Add CounterClockWise(CCW)

Author: TaeJoongYoon

CounterClockWise/CounterClockWise.playground/Contents.swift

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+/*
+ CounterClockWise(CCW) Algorithm
+ The user cross-multiplies corresponding coordinates to find the area encompassing the polygon,
+ and subtracts it from the surrounding polygon to find the area of the polygon within.
+ This code is based on the "Shoelace formula" by Carl Friedrich Gauss
+ https://en.wikipedia.org/wiki/Shoelace_formula
+ */
+
+import Foundation
+
+// MARK : Point struct for defining 2-D coordinate(x,y)
+public struct Point{
+  // Coordinate(x,y)
+  var x: Int
+  var y: Int
+  
+  public init(x: Int ,y: Int){
+    self.x = x
+    self.y = y
+  }
+}
+
+// MARK : Function that determine the area of a simple polygon whose vertices are described
+//        by their Cartesian coordinates in the plane.
+func ccw(points: [Point]) -> Int{
+  let polygon = points.count
+  var orientation = 0
+  
+  // Take the first x-coordinate and multiply it by the second y-value,
+  // then take the second x-coordinate and multiply it by the third y-value,
+  // and repeat as many times until it is done for all wanted points.
+  for i in 0..<polygon{
+      orientation += (points[i%polygon].x*points[(i+1)%polygon].y
+                      - points[(i+1)%polygon].x*points[i%polygon].y)
+  }
+  
+  // If the points are labeled sequentially in the counterclockwise direction,
+  // then the sum of the above determinants is positive and the absolute value signs can be omitted
+  // if they are labeled in the clockwise direction, the sum of the determinants will be negative.
+  // This is because the formula can be viewed as a special case of Green's Theorem.
+  switch orientation {
+  case Int.min..<0:
+    return -1 // if operation < 0 : ClockWise
+  case 0:
+    return 0 // if operation == 0 : Parallel
+  default:
+    return 1 // if operation > 0 : CounterClockWise
+  }
+}
+
+// A few simple tests
+
+
+// Triangle
+var p1 = Point(x: 5, y: 8)
+var p2 = Point(x: 9, y: 1)
+var p3 = Point(x: 3, y: 6)
+
+print(ccw(points: [p1,p2,p3])) // -1 means ClockWise
+
+// Quadrilateral
+var p4 = Point(x: 5, y: 8)
+var p5 = Point(x: 2, y: 3)
+var p6 = Point(x: 6, y: 1)
+var p7 = Point(x: 9, y: 3)
+
+print(ccw(points: [p4,p5,p6,p7])) // 1 means CounterClockWise
+
+// Pentagon
+var p8 = Point(x: 5, y: 11)
+var p9 = Point(x: 3, y: 4)
+var p10 = Point(x: 5, y: 6)
+var p11 = Point(x: 9, y: 5)
+var p12 = Point(x: 12, y: 8)
+
+print(ccw(points: [p8,p9,p10,p11,p12])) // 1 means CounterClockWise

CounterClockWise/CounterClockWise.playground/contents.xcplayground

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+<?xml version="1.0" encoding="UTF-8" standalone="yes"?>
+<playground version='5.0' target-platform='ios' executeOnSourceChanges='false'>
+    <timeline fileName='timeline.xctimeline'/>
+</playground>

CounterClockWise/CounterClockWise.playground/playground.xcworkspace/contents.xcworkspacedata

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+<?xml version="1.0" encoding="UTF-8"?>
+<!DOCTYPE plist PUBLIC "-//Apple//DTD PLIST 1.0//EN" "http://www.apple.com/DTDs/PropertyList-1.0.dtd">
+<plist version="1.0">
+<dict>
+	<key>IDEDidComputeMac32BitWarning</key>
+	<true/>
+</dict>
+</plist>

CounterClockWise/CounterClockWise.playground/playground.xcworkspace/xcshareddata/IDEWorkspaceChecks.plist

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+/*
+ CounterClockWise(CCW) Algorithm
+ The user cross-multiplies corresponding coordinates to find the area encompassing the polygon,
+ and subtracts it from the surrounding polygon to find the area of the polygon within.
+ This code is based on the "Shoelace formula" by Carl Friedrich Gauss
+ https://en.wikipedia.org/wiki/Shoelace_formula
+ */
+
+
+import Foundation
+
+// MARK : Point struct for defining 2-D coordinate(x,y)
+public struct Point{
+  // Coordinate(x,y)
+  var x: Int
+  var y: Int
+  
+  public init(x: Int ,y: Int){
+    self.x = x
+    self.y = y
+  }
+}
+
+// MARK : Function that determine the area of a simple polygon whose vertices are described
+//        by their Cartesian coordinates in the plane.
+func ccw(points: [Point]) -> Int{
+  let polygon = points.count
+  var orientation = 0
+  
+  // Take the first x-coordinate and multiply it by the second y-value,
+  // then take the second x-coordinate and multiply it by the third y-value,
+  // and repeat as many times until it is done for all wanted points.
+  for i in 0..<polygon{
+    orientation += (points[i%polygon].x*points[(i+1)%polygon].y
+      - points[(i+1)%polygon].x*points[i%polygon].y)
+  }
+  
+  // If the points are labeled sequentially in the counterclockwise direction,
+  // then the sum of the above determinants is positive and the absolute value signs can be omitted
+  // if they are labeled in the clockwise direction, the sum of the determinants will be negative.
+  // This is because the formula can be viewed as a special case of Green's Theorem.
+  switch orientation {
+  case Int.min..<0:
+    return -1 // if operation < 0 : ClockWise
+  case 0:
+    return 0 // if operation == 0 : Parallel
+  default:
+    return 1 // if operation > 0 : CounterClockWise
+  }
+}