0) break; i0=i-1;    // find start of hole
        for (;i<xs;i++) if (map[i][j]!=0) break; i1=i;      // find end of hole
        if (i0<  0) continue;               // skip bad circumstances (edges or no hole found)
        if (i1>=xs) continue;
        if (map[i0][j]==0) continue;
        if (map[i1][j]==0) continue;
        l.i0=i0;
        l.i1=i1;
        l.j0=j ;
        l.j1=j ;
        l.id=-1;
        lin.add(l);
        }
    for (i=0;i<xs;i++) // search columns
     for (j=0;j<ys;)
        {
        int j0,j1;
        for (;j<ys;j++) if (map[i][j]==0) break; j0=j-1;    // find start of hole
        for (;j<ys;j++) if (map[i][j]!=0) break; j1=j  ;    // find end of hole
        if (j0<  0) continue;               // skip bad circumstances (edges or no hole found)
        if (j1>=ys) continue;
        if (map[i][j0]==0) continue;
        if (map[i][j1]==0) continue;
        l.i0=i ;
        l.i1=i ;
        l.j0=j0;
        l.j1=j1;
        l.id=-1;
        lin.add(l);
        }
    // segmentate lin[] ... group lines of the same hole together by lin[].id
    // segmentation based on vector lines data
    // you can also segmentate the map[][] directly as bitmap during hole detection
    for (i=0;i<lin.num;i++) lin[i].id=i;    // all lines are separate
    for (;;)                            // join what you can
        {
        for (e=0,a=lin.dat,i=0;i<lin.num;i++,a++)
            {
            for (b=a,j=i;j<lin.num;j++,b++)
             if (a->id!=b->id)
                {
                // if a,b not intersecting or neighbouring
                if (a->i0>b->i1) continue;
                if (b->i0>a->i1) continue;
                if (a->j0>b->j1) continue;
                if (b->j0>a->j1) continue;
                // if they do mark e for join groups
                e=1; break;
                }
            if (e) break;                       // join found ... stop searching
            }
        if (!e) break;                          // no join found ... stop segmentation
        i0=a->id;                               // joid ids ... rename i1 to i0
        i1=b->id;
        for (a=lin.dat,i=0;i<lin.num;i++,a++)
         if (a->id==i1)
          a->id=i0;
        }
    // sort lin[] by id
    for (e=1;e;) for (e=0,a=&lin[0],b=&lin[1],i=1;i<lin.num;i++,a++,b++)
     if (a->id>b->id) { l=*a; *a=*b; *b=l; e=1; }
    // re id lin[] and prepare start/stop indexes
    for (i0=-1,i1=-1,a=&lin[0],i=0;i<lin.num;i++,a++)
     if (a->id==i1) a->id=i0;
      else { i0++; i1=a->id; a->id=i0; ix.add(i); }
    ix.add(lin.num);

    // polygonize
    lin_i0=lin.num;
    for (j=1;j<ix.num;j++)  // process hole
        {
        i0=ix[j-1]; i1=ix[j];
        // create border pnt[] list (unique points only)
        pnt.num=0; p.used=0; p.p0=-1; p.p1=-1;
        for (a=&lin[i0],i=i0;i<i1;i++,a++)
            {
            p.i=a->i0;
            p.j=a->j0;
            map[p.i][p.j]=0;
            for (aa=&pnt[0],e=0;e<pnt.num;e++,aa++)
             if ((aa->i==p.i)&&(aa->j==p.j)) { e=-1; break; }
            if (e>=0) pnt.add(p);
            p.i=a->i1;
            p.j=a->j1;
            map[p.i][p.j]=0;
            for (aa=&pnt[0],e=0;e<pnt.num;e++,aa++)
             if ((aa->i==p.i)&&(aa->j==p.j)) { e=-1; break; }
            if (e>=0) pnt.add(p);
            }
        // mark not border points
        for (aa=&pnt[0],i=0;i<pnt.num;i++,aa++)
         if (!aa->used)                     // ignore marked points
          if ((aa->i>0)&&(aa->i<xs-1))      // ignore map[][] border points
           if ((aa->j>0)&&(aa->j<ys-1))
            {                               // ignore if any non hole cell around
            if (map[aa->i-1][aa->j-1]>0) continue;
            if (map[aa->i-1][aa->j  ]>0) continue;
            if (map[aa->i-1][aa->j+1]>0) continue;
            if (map[aa->i  ][aa->j-1]>0) continue;
            if (map[aa->i  ][aa->j+1]>0) continue;
            if (map[aa->i+1][aa->j-1]>0) continue;
            if (map[aa->i+1][aa->j  ]>0) continue;
            if (map[aa->i+1][aa->j+1]>0) continue;
            aa->used=1;
            }
        // delete marked points
        for (aa=&pnt[0],e=0,i=0;i<pnt.num;i++,aa++)
         if (!aa->used) { pnt[e]=*aa; e++; } pnt.num=e;

