连通不规则多边形算法

多边形连通和最小生成树本质上是一样的，问题在于确定权值。
下面算法由js实现，演示由svg提供。
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<html>
<head>
    <script>
        let shown='hidden';
        //核心算法
        let caculatePath=function(){
            /*显示和隐藏，算法无关*/
            for(let i=0;i<panel.children.length;i++){
                panel.children[i].style.visibility=shown;
            }
            lineGroup.innerHTML=null;
            if(shown=='hidden'){
                shown='visible';
            }else{
                shown='hidden';
                return;
            }
            getEvent().target.style.visibility='visible';
            let gons=getPolygons(getEvent().target);
            let target=document.getElementById('target');
            /*----------END----------*/
             
            //closeList表示已经连通的图形，无需再连通
            let closeList=[];
            //未连通的图形
            let openList=[];
             
            //放入外框图形
            closeList.push(gons[0]);
            //放入其他图形
            for(let i=1;i<gons.length;i++){
                openList.push(gons[i]);
            }
            let cache={};
            while(openList.length>0){
                let min={dist:Number.MAX_SAFE_INTEGER};
                let imin,jmin;
                for(let i=0;i<openList.length;i++){
                    for(let j=0;j<closeList.length;j++){
                        //缓存之前的计算值,提高计算效率，这里应该利用最小堆，但是js没有默认实现，先不管
                        let cacheKey=openList[i].index+':'+closeList[j].index;
                        let d=cache[cacheKey];
                        if(!d){
                            d=polygon2Polygon(openList[i],closeList[j]);
                        }
                        cache[cacheKey]=d;
                        if(d.dist<min.dist){
                            min=d;
                            imin=i;
                            jmin=j;
                        }
                    }
                     
                }
                 
                //构建父子级
                if(closeList[jmin].child==null){
                    closeList[jmin].child=[];
                }
                closeList[jmin].child.push(
                {
                    node:openList[imin],
                    target:min.target,
                    source:min.source,
                });
                 
                closeList.push(openList[imin]);
                openList.splice(imin,1);
                 
            }
            //测试
            collect(gons[0],getEvent().target);
 
            return gons[0]
        };
 
        /**
         * 返回{ dist:最小距离,source:parent链接点，target：child链接点}
         * @param poly1
         * @param poly2
         */
        let polygon2Polygon=function(poly1,poly2){
            let point,min={dist:Number.MAX_SAFE_INTEGER};
            for(let i=0;i<poly1.length;i++){
                point=poly1[i];
                let d=point2Polygon(point,poly2);
                if(d.dist<min.dist){
                    min=d;
                    min.target=point;
                    min.source=d.anchor;
                }
            }
 
            for(let i=0;i<poly2.length;i++){
                point=poly2[i];
                let d=point2Polygon(point,poly1);
                if(d.dist<min.dist){
                    min=d;
                    min.target=d.anchor;
                    min.source=point;
                }
            }
 
            return min;
        };
 
        //计算图形和点之间的最小距离，返回线，距离
        let point2Polygon=function(point,poly){
            let min=Number.MAX_SAFE_INTEGER;
            let anchor,d;
            for(let i=0;i<poly.length;i++){
                let p1=poly[i],p2;
                let i1;
                if(i==poly.length-1)
                    i1=0;
                else
                    i1=i+1;
                p2=poly[i1];
                 
                d= distToSegment(point,p1,p2);
                if(min>d.dist){
                    min=d.dist;
                    anchor=d.p;
                }
                 
            }
            return {
                dist:min,
                anchor:anchor,
            }
        };
 
        /*-------------点到线段距离------------*/
        function sqr(x) { return x * x }
        function dist2(v, w) { return sqr(v.x - w.x) + sqr(v.y - w.y) }
 
        //返回距离和连接点
        function distToSegment(p, v, w) {
            let l2 = dist2(v, w);
            if (l2 == 0) return dist2(p, v);
            let t = ((p.x - v.x) * (w.x - v.x) + (p.y - v.y) * (w.y - v.y)) / l2;
 
            t = Math.max(0, Math.min(1, t));
            let w1={ x: v.x + t * (w.x - v.x),
                y: v.y + t * (w.y - v.y) };
            return {dist:Math.sqrt(dist2(p, w1)),
                p:w1};
        }
        /*-------------END---------------*/
 
