/*

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

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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

}