        // connect neighbouring points distance=1
        for (i0=   0,aa=&pnt[i0];i0<pnt.num;i0++,aa++)
         if (aa->used<2)
          for (i1=i0+1,bb=&pnt[i1];i1<pnt.num;i1++,bb++)
           if (bb->used<2)
            {
            i=aa->i-bb->i; if (i<0) i=-i; e =i;
            i=aa->j-bb->j; if (i<0) i=-i; e+=i;
            if (e!=1) continue;
            aa->used++; if (aa->p0<0) aa->p0=i1; else aa->p1=i1;
            bb->used++; if (bb->p0<0) bb->p0=i0; else bb->p1=i0;
            }
        // try to connect neighbouring points distance=sqrt(2)
        for (i0=   0,aa=&pnt[i0];i0<pnt.num;i0++,aa++)
         if (aa->used<2)
          for (i1=i0+1,bb=&pnt[i1];i1<pnt.num;i1++,bb++)
           if (bb->used<2)
            if ((aa->p0!=i1)&&(aa->p1!=i1))
             if ((bb->p0!=i0)&&(bb->p1!=i0))
            {
            if ((aa->used)&&(aa->p0==bb->p0)) continue; // avoid small closed loops
            i=aa->i-bb->i; if (i<0) i=-i; e =i*i;
            i=aa->j-bb->j; if (i<0) i=-i; e+=i*i;
            if (e!=2) continue;
            aa->used++; if (aa->p0<0) aa->p0=i1; else aa->p1=i1;
            bb->used++; if (bb->p0<0) bb->p0=i0; else bb->p1=i0;
            }
        // try to connect to closest point
        int ii,dd;
        for (i0=   0,aa=&pnt[i0];i0<pnt.num;i0++,aa++)
         if (aa->used<2)
            {
            for (ii=-1,i1=i0+1,bb=&pnt[i1];i1<pnt.num;i1++,bb++)
             if (bb->used<2)
              if ((aa->p0!=i1)&&(aa->p1!=i1))
               if ((bb->p0!=i0)&&(bb->p1!=i0))
                {
                i=aa->i-bb->i; if (i<0) i=-i; e =i*i;
                i=aa->j-bb->j; if (i<0) i=-i; e+=i*i;
                if ((ii<0)||(e<dd)) { ii=i1; dd=e; }
                }
            if (ii<0) continue;
            i1=ii; bb=&pnt[i1];
            aa->used++; if (aa->p0<0) aa->p0=i1; else aa->p1=i1;
            bb->used++; if (bb->p0<0) bb->p0=i0; else bb->p1=i0;
            }

        // add connected points to lin[] ... this is hole perimeter !!!
        // lines are 2 x duplicated so some additional code for sort the order of line swill be good idea
        l.id=lin[ix[j-1]].id;
        for (i0=0,aa=&pnt[i0];i0<pnt.num;i0++,aa++)
            {
            l.i0=aa->i;
            l.j0=aa->j;
            // [edit3] this avoid duplicating lines
            if (aa->p0>i0) { bb=&pnt[aa->p0]; l.i1=bb->i; l.j1=bb->j; lin.add(l); }
            if (aa->p1>i0) { bb=&pnt[aa->p1]; l.i1=bb->i; l.j1=bb->j; lin.add(l); }
            //if (aa->p0>=0) { bb=&pnt[aa->p0]; l.i1=bb->i; l.j1=bb->j; lin.add(l); }
            //if (aa->p1>=0) { bb=&pnt[aa->p1]; l.i1=bb->i; l.j1=bb->j; lin.add(l); }
            }
        }
    }
//---------------------------------------------------------------------------

您只需将我的 List<T> 模板替换为 std::list 或其他任何内容(该模板我无法共享).它是 T ...

You just need to replace my List<T> template with std::list or whatever (that template I cannot share). It is an dynamic 1D array of T ...

• 列表x; 与 int x[];
相同
• x.add(); 将空项添加到 x
• x.add(a); 向 x 添加一个项目
• x.reset() 清空数组
• x.allocate(size) 预先分配空间以避免运行缓慢的重新分配
• x.num 是 x[] 中的项目数 ... 在项目中使用的大小

• List<int> x; is the same as int x[];
• x.add(); add empty item to x
• x.add(a); add a item to x
• x.reset() clears the array
• x.allocate(size) preallocate space to avoid reallocations on the run which is slow
• x.num is number of items in x[] ... used size in items

在原始代码中只是静态数组，所以如果您感到困惑，请检查它.

in the original code are only static arrays so if you are confused check with it instead.

