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Commit 73baaaa

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Merge pull request #797 from TaeJoongYoon/master
Add CounterClockWise(CCW)
2 parents cf518c0 + e48117c commit 73baaaa

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/*
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CounterClockWise(CCW) Algorithm
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The user cross-multiplies corresponding coordinates to find the area encompassing the polygon,
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and subtracts it from the surrounding polygon to find the area of the polygon within.
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This code is based on the "Shoelace formula" by Carl Friedrich Gauss
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https://en.wikipedia.org/wiki/Shoelace_formula
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*/
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import Foundation
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// MARK : Point struct for defining 2-D coordinate(x,y)
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public struct Point{
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// Coordinate(x,y)
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var x: Int
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var y: Int
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public init(x: Int ,y: Int){
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self.x = x
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self.y = y
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}
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}
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// MARK : Function that determine the area of a simple polygon whose vertices are described
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// by their Cartesian coordinates in the plane.
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func ccw(points: [Point]) -> Int{
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let polygon = points.count
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var orientation = 0
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// Take the first x-coordinate and multiply it by the second y-value,
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// then take the second x-coordinate and multiply it by the third y-value,
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// and repeat as many times until it is done for all wanted points.
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for i in 0..<polygon{
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orientation += (points[i%polygon].x*points[(i+1)%polygon].y
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- points[(i+1)%polygon].x*points[i%polygon].y)
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}
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// If the points are labeled sequentially in the counterclockwise direction,
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// then the sum of the above determinants is positive and the absolute value signs can be omitted
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// if they are labeled in the clockwise direction, the sum of the determinants will be negative.
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// This is because the formula can be viewed as a special case of Green's Theorem.
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switch orientation {
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case Int.min..<0:
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return -1 // if operation < 0 : ClockWise
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case 0:
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return 0 // if operation == 0 : Parallel
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default:
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return 1 // if operation > 0 : CounterClockWise
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}
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}
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// A few simple tests
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// Triangle
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var p1 = Point(x: 5, y: 8)
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var p2 = Point(x: 9, y: 1)
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var p3 = Point(x: 3, y: 6)
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print(ccw(points: [p1,p2,p3])) // -1 means ClockWise
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// Quadrilateral
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var p4 = Point(x: 5, y: 8)
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var p5 = Point(x: 2, y: 3)
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var p6 = Point(x: 6, y: 1)
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var p7 = Point(x: 9, y: 3)
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print(ccw(points: [p4,p5,p6,p7])) // 1 means CounterClockWise
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// Pentagon
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var p8 = Point(x: 5, y: 11)
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var p9 = Point(x: 3, y: 4)
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var p10 = Point(x: 5, y: 6)
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var p11 = Point(x: 9, y: 5)
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var p12 = Point(x: 12, y: 8)
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print(ccw(points: [p8,p9,p10,p11,p12])) // 1 means CounterClockWise
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<?xml version="1.0" encoding="UTF-8" standalone="yes"?>
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<playground version='5.0' target-platform='ios' executeOnSourceChanges='false'>
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<timeline fileName='timeline.xctimeline'/>
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</playground>

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

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<?xml version="1.0" encoding="UTF-8"?>
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<!DOCTYPE plist PUBLIC "-//Apple//DTD PLIST 1.0//EN" "http://www.apple.com/DTDs/PropertyList-1.0.dtd">
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<plist version="1.0">
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<dict>
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<key>IDEDidComputeMac32BitWarning</key>
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<true/>
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</dict>
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</plist>
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/*
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CounterClockWise(CCW) Algorithm
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The user cross-multiplies corresponding coordinates to find the area encompassing the polygon,
4+
and subtracts it from the surrounding polygon to find the area of the polygon within.
5+
This code is based on the "Shoelace formula" by Carl Friedrich Gauss
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https://en.wikipedia.org/wiki/Shoelace_formula
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*/
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9+
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import Foundation
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// MARK : Point struct for defining 2-D coordinate(x,y)
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public struct Point{
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// Coordinate(x,y)
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var x: Int
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var y: Int
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public init(x: Int ,y: Int){
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self.x = x
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self.y = y
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}
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}
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// MARK : Function that determine the area of a simple polygon whose vertices are described
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// by their Cartesian coordinates in the plane.
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func ccw(points: [Point]) -> Int{
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let polygon = points.count
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var orientation = 0
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// Take the first x-coordinate and multiply it by the second y-value,
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// then take the second x-coordinate and multiply it by the third y-value,
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// and repeat as many times until it is done for all wanted points.
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for i in 0..<polygon{
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orientation += (points[i%polygon].x*points[(i+1)%polygon].y
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- points[(i+1)%polygon].x*points[i%polygon].y)
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}
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// If the points are labeled sequentially in the counterclockwise direction,
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// then the sum of the above determinants is positive and the absolute value signs can be omitted
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// if they are labeled in the clockwise direction, the sum of the determinants will be negative.
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// This is because the formula can be viewed as a special case of Green's Theorem.
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switch orientation {
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case Int.min..<0:
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return -1 // if operation < 0 : ClockWise
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case 0:
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return 0 // if operation == 0 : Parallel
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default:
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return 1 // if operation > 0 : CounterClockWise
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}
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}
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‎CounterClockWise/Images/Shoelace.png‎

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‎CounterClockWise/Images/pentagon.png‎

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