GPS定位轨迹抽稀之道格拉斯-普克（Douglas-Peuker)算法详解

1. 抽稀

2. 原理

3. 具体思路

4. 代码示例

道格拉斯-普克算法是我们常用的一种轨迹点的抽稀算法，抽稀出来的点可以尽可能的维持原先轨迹点的大体轮廓，剔除一些非必要的点

2. 原理

假设在平面坐标系上有一条由N个坐标点组成的曲线，已设定一个阈值epsilon。
（1）首先，将起始点与结束点用直线连接，再找出到该直线的距离最大，同时又大于阈值epsilon的点并记录下该点的位置（这里暂且称其为最大阈值点），如图所示：

（2）接着，以该点为分界点，将整条曲线分割成两段(这里暂且称之为左曲线和右曲线)，将这两段曲线想象成独立的曲线然后重复操作（1），找出两边的最大阈值点，如图所示：

（3）最后，重复操作（2）（1）直至再也找不到最大阈值点为止，然后将所有最大阈值点按顺序连接起来便可以得到一条更简化的，更平滑的，与原曲线十分近似的曲线，如图所示：

3. 具体思路

对每一条曲线的首末点虚连一条直线,求所有点与直线的距离,并找出最大距离值dmax ,用dmax与限差D相比:若dmax < D ,这条曲线上的中间点所有舍去;若dmax ≥D ,保留dmax 相应的坐标点,并以该点为界,把曲线分为两部分,对这两部分反复使用该方法。控制限差值的大小可以控制抽稀的粒度。

4. 代码示例

public class GpsData {private  int index;public GpsData(){}/*** 纬度*/private double latitudeEx;/*** 经度*/private double longitudeEx;public double getLatitudeEx() {return latitudeEx;}public void setLatitudeEx(double latitudeEx) {this.latitudeEx = latitudeEx;}public double getLongitudeEx() {return longitudeEx;}public void setLongitudeEx(double longitudeEx) {this.longitudeEx = longitudeEx;}public int getIndex() {return index;}public void setIndex(int index) {this.index = index;}
}

