Quickhull is an algorithm that is similar to the quicksort using a divide and conquer strategy to find the convex hull for scattered points. The green line in the plot is the initial base line and gray lines are the intermediate base line. The final convex hull is shown in red.

Get Random Points Get convex hull

source code: qh.js

function getRandomPoints(numPoint, xMax, yMax) {
    var points = new Array();
    var phase = Math.random() * Math.PI * 2;
    for (var i = 0; i < numPoint/2; i++) {
        var r =  Math.random()*xMax/4;
        var theta = Math.random() * 1.5 * Math.PI + phase;
        points.push( [ xMax /4 + r * Math.cos(theta), yMax/2 + 2 * r * Math.sin(theta) ] )
    }
    var phase = Math.random() * Math.PI * 2;
    for (var i = 0; i < numPoint/2; i++) {
        var r =  Math.random()*xMax/4;
        var theta = Math.random() * 1.5 * Math.PI + phase;
        points.push( [ xMax /4 * 3 +  r * Math.cos(theta), yMax/2 +  r * Math.sin(theta) ] )
    }
    return points
}


function getDistant(cpt, bl) {
    Vy = bl[1][0] - bl[0][0];
    Vx = bl[0][1] - bl[1][1];
    return (Vx * (cpt[0] - bl[0][0]) + Vy * (cpt[1] -bl[0][1]))
}


function findMostDistantPointFromBaseLine(baseLine, points) {
    var maxD = 0;
    var maxPt = new Array();
    var newPoints = new Array();
    for (var idx in points) {
        var pt = points[idx];
        var d = getDistant(pt, baseLine);

        if ( d > 0) {
            newPoints.push(pt);
        } else {
            continue;
        }

        if ( d > maxD ) {
            maxD = d;
            maxPt = pt;
        }

    }
    return {'maxPoint':maxPt, 'newPoints':newPoints}
}




var allBaseLines = new Array();
function buildConvexHull(baseLine, points) {

    //plotBaseLine(baseLine,'rgb(180,180,180)');
    allBaseLines.push(baseLine)
    var convexHullBaseLines = new Array();
    var t = findMostDistantPointFromBaseLine(baseLine, points);
    if (t.maxPoint.length) {
        convexHullBaseLines = convexHullBaseLines.concat( buildConvexHull( [baseLine[0],t.maxPoint], t.newPoints) );
        convexHullBaseLines = convexHullBaseLines.concat( buildConvexHull( [t.maxPoint,baseLine[1]], t.newPoints) );
        return convexHullBaseLines;
    } else {
        return [baseLine];
    }
}


function getConvexHull(points) {
    //find first baseline
    var maxX, minX;
    var maxPt, minPt;
    for (var idx in points) {
        var pt = points[idx];
        if (pt[0] > maxX || !maxX) {
            maxPt = pt;
            maxX = pt[0];
        }
        if (pt[0] < minX || !minX) {
            minPt = pt;
            minX = pt[0];
        }
    }
    var ch = [].concat(buildConvexHull([minPt, maxPt], points),
                       buildConvexHull([maxPt, minPt], points))
    return ch;
}


function plotBaseLine(baseLine,color) {
    var ctx = document.getElementById('qh_demo').getContext('2d');
    var pt1 = baseLine[0]
    var pt2 = baseLine[1];
    ctx.save()
    ctx.strokeStyle = color;
    ctx.beginPath();
    ctx.moveTo(pt1[0],pt1[1]);
    ctx.lineTo(pt2[0],pt2[1]);
    ctx.stroke();
    ctx.restore();
}



var pts;

function qhPlotPoints() {
    ctx = document.getElementById('qh_demo').getContext('2d');
    ctx.clearRect(0,0,200,200);
    ctx.fillStyle = 'rgb(0,0,0)';
    pts = getRandomPoints(250,200,200);
    for (var idx in pts) {
        var pt = pts[idx];
        ctx.fillRect(pt[0],pt[1],2,2);
    }
}



function qhPlotConvexHull() {
    var ch = getConvexHull(pts);
    var eBL = allBaseLines[0];
    function plotIntermediateBL() {
        var l = allBaseLines.shift();
        if (l) {
            plotBaseLine(l, 'rgb(180,180,180)');
            setTimeout(plotIntermediateBL, 250);
        } else {
            for (var idx in ch) {
                var baseLine = ch[idx];
                plotBaseLine(baseLine, 'rgb(255,0,0)');
            }
            plotBaseLine(eBL,'rgb(0,255,0)');
        }
    }
    plotIntermediateBL();
}


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Tags: algorithm, programming