在Scala中由给定顶点计算凸图的面积

import scala.collection.mutable.ArrayBuffer
import scala.math.abs

case class Point(x: Double, y: Double)

def distance(p1: Point, p2: Point): Double = {
  val dx = p1.x - p2.x
  val dy = p1.y - p2.y
  math.sqrt(dx * dx + dy * dy)
}

def convexHull(points: Array[Point]): Array[Point] = {
  val sortedPoints = points.sortBy(_.x)
  val upperHull = new ArrayBuffer[Point]()
  val lowerHull = new ArrayBuffer[Point]()

  for (point <- sortedPoints) {
    while (upperHull.length >= 2 && 
           crossProduct(upperHull(upperHull.length - 2), upperHull.last, point) <= 0) {
      upperHull.remove(upperHull.length - 1)
    }
    upperHull.append(point)
  }

  for (point <- sortedPoints.reverse) {
    while (lowerHull.length >= 2 && 
           crossProduct(lowerHull(lowerHull.length - 2), lowerHull.last, point) <= 0) {
      lowerHull.remove(lowerHull.length - 1)
    }
    lowerHull.append(point)
  }

  upperHull.remove(upperHull.length - 1)
  lowerHull.remove(lowerHull.length - 1)
  upperHull.toArray ++ lowerHull.toArray
}

def crossProduct(p1: Point, p2: Point, p3: Point): Double = {
  val x1 = p2.x - p1.x
  val y1 = p2.y - p1.y
  val x2 = p3.x - p1.x
  val y2 = p3.y - p1.y
  x1 * y2 - x2 * y1
}

def convexHullArea(convexHull: Array[Point]): Double = {
  var area = 0.0
  val n = convexHull.length

  for (i <- 0 until n) {
    val j = (i + 1) % n
    area += convexHull(i).x * convexHull(j).y - convexHull(j).x * convexHull(i).y
  }

  abs(area / 2)
}

val points = Array(Point(0, 0), Point(1, 0), Point(1, 1), Point(0, 1))
val convexHullPoints = convexHull(points)
val area = convexHullArea(convexHullPoints)

println(s"The area of the convex hull is $area")