From 35ca62c82b39506203e551c8d05938113aec3e2f Mon Sep 17 00:00:00 2001 From: TaeJoongYoon Date: Wed, 17 Oct 2018 04:05:46 +0900 Subject: [PATCH 1/2] Add CounterClockWise(CCW) --- .../Contents.swift | 76 +++++++++++ .../contents.xcplayground | 4 + .../contents.xcworkspacedata | 7 ++ .../xcshareddata/IDEWorkspaceChecks.plist | 8 ++ CounterClockWise/CounterClockWise.swift | 50 ++++++++ CounterClockWise/Images/Pentagon_img.png | Bin 0 -> 20639 bytes CounterClockWise/Images/Quadrilateral_img.jpg | Bin 0 -> 9081 bytes CounterClockWise/Images/Shoelace.png | Bin 0 -> 77353 bytes CounterClockWise/Images/Triangle_img.jpg | Bin 0 -> 10346 bytes CounterClockWise/Images/pentagon.png | Bin 0 -> 25285 bytes CounterClockWise/Images/quadrilateral.png | Bin 0 -> 22372 bytes CounterClockWise/Images/triangle.png | Bin 0 -> 19654 bytes CounterClockWise/README.md | 118 ++++++++++++++++++ README.markdown | 1 + 14 files changed, 264 insertions(+) create mode 100644 CounterClockWise/CounterClockWise.playground/Contents.swift create mode 100644 CounterClockWise/CounterClockWise.playground/contents.xcplayground create mode 100644 CounterClockWise/CounterClockWise.playground/playground.xcworkspace/contents.xcworkspacedata create mode 100644 CounterClockWise/CounterClockWise.playground/playground.xcworkspace/xcshareddata/IDEWorkspaceChecks.plist create mode 100644 CounterClockWise/CounterClockWise.swift create mode 100644 CounterClockWise/Images/Pentagon_img.png create mode 100644 CounterClockWise/Images/Quadrilateral_img.jpg create mode 100644 CounterClockWise/Images/Shoelace.png create mode 100644 CounterClockWise/Images/Triangle_img.jpg create mode 100644 CounterClockWise/Images/pentagon.png create mode 100644 CounterClockWise/Images/quadrilateral.png create mode 100644 CounterClockWise/Images/triangle.png create mode 100644 CounterClockWise/README.md diff --git a/CounterClockWise/CounterClockWise.playground/Contents.swift b/CounterClockWise/CounterClockWise.playground/Contents.swift new file mode 100644 index 000000000..ffa91ecbb --- /dev/null +++ b/CounterClockWise/CounterClockWise.playground/Contents.swift @@ -0,0 +1,76 @@ +/* + 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.. 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 diff --git a/CounterClockWise/CounterClockWise.playground/contents.xcplayground b/CounterClockWise/CounterClockWise.playground/contents.xcplayground new file mode 100644 index 000000000..9f5f2f40c --- /dev/null +++ b/CounterClockWise/CounterClockWise.playground/contents.xcplayground @@ -0,0 +1,4 @@ + + + + \ No newline at end of file diff --git a/CounterClockWise/CounterClockWise.playground/playground.xcworkspace/contents.xcworkspacedata b/CounterClockWise/CounterClockWise.playground/playground.xcworkspace/contents.xcworkspacedata new file mode 100644 index 000000000..919434a62 --- /dev/null +++ b/CounterClockWise/CounterClockWise.playground/playground.xcworkspace/contents.xcworkspacedata @@ -0,0 +1,7 @@ + + + + + diff --git a/CounterClockWise/CounterClockWise.playground/playground.xcworkspace/xcshareddata/IDEWorkspaceChecks.plist b/CounterClockWise/CounterClockWise.playground/playground.xcworkspace/xcshareddata/IDEWorkspaceChecks.plist new file mode 100644 index 