现在如何使用它:

h.scann_beg(); for (i=0;i<view.pnt.num;i++) { p=view.pnt[i].p0.p; h.scann_pnt(p[0],p[1]); } h.scann_end();
h.cell_size(2.5);
h.holes_beg(); for (i=0;i<view.pnt.num;i++) { p=view.pnt[i].p0.p; h.holes_pnt(p[0],p[1]); } h.holes_end();

其中 view.pnt[] 是输入点列表，其中包含:view.pnt[i].p0.p[ 2 ]= { x,y }

where view.pnt[] is list of input points and inside it: view.pnt[i].p0.p[ 2 ]= { x,y }

输出在 h.lin[] 和 lin_i0 其中:

Output is in h.lin[] and lin_i0 where:

• h.lin[i] i= <0,lin_i0 ) 是内部 H,V 线
• h.lin[i] i= <lin_i0,h.lin.num ) 是周长

• h.lin[i] i= < 0,lin_i0 ) are the inside H,V lines
• h.lin[i] i= < lin_i0,h.lin.num ) are the perimeter

周界线没有排序并且重复了两次，因此只需对它们进行排序并删除重复项(太懒了).lin[] 里面是线所属的孔0,1,2,3,...的id ..id，i,j 地图内的坐标.因此，要正确输出到您的世界坐标，请执行以下操作:

The perimeter lines are not ordered and are duplicated twice so just order them and remove duplicates (too lazy for that). Inside lin[] are id .. id of hole 0,1,2,3,... to which the line belongs and i,j coordinates inside map. so for proper output into your world coordinates do something like this:

int i,j;
holes h;                // holes class
double *p;              // input point list ptr

h.scann_beg(); for (i=0;i<view.pnt.num;i++) { p=view.pnt[i].p0.p; h.scann_pnt(p[0],p[1]); } h.scann_end();
h.cell_size(2.5);
h.holes_beg(); for (i=0;i<view.pnt.num;i++) { p=view.pnt[i].p0.p; h.holes_pnt(p[0],p[1]); } h.holes_end();

DWORD coltab[]=
    {
    0x000000FF,
    0x0000FF00,
    0x00FF0000,
    0x0000FFFF,
    0x00FFFF00,
    0x00FF00FF,
    0x00FFFFFF,
    0x00000088,
    0x00008800,
    0x00880000,
    0x00008888,
    0x00888800,
    0x00880088,
    0x00888888,
    };

for (i=0;i<h.lin.num;i++)                   // draw lin[]
    {
    glview2D::_lin a;
    holes::_line *b=&h.lin[i];
    h.l2g(a.p0.p[0],a.p0.p[1],b->i0,b->j0);
    h.l2g(a.p1.p[0],a.p1.p[1],b->i1,b->j1);
    if (i<h.lin_i0) // H,V lines inside hole(b->id) .. gray  [edit3] was <= which is wrong and miss-color first perimeter line
        {
        a.col=0x00808080;
        }
    else{               // hole(b->id) perimeter lines ... each hole different collor
        if ((b->id>=0)&&(b->id<14)) a.col=coltab[b->id];
        if (b->id==-1) a.col=0x00FFFFFF;    // special debug lines
        if (b->id==-2) a.col=0x00AA8040;    // special debug lines
        }
    view.lin.add(a); // here draw your line or add it to your polygon instead
    }

• 我的 view.lin[] 有成员: p0,p1, 分别是 view.pnt[] 和 col 即颜色
• my view.lin[] has members: p0,p1, which are points as view.pnt[] and col which is color

当孔太小时，我只看到了一个问题(直径 < 3 个单元格) 否则没问题

I saw only one issue with this when holes are too small (diameter < 3 cells) otherwise is OK

[edit4] 重新排列周界线

要这样做而不是这样做:

to do that just instead of this:

        /* add connected points to lin[] ... this is hole perimeter !!!
        // lines are 2 x duplicated so some additional code for sort the order of line swill be good idea
        l.id=lin[ix[j-1]].id;
        for (i0=0,aa=&pnt[i0];i0<pnt.num;i0++,aa++)
            {
            l.i0=aa->i;
            l.j0=aa->j;
            // [edit3] this avoid duplicating lines
            if (aa->p0>i0) { bb=&pnt[aa->p0]; l.i1=bb->i; l.j1=bb->j; lin.add(l); }
            if (aa->p1>i0) { bb=&pnt[aa->p1]; l.i1=bb->i; l.j1=bb->j; lin.add(l); }
            //if (aa->p0>=0) { bb=&pnt[aa->p0]; l.i1=bb->i; l.j1=bb->j; lin.add(l); }
            //if (aa->p1>=0) { bb=&pnt[aa->p1]; l.i1=bb->i; l.j1=bb->j; lin.add(l); }
            } */

