Voronoi泰森多边形的实现

实现几何计算，然后实现凸包、Delaunay三角和Voronoi多边形。使用node运行。

几何计算实现点，直线一般式方程、两点式方程、点截式方程、直线交点、点与直线关系，三角形、矩形外接三角形，矩形，圆、三角形外接圆、点与圆关系计算。

凸包算法

    graham() {
        let vs = this.children.filter(e=>e.getClass() == "Vertex");
        // find p0-y vectex
        let p0 = vs[0];

        for (let v of vs) {
            if ( (v.y < p0.y) || (v.y==p0.y && v.x d2)
                return 1;
            else {
                p0.getDistance(a) - p0.getDistance(b) > 0 ? 1 : -1;
            }
        });


        let ps = [].concat(vs);

        let stack = new Array(ps.shift(), ps.shift());
        for (let current of ps) {

            let d;
            do {
                let top = stack.peek();
                let sec = stack[stack.length-2];

                let line = Line.TwoPoint(sec,top);
                d = line.position(current);
                
                if (d>0)
                    top = stack.pop();

            } while (d > 0);
            
            stack.push(current);
        }
}

显示如下：

德洛内三角

    DelaunayBowyer() {
        let indices = this.children
        .filter(e=>e.getClass() == "Vertex")
        .sort((a,b)=>{
            return a.x == b.x ? 0 : (a.x < b.x ? -1 : 1);
        });

        let maxx = 0, maxy = 0, minx = Number.MAX_SAFE_INTEGER, miny = Number.MAX_SAFE_INTEGER;
        indices.forEach(v=>{
            if (v.x < minx) minx = v.x;
            if (v.x > maxx) maxx = v.x;
            if (v.y < miny) miny = v.y;
            if (v.y > maxy) maxy = v.y;
        });
        let r = new Rectangle(new Point(minx, miny), new Point(maxx, maxy));
        let supert = Triangle.ExternalTriangleFromRectangle(r);


        let vs = indices.concat([ supert.p0, supert.p1, supert.p2 ]);     
        let ts =[ supert ];     
        for (let v of vs) {

            let edge = new CountArray();
            let i = ts.length - 1;
            while (i>=0) {
                let t = ts[i--];              
                let c = Circle.Circumcircle(t);

                let position = c.test(v);
                if (position == "out") {
                    continue ;
                }
                else {                
                    edge.push(new Pair(t.p0, t.p1));
                    edge.push(new Pair(t.p1, t.p2));
                    edge.push(new Pair(t.p2, t.p0));
                    ts.remove(t);
                }
            }


            let nedge = edge.getArray();
            for (let i=0; i=0; i--) {
            let t = ts[i];

            if (t.p0.getClass() == "Point" || t.p1.getClass() == "Point" || t.p2.getClass() == "Point") {
                ts.remove(t);
                continue ;
            }

            this.children.push(t);
        }

        return ts;
    }

显示如下，未上色和和上色的：

  

泰森多边形：

    Voronoi() {

        let vs = this.children.filter(e=>e.getClass() == "Vertex");
        let ts = this.children.filter(e=>e.getClass() == "Triangular");

        let gl = [];

        for (let v of vs) {

            let bounds = [];
            for (let t of ts)
                if (t.p0 == v || t.p1 == v || t.p2 == v)
                    bounds.push(t);

            let sort = [];
            let e = bounds[0].exclude(v)[0];
            let t;

            while (bounds.length > 0) {

                let bFound = false;
                for (t of bounds) {
                    if (t.hasEdge(v, e)) {
                        e = t.exclude(v, e)[0];
                        bFound = true;
                        break;
                    }
                }

                if (bFound) {
                    bounds.remove(t);
                    sort.push(t);
                }
                else {
                    break ;
                }

            }

            if (bounds.length == 0)
                gl.push(sort);

        }

        for (let g of gl) {
            
            let cps = [];
            for (let s of g) {
                let c = Circle.Circumcircle(s);
                if (c.x <= 0 && c.y <= 0)
                    return ;
                cps.push(c.p);
            }

            let p = new Path(cps);
            this.children.push(p);
            
        }

    }

显示如下，带背景和去掉背景的：