Calculating area of convex figures from given vertices in Scala - scala

Question

I have been given a set of vertices, which can vary from 3 to 20, and I need to implement a generic method to calculate the area of the polygon defined by those vertices [This vertices are placed in a 2D plane and the defined polygon is not self-intersecting]
The polygon vertices are give as:
N //Num sides Polygon
x1 y1
x2 y2
x3 y3
...
xn yn
With that in mind what I was planning to do is to polygon triangulation:
Where I pick one initial vertex and then split the rest of the polygon into triangles (fan triangulation), like this:
The area of a irregular triangle can be calculated like this:
val s : Double = (a+b+c)/2;
val area : Double = Math.sqrt(s*(s-a)*(s-b)*(s-c));
So I wrote the following code to calculate the area following this approach:
case class Point(val x: Double, val y: Double)
import scala.collection.mutable.ListBuffer
// Method to calculate length of side between to vertices
def distance(ori: Point, des: Point): Double = {
Math.sqrt(Math.pow(ori.x - des.x, 2) + Math.pow(ori.y - des.y, 2))
}
def main(args: Array[String]) {
// Number of sides in the Polynom
val sidesPoly = scala.io.StdIn.readLine().toInt
var listPoints = new ListBuffer[Point]()
// ListBuffer with the input sides
for(i <- 1 to sidesPoly){
val tuple = scala.io.StdIn.readLine().split(" ")
val newPoint = new Point(tuple(0).toDouble, tuple(1).toDouble)
listPoints += newPoint
}
// Iterating list in Fan mode to split the polygon into triangles
var area : Double = 0
for(i <- 1 to listPoints.size-2){
var triangle = new ListBuffer[Point]()
//We divide the polygon into triangles
val side1 = distance(listPoints(0),listPoints(i))
val side2 = distance(listPoints(i),listPoints(i+1))
val side3 = distance(listPoints(i+1),listPoints(0))
// Calculating the area of the triangle
val s = (side1+side2+side3)/2
val triangleArea = Math.sqrt(s*(s-side1)*(s-side2)*(s-side3))
// Adding the area of the triangle to the total Polygon Area
area += triangleArea
}
println(area)
}
The problem I faced is the method doesn't work with concave polygons.
Does anyone know a better approach than Fan Triangulation for concave polygons?

Answer 1

Found this approach which works for both, concave and convex:
case class Point(val x: Double, val y: Double)
import scala.collection.mutable.ListBuffer
// Method to calculate the Area under each side of the polygon
def calculateAreaUnderSegment(A: Point , B: Point): Double = {
val averHeight = (A.y + B.y)/2
val width = (A.x - B.x)
width * averHeight
}
def main(args: Array[String]) {
// Numer of sides Polygon
val sidesPoly = scala.io.StdIn.readLine().toInt
//List of Vertices Polygon
var listPoints = new ListBuffer[Point]()
for(i <- 1 to sidesPoly){
val tuple = scala.io.StdIn.readLine().split(" ")
val newPoint = new Point(tuple(0).toDouble, tuple(1).toDouble)
listPoints += newPoint
}
// Iterating over each pair of vertex
var area : Double = 0
for(i <- 0 to listPoints.size-2){
area += calculateAreaUnderSegment(listPoints(i),listPoints(i+1))
}
// For the last segment (to come back to the original vertex)
area += calculateAreaUnderSegment(listPoints(listPoints.size-1),listPoints(0))
println(area)
}