这样做:

    // add connected points to lin[] ... this is hole perimeter !!!
    l.id=lin[ix[j-1]].id;
    // add index of points instead points
    int lin_i1=lin.num;
    for (i0=0,aa=&pnt[i0];i0<pnt.num;i0++,aa++)
        {
        l.i0=i0;
        if (aa->p0>i0) { l.i1=aa->p0; lin.add(l); }
        if (aa->p1>i0) { l.i1=aa->p1; lin.add(l); }
        }
    // reorder perimeter lines
    for (i0=lin_i1,a=&lin[i0];i0<lin.num-1;i0++,a++)
     for (i1=i0+1  ,b=&lin[i1];i1<lin.num  ;i1++,b++)
        {
        if (a->i1==b->i0) { a++; l=*a; *a=*b; *b=l;                                a--; break; }
        if (a->i1==b->i1) { a++; l=*a; *a=*b; *b=l; i=a->i0; a->i0=a->i1; a->i1=i; a--; break; }
        }
    // convert point indexes to points
    for (i0=lin_i1,a=&lin[i0];i0<lin.num;i0++,a++)
        {
        bb=&pnt[a->i0]; a->i0=bb->i; a->j0=bb->j;
        bb=&pnt[a->i1]; a->i1=bb->i; a->j1=bb->j;
        }

[Edit5] holes::holes_end 内的多边形化如何工作

How polygonize inside holes::holes_end works

作为输入，您需要所有 H,V 线 lin[] 按孔分段/分组/排序的列表和密度图 map[][].

As input for this you need the list of all H,V lines lin[] segmentated/grouped/sorted by hole and the density map map[][].

1. 遍历所有孔

1. 遍历加工孔的所有 H、V 线

创建所有唯一线端点的列表pnt[](无重复).因此，为每条线取 2 个端点，并查看每个点是否已经在列表中.如果不添加，则忽略它.

Create list of all unique line endpoints pnt[] (no duplicates). So take 2 endpoints for each line and look if each point is already in the list. If not add it there else ignore it.

从列表中删除所有非边界点

因此，通过查看密度中的 4 个邻居来删除所有与非孔区域不接触的点 map[][]

So remove all points that have no contact with non-hole area by looking into 4 neighbors in the density map[][]

对点进行连通分量分析

1. 设置 used=0;p0=-1;p1=-1; 用于 pnt[] 列表中的所有点

2. 用 distance=1

1. set used=0; p0=-1; p1=-1; for all points in pnt[] list

2. connect points with distance=1

使用 used<2 遍历所有点 pnt[]，这意味着它们尚未完全使用，并且对于每个这样的点搜索 pnt[] 再次用于另一个具有 distance = 1 的点.这意味着它是它的 4 个邻居并且应该被连接所以 add 连接信息到他们的展位(使用 p0 或 p1 索引是未使用的 (-1)) 并增加两个点的使用量.

loop through all points pnt[] with used<2 which means they are not fully used yet and for each such point search pnt[] again for another such point that has also distance = 1 to it. It means it is its 4-neighbors and should be connected so add the connection info to booth of them (use p0 or p1 index which ever is unused (-1)) and increment usage of both points.

尝试用 distance=sqrt(2)

与 #2 几乎相同，只是现在选择 8 个邻居的对角线的距离.这次也避免了闭环，所以不要连接已经连接到它的点.

is almost the same as #2 except the distance which now selects diagonals of 8-neighbors. This time also avoid closed loops so do not connect point that is already connected to it.

尝试连接最近的点

再次与#2,#3几乎相同，但选择最近的点并避免闭环.

again is almost the same as #2,#3 but select the closest point instead and also avoid closed loops.

从 pnt[]

所以选择列表中的第一个点并将其添加到多边形中.然后将连接点添加到它(无论您以哪种方式启动 p0 或 p1).然后添加它的连接点(不同于之前添加的点到多边形以避免前后循环).添加与 pnt[] 中的点一样多的点.

so pick first point in list and add it to the polygon. then add the connected point to it (does not matter which way you start p0 or p1). Then add its connected point (different then previous added point to polygon to avoid back and forward loops). Add so many points as you have points in a pnt[].

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