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我目前设计到的场景是#xff1a;以路面上行驶的汽车为例#xff0c;即在地图应用中#xff0c;对GPS轨迹数据进行压缩#xff0c;减少数据传输和存储开销#xff0c;因为轨迹点太频繁了#xff0c;占用空间太大#xff0c;运行节点太慢了#xff0c…场景
我目前设计到的场景是以路面上行驶的汽车为例即在地图应用中对GPS轨迹数据进行压缩减少数据传输和存储开销因为轨迹点太频繁了占用空间太大运行节点太慢了经过小组讨论需要上这个算法。
涉及到的算法
Douglas-Peucker算法该算法通过递归地将轨迹分割为线段并丢弃那些与整体轨迹偏差较小的线段从而实现轨迹的压缩。 Visvalingam-Whyatt算法该算法基于三角形面积的概念通过不断移除面积最小的点来达到轨迹压缩的目的 图片来源郑宇博士《computing with spatial trajectories》
Haversine公式计算距离和Douglas-Peucker压缩算法代码实现-scala版
import org.apache.spark.sql.{DataFrame, SparkSession}
import org.apache.spark.sql.functions._
import scala.math._// 定义表示点的类
case class Point(lon: Double, lat: Double, time: String, id: String)// Haversine距离计算函数
def haversineDistance(point1: Point, point2: Point): Double {val R 6371000.0 // 地球半径米val dLat toRadians(point2.lat - point1.lat)val dLon toRadians(point2.lon - point1.lon)val a pow(sin(dLat / 2), 2) cos(toRadians(point1.lat)) * cos(toRadians(point2.lat)) * pow(sin(dLon / 2), 2)val c 2 * atan2(sqrt(a), sqrt(1 - a))R * c
}// Douglas-Peucker轨迹压缩函数
def douglasPeucker(points: List[Point], epsilon: Double): List[Point] {if (points.length 3) {return points}val dmax points.view.zipWithIndex.map { case (point, index) if (index ! 0 index ! points.length - 1) {perpendicularDistance(point, points.head, points.last)} else {0.0}}.maxif (dmax epsilon) {val index points.view.zipWithIndex.maxBy { case (point, index) if (index ! 0 index ! points.length - 1) {perpendicularDistance(point, points.head, points.last)} else {0.0}}._2val recResults1 douglasPeucker(points.take(index1), epsilon)val recResults2 douglasPeucker(points.drop(index), epsilon)recResults1.init ::: recResults2} else {List(points.head, points.last)}
}// 创建Spark会话
val spark SparkSession.builder().appName(TrajectoryCompression).getOrCreate()// 创建包含lon、lat、time和id列的示例DataFrame
//https://blog.csdn.net/qq_52128187?typeblog,by_laoli
val data Seq((40.7128, -74.0060, 2023-11-18 08:00:00, 1),(40.7215, -74.0112, 2023-11-18 08:05:00, 1),(40.7312, -74.0146, 2023-11-18 08:10:00, 1),(40.7356, -74.0162, 2023-11-18 08:15:00, 1),(40.7391, -74.0182, 2023-11-18 08:20:00, 1),(40.7483, -74.0224, 2023-11-18 08:25:00, 1),(40.7527, -74.0260, 2023-11-18 08:30:00, 1)
).toDF(lon, lat, time, id)// 为DataFrame添加id列
val dfWithId data.withColumn(id, monotonically_increasing_id())// 将DataFrame转换为Point列表
val points dfWithId.as[(Double, Double, String, Long)].collect().map(p Point(p._1, p._2, p._3, p._4.toString)).toList// 执行轨迹压缩
val compressedPoints douglasPeucker(points, epsilon 10) // 设置您期望的epsilon值// 将压缩后的数据重新转换为DataFrame
import spark.implicits._
val df2 compressedPoints.toDF(lon, lat, time, id)参考文章
Douglas, D.H., and Peucker, T.K. Algorithms for the reduction of the number of points required to represent a digitized line or its caricature. The Canadian Cartographer 10.2 (1973): 112-122.Visvalingam, M., and Whyatt, J.D. Line generalization by repeated elimination of the smallest-area triangle. Cartographic Journal 30.1 (1993): 46-51.轨迹数据压缩的Douglas-Peucker算法附代码及原始数据 - 知乎