public class Douglas extends JFrame {/*** 存储采样点数据链表*/
public static List<GpsData > points = new ArrayList<GpsData >();
/*** 控制数据经度压缩的极差*/
private static final double D = 0.0001;/*** 对矢量曲线进行压缩** @param from 曲线的起始点* @param to   曲线的终止点*/
public static void compress(GpsData from, GpsData to) {/*** 压缩算法的开关*/boolean switchvalue = false;/*** 由起始点和终止点构成直线方程一般式的系数*/double fromLat = Double.valueOf(from.getLatitudeEx());double fromLng = Double.valueOf(from.getLongitudeEx());double toLat = Double.valueOf(to.getLatitudeEx());double toLng = Double.valueOf(to.getLongitudeEx());double A = (fromLat - toLat)/ Math.sqrt(Math.pow((fromLat - toLat), 2)+ Math.pow((fromLng - toLng), 2));/*** 由起始点和终止点构成直线方程一般式的系数*/double B = (toLng - fromLng)/ Math.sqrt(Math.pow((fromLat - toLat), 2)+ Math.pow((fromLng - toLng), 2));/*** 由起始点和终止点构成直线方程一般式的系数*/double C = (fromLng * toLat - toLng * fromLat)/ Math.sqrt(Math.pow((fromLat - toLat), 2)+ Math.pow((fromLng - toLng), 2));double d = 0;double dmax = 0;int m = points.indexOf(from);int n = points.indexOf(to);if (n == m + 1){ return;}GpsData middle = null;List<Double> distance = new ArrayList<>();for (int i = m + 1; i < n; i++) {double blng = Double.valueOf(points.get(i).getLongitudeEx());double blat = Double.valueOf(points.get(i).getLatitudeEx());d = Math.abs(A * (blng) + B * (blat) + C) / Math.sqrt(Math.pow(A, 2) + Math.pow(B, 2));distance.add(d);}dmax = distance.get(0);for (int j = 1; j < distance.size(); j++) {if (distance.get(j) > dmax){dmax = distance.get(j);}}if (dmax > D) {switchvalue = true;} else{switchvalue = false;}if (!switchvalue) {//删除Points(m,n)内的坐标for (int i = m + 1; i < n; i++) {points.get(i).setIndex(-1);}} else {for (int i = m + 1; i < n; i++) {double blng = Double.valueOf(points.get(i).getLongitudeEx());double blat = Double.valueOf(points.get(i).getLatitudeEx());if ((Math.abs(A * (blng) + B* (blat) + C)/ Math.sqrt(Math.pow(A, 2) + Math.pow(B, 2)) == dmax)){middle = points.get(i);}}compress(from, middle);compress(middle, to);}
}public static List<GpsData > douglasData(List<GpsData> source) {points = source;System.out.println("压缩前：");for (int i = 0; i < points.size(); i++) {GpsData p = points.get(i);System.out.print("[" + p.getLongitudeEx() + "," + p.getLatitudeEx() + "],");}if(!CollectionUtils.isEmpty(points)){compress(points.get(0), points.get(points.size() - 1));}System.out.println("\n压缩后：");List<GpsData > list = new ArrayList<>();for (int i = 0; i < points.size(); i++) {GpsData p = points.get(i);if (p.getIndex()>-1) {list.add(p);System.out.println("[" + p.getLongitudeEx() + "," + p.getLatitudeEx() + "],");}}return list;
}public static void main(String[] args) {List<GpsData> list = new ArrayList<>();GpsData data=null;String[] $points = new String []{"117.212448,39.133785", "117.212669,39.133667", "117.213165,39.133297", "117.213203,39.13327", "117.213554,39.133099", "117.213669,39.13295", "117.213921,39.132462", "117.214088,39.132126", "117.214142,39.131962", "117.214188,39.13176", "117.214233,39.131397", "117.21418,39.13055", "117.214279,39.130459", "117.214539,39.130375", "117.214874,39.130188", "117.216881,39.128716", "117.217598,39.127995", "117.217972,39.12759", "117.218338,39.127178", "117.218407,39.127071", "117.218567,39.126911", "117.219704,39.125702", "117.219795,39.12561", "117.220284,39.125114", "117.220619,39.124802", "117.221046,39.124348", "117.221138,39.124245", "117.221268,39.124092", "117.222321,39.122955", "117.222824,39.122406", "117.222916,39.122311", "117.223663,39.121544", "117.2239,39.121452", "117.224113,39.12159", "117.224251,39.121677", "117.225136,39.122208", "117.225281,39.122292", "117.225319,39.122311", "117.226273,39.122875", "117.226685,39.123127", "117.227371,39.12352", "117.227806,39.123779", "117.228477,39.124134", "117.228531,39.124161", "117.228531,39.124161", "117.228668,39.124187", "117.228897,39.124325", "117.229767,39.12479", "117.230927,39.12545", "117.231186,39.12561", "117.231659,39.125908", "117.231834,39.126026", "117.232018,39.126186", "117.232185,39.126362", "117.232353,39.126583", "117.232658,39.126972", "117.232658,39.126972", "117.233124,39.12748", "117.233253,39.127609", "117.233368,39.127689", "117.233513,39.127762", "117.233665,39.127823", "117.233734,39.127846", "117.233833,39.127865", "117.233994,39.127888", "117.234138,39.127892", "117.234329,39.127884", "117.234612,39.127838", "117.234955,39.127754", "117.235252,39.12767", "117.236282,39.12738", "117.237137,39.127129", "117.237671,39.126961", "117.237953,39.126949", "117.238213,39.126865", "117.238472,39.126793", "117.2397,39.126434", "117.242233,39.125698", "117.243538,39.12532", "117.243645,39.125298",};System.out.println("抽稀前---------------"+$points.length);for(int i=0;i<$points.length;i++){data= new GpsData();data.setLongitudeEx(Double.valueOf($points[i].split(",")[0]));data.setLatitudeEx(Double.valueOf($points[i].split(",")[1]));list.add(data);}List<GpsData> gpsDataList=  douglasData(list);System.out.println("---------------"+gpsDataList.size());System.out.println(gpsDataList.toString());
}
}

以上内容借鉴文章（https://www.jianshu.com/p/bf595477a124，https://blog.csdn.net/baidu_39547612/article/details/90474486）