道格拉斯-普克抽稀算法，是用来对大量冗余的图形数据点进行压缩以提取必要的数据点。该算法实现抽稀的过程是：先将一条曲线首尾点虚连一条直线，求其余各点到该直线的距离，取其最大者与规定的临界值相比较，若小于临界值，则将直线两端间各点全部舍去，否则将离该直线距离最大的点保留，并将原线条分成两部分，对每部分线条再实施该抽稀过程，直到结束。抽稀结果点数随选取限差临界值的增大而减少，应用时应根据精度来选取限差临界值，以获得最好的效果。
以下转载自：垂距法与道格拉斯-普克法删除冗余顶点效率的比较
道格拉斯- 普克法可描述为:将一条曲线首末顶点虚连一条直线 ,求出其余各顶点到该直线的距离 ,选其最大者与规定的限差相比较 ,若小于等于限差 ,则将直线两端间各点全部删去;若大于限差 ,则离该直线距离最大的顶点保留 ,并以此为界 ,把曲线分为两部分 ,对这两部分重复使用上述方法 ,直至最终无法作进一步的压缩为止 (见图 3)。
道格拉斯 2 普克法有一个十分突出的优点 ,即它是一个整体算法 ,在一般情况下可保留较大弯曲形态上的特征点。经道格拉斯-普克法压缩后得到的图形如图 4所示。由于该算法可准确删除小弯曲上的定点 ,故能从体上有效地保持线要素的形态特征。正是因为道格拉斯-普克法具有这样突出的优点 ,所以已经在线要素地自动制图中得到了较广泛的应用。但道格拉斯- 普克法较垂距法复杂 ,且通常编程实现时需要采用递归方 ,有一定的难度。
转载end
以下是javascript版本的实现
<!DOCTYPE html PUBLIC "-//W3C//DTD XHTML 1.0 Transitional//EN" "http://www.w3.org/TR/xhtml1/DTD/xhtml1-transitional.dtd">
<html xmlns="http://www.w3.org/1999/xhtml">
<head>
<meta http-equiv="Content-Type" content="text/html; charset=utf-8"/>
<title>DouglasPeucker</title>
</head>
<body>
<div id="processBefore" style="background-color:#ccc;height:100px;position:relative;"></div>
<div id="processAfter" style="background-color:#ccc;height:100px;margin-top:10px;position:relative;"></div>
</body>
<script type="text/javascript" src="Items/js/K1.source.js">
var points = [{
x: 10,
y: 10
}, {
x: 20,
y: 30
}, {
x: 30,
y: 12
}, {
x: 35,
y: 5
}, {
x: 40,
y: 22
}, {
x: 50,
y: 12
}, {
x: 80,
y: 40
}];
var Helper = {
renderPointsTo: function(points, anchor) {
var d;
for (var i = 0, p, a = K(anchor); i < points.length; i++) {
p = points[i];
if (a) {
a.appendChild(K('div', {}, {
position: 'absolute',
left: p.x + 'px',
top: p.y + 'px',
width: '5px',
height: '5px',
backgroundColor: 'green',
fontSize: '1px'
}));
}
}
}
};
Helper.renderPointsTo(points, 'processBefore');
var DouglasPeucker = {
getProcessPoints: function(points, tolerance) {
/// <summary>获取处理后的点</summary>
/// <param name="points" type="Array">包含点的数组</param>
/// <param name="tolerance" type="Float">取样临界值</param>
/// <returns type="Array" />
if (!K.isArr(points) || !points.length) { //当points不是数组或没有值时，直接返回一个空数组
return [];
}
if (points.length < 3) return points; //小于3个点时不抽稀，因为1个或2个点无法进行抽稀
var firstPoint = 0,
lastPoint = points.length - 1; //取开始点与结束点的下标
var pointIndexsToKeep = []; //保存需要点下标的数组
pointIndexsToKeep.push(firstPoint);
pointIndexsToKeep.push(lastPoint); //开始与结束不进行处理，直接保留
while (points[firstPoint] == points[lastPoint]) { //处理闭合情况，闭合时，强制断开
lastPoint--;
}
this.reduce(points, firstPoint, lastPoint, tolerance, pointIndexsToKeep); //抽稀
var resultPoints = []; //返回的点数组
pointIndexsToKeep.sort(function(a, b) { //排序，这个可排可不排
return a - b;
});
for (var i = 0; i < pointIndexsToKeep.length; i++) {
resultPoints.push(points[pointIndexsToKeep[i]]);
}
return resultPoints;
},
reduce: function(points, firstPoint, lastPoint, tolerance, pointIndexsToKeep) {
/// <summary>抽稀处理</summary>
/// <param name="points" type="Array">待抽稀的数组</param>
/// <param name="firstPoint" type="Integer">起点</param>
/// <param name="lastPoint" type="Integer">终点</param>
/// <param name="tolerance" type="Float">取样临界值</param>
/// <param name="pointIndexsToKeep" type="Array">保留点下标的数组</param>
var maxDis = 0,
idxFarthest = 0; //定义最大长度及最远点的下标
for (var i = firstPoint, dis; i < lastPoint; i++) {
dis = this.perpendicularDistance(points[firstPoint], points[lastPoint], points[i]); //获取当前点到起点与
if (dis > maxDis) { //保存最远距离
maxDis = dis;
idxFarthest = i;
}
}
if (maxDis > tolerance && idxFarthest != 0) { //如果最远距离大于临界值
pointIndexsToKeep.push(idxFarthest);
this.reduce(points, firstPoint, idxFarthest, tolerance, pointIndexsToKeep);
this.reduce(points, idxFarthest, lastPoint, tolerance, pointIndexsToKeep);
}
},
perpendicularDistance: function(beginPoint, endPoint, comparePoint) {
/// <summary>计算给出的comparePoint到beginPoint与endPoint组成的直线的垂直距离</summary>
/// <param name="beginPoint" type="Object">起始点</param>
/// <param name="endPoint" type="Object">结束点</param>
/// <param name="comparePoint" type="Object">比较点</param>
/// <returns type="Float" />
//Area = |(1/2)(x1y2 + x2y3 + x3y1 - x2y1 - x3y2 - x1y3)| *Area of triangle
//Base = v((x1-x2)2+(y1-y2)2) *Base of Triangle*
//Area = .5*Base*H *Solve for height
//Height = Area/.5/Base
var area = Math.abs(0.5 * (beginPoint.x * endPoint.y + endPoint.x * comparePoint.y + comparePoint.x * beginPoint.y -
endPoint.x * beginPoint.y - comparePoint.x * endPoint.y - beginPoint.x * comparePoint.y));
var bottom = Math.sqrt(Math.pow(beginPoint.x - endPoint.x, 2) + Math.pow(beginPoint.y - endPoint.y, 2));
var height = area / bottom * 2;
return height;
}
};
Helper.renderPointsTo(DouglasPeucker.getProcessPoints(points, 14), 'processAfter');
</script>
</html>宣传下我的区块管理框架Magix：https://github.com/thx/magix
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