AreaCalculator.scala

// concepts:
// - functional style: higher-order functions, type aliases
// - testing in REPL

object AreaCalculatorApp {
  def main(args: Array[String]) = println(area(readVertices(args(0))))

  type Vertex = (Double, Double)
  
  def area(vertices: Seq[Vertex]) = triangulate(vertices) map(triangleArea _) sum

  def triangulate(vertices: Seq[Vertex]) = vertices match { case a :: b :: c :: t => t.foldLeft(List((a, b, c)))(nextTriangle _) }
    
  type Triangle = (Vertex, Vertex, Vertex)

  def nextTriangle(prevTriangles: List[Triangle], d: Vertex) = prevTriangles last match { case (a, b, c) => prevTriangles :+ (a, c, d) }
  
  def triangleArea(triangle: Triangle) = triangle match { 
    case (a, b, c) => math.abs(a._1 * b._2 - a._1 * c._2 + b._1 * c._2 - b._1 * a._2 + c._1 * a._2 - c._1 * b._2) / 2 
  }

  def readVertices(path: String) = toVertices(fileContentsAsSeqOfDoubles(path))

  def fileContentsAsSeqOfDoubles(path: String) = (io.Source fromPath(path) mkString) split("\\s") filter(_.length > 0) map(_.toDouble)

  def toVertices(coords: Seq[Double]) = coords grouped(2) map((p: Seq[Double]) => (p(0), p(1))) toSeq
}

The Problem

A convex polygon is given by the list of the coordinates of it's vertices where the vertices appear in clockwise order; e.g.
0 0
0 1
1 0
1 1
represents a 1x1 square. We need to calculate the area of this polygon.

A convex polygon can be trivially triangulated [draw a picture]. There is a well-known formula for calculating the area of a triangle given it's vertex coordinates: http://en.wikipedia.org/wiki/Triangle#Using_coordinates

Compiling and running an app

[show how to compile a file using scalac and how to run it using scala]

App structure

a singleton object with a main(Array[String]): Unit method is an application

Higher-order methods

• fileContentsAsSeqOfDoubles(): filter() takes a predicate
• toVertices(): the argument to map is a function written as a literal: (args) => body
  The operator syntax allows to omit dots when calling methods.

Type aliases

Instead of writing (Vertex, Vertex, Vertex) we can write Triangle -- it refers to the same type

Methods as function values

area(): in triangleArea _ the underscore turns a method into a function value which can be passed to higher-order methods/functions (partial application)

Testing in REPL

• :load AreaCalculator.scala
• import AreaCalculatorApp._
• val dl = fileContentsAsSeqOfDoubles("square1.txt")
• val vs = toVertices(dl)
• area(vs)