 
 
        /*-------无关算法分界线--------*/
 
        //创建连线
        let createLineElement=function(){
            let line= document.createElementNS('http://www.w3.org/2000/svg','line');
            line.style.stroke='black';
            line.style['stroke-width']=2;
            line.setAttributeNS('','marker-end','url(#arrow)');
            return line;
        };
 
 
        let collect=function(p){
            if(p.child){
                for(let i=0;i<p.child.length;i++){
 
                    let np=createLineElement();
                    let s=p.child[i].source;
                    let t=p.child[i].target;
 
 
                    let x1,y1,x2,y2;
                    if(s instanceof Array){
                        x1=(s[0].x+s[1].x)/2;
                        y1=(s[0].y+s[1].y)/2;
                    }else{
                        x1=s.x;
                        y1=s.y;
                    }
 
                    if(t instanceof Array){
                        x2=(t[0].x+t[1].x)/2;
                        y2=(t[0].y+t[1].y)/2;
                    }else{
                        x2=t.x;
                        y2=t.y;
                    }
 
 
                    np.setAttribute('x1',x1);
                    np.setAttribute('y1',y1);
 
                    np.setAttribute('x2',x2);
                    np.setAttribute('y2',y2);
                    lineGroup.appendChild(np);
 
                    collect(p.child[i].node);
                }
            }
        };
 
        let getEvent = function(){
            return window.event || arguments.callee.caller.arguments[0];
        };
 
        let printChild=function(p){
            console.log('node:',p.index);
            if(p.child){
                console.log('{',p.index,'--child:');
                for(let i=0;i<p.child.length;i++){
                    console.log('source:',p.child[i].source);
                    console.log('target:',p.child[i].target);
                    printChild(p.child[i].node);
                }
                console.log('--',p.index,'}');
            }
        }
        //从path里获取所有的多边形
        let getPolygons=function(p){
            let d=p.getAttribute('d');
            if(d){
                let polygons=d.split('M');
                let result=[];
                for(let i=1;i<polygons.length;i++){
                    let seg = polygons[i];
 
                    let plist=[];
                    result.push(plist);
                    plist.index=i-1;
                    let status=0;
                    let np,pindex=0;
                    for(let j=0;j<seg.length;j++){
                        let c = seg.charAt(j);
                        if(status==0){
                            //初始化状态
                            if(c==' '||c=='L'||c=='Z'){
 
                            }else{
                                np={};
                                np.index=pindex++;
                                plist.push(np);
                                np.x=c;
                                np.y='';
                                status=1;
                            }
                        }else if(status == 1){
                            //开始写x
                            if(c==' '||c==','){
                                //开始写y
                                np.x=parseFloat(np.x);
                                status=2;
                            }else if(c=='L'){
 
                            }else{
                                np.x+=c;
                            }
                        }else if(status == 2){
                            if(c==' '||c=='Z'||c=='L'){
                                np.y=parseFloat(np.y);
                                status = 0;
                            }else{
                                np.y+=c;
                            }
                        }
                    }
                }
                return result;
            }
        }
        window.onload=function(){
            let panel=document.getElementById('panel');
             
            for(let i=0,len=panel.children.length;i<len;i++){
                panel.children[i].onclick=caculatePath;
            }
        }
    </script>
</head>
<body>
    <svg  width='100%' height='100%' style="border:1px solid">
        <defs>
            <marker id="arrow" markerWidth="5" markerHeight="5" refx="0" refy="3" orient="auto" markerUnits="strokeWidth">
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        </g>
        <g id="lineGroup"></g>
    </svg>
     
    <div style="position:fixed;right:10%;height:100px;width:200px;top:50px;background-color:#ccc;text-align:center;line-height:1.95">
    <div style="">点击左侧图形</div> <div>查看最小连通图</div></div>
</body>
</html>