场景：

我目前设计到的场景是：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

1. 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。
   1. 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
    }
  }.max

  if (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
      }
    }._2

    val recResults1 = douglasPeucker(points.take(index+1), 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?type=blog,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