000000000..18d981003 --- /dev/null +++ b/CounterClockWise/CounterClockWise.playground/playground.xcworkspace/xcshareddata/IDEWorkspaceChecks.plist @@ -0,0 +1,8 @@ + + + + + IDEDidComputeMac32BitWarning + + + diff --git a/CounterClockWise/CounterClockWise.swift b/CounterClockWise/CounterClockWise.swift new file mode 100644 index 000000000..07c422ea5 --- /dev/null +++ b/CounterClockWise/CounterClockWise.swift @@ -0,0 +1,50 @@ +/* + 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 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z8ZQz(cD!FPmO~U6F{5+0$_$+gL#!AfGJr@xHSnes#72ecU zy4ahMrR0LZ)6Z3@H!TY+uy8m;RRxw5FChU1jaqdT3QJMmsZ^Cqc#-(M3C})Yi5m3e zZkNwg-KV*de_q<^;qVje;0+z$Zrk;y)O7q`x~7Spen>Tin+v#|Zck;#!>YTg9M2sB zvU#kyP7iUZx*Mgm%2tw%I|upgwv1rxEw>U-dn^|ELK;i{@PpB(R%pa;<>4)bWC=R1Gn8w{i^ zCBRL)>X3OoxX*azplvC;re(7z#Mbb3?nH>crWx(qd2+4s0F8A3=KzMS$jFU&9sWFw zAKb|V#V^`#fr3uIx$wdM?fA>YAtLT&6}{BaNKn#dlcIbjQti&fXv~t?S+rnLq*v86DzOI+PdkMAHYHND{pYVk7?4@(0x+`M2$E?nF*g zRiXIn@ny@Of#QPkz;x!3`d-6VMfP@Pbq0^#i$K1iC_p?A59lO(`n=myP->MsTygQ@ z=A2_d-8q3MCw)b$aHsb|5EuD&oaQ!?2^tiR3K$o4bRN0ebOvPN+NIy5w+{`L3YRPa z2)CaRF16cq7%Isl=$=X6iNL}I1u*1__B>46ZIT9TDP$bR@8AMN_2_ Int{ + let polygon = points.count + var orientation = 0 + + for i in 0.. 0 : CounterClockWise + } +} +``` + +Put this code in a playground and test it like so: + +```swift +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 +``` + +Here's how it works. When given an `[Photo]`, `ccw(points:)` calculates the direction of the given points according to the Shoelaces formula. + + + +`orientation` is less than 0, the direction is clockwise. + +`orientation` is equal to 0, the direction is parallel. + +`orientation` is greater than 0, the direction is counterclockwise. + + + +## An example + +**In Triangle** + +```swift +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 +``` + +![triangle](/Users/taejoongyoon/Developer/Swift/swift-algorithm-club/CounterClockWise/Images/Triangle_img.jpg) + +![triangleExpression](/Users/taejoongyoon/Developer/Swift/swift-algorithm-club/CounterClockWise/Images/triangle.png) + + + +**In Quadrilateral** + +```swift +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 +``` + +![Quadrilateral](/Users/taejoongyoon/Developer/Swift/swift-algorithm-club/CounterClockWise/Images/Quadrilateral_img.jpg) + +![triangleExpression](/Users/taejoongyoon/Developer/Swift/swift-algorithm-club/CounterClockWise/Images/quadrilateral.png) + + + +**In Pentagon** + +```swift +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 +``` + +![triangle](/Users/taejoongyoon/Developer/Swift/swift-algorithm-club/CounterClockWise/Images/Pentagon_img.png) + +![triangleExpression](/Users/taejoongyoon/Developer/Swift/swift-algorithm-club/CounterClockWise/Images/pentagon.png) + + + +You probably won't need to use the CCW in any real-world problems, but it's cool to play around with geometry algorithm. The formula was described by Meister (1724-1788) in 1769 and by Gauss in 1795. It can be verified by dividing the polygon into triangles, and can be considered to be a special case of Green's theorem. + + + +*Written for Swift Algorithm Club by TaeJoong Yoon* \ No newline at end of file diff --git a/README.markdown b/README.markdown index 90b310752..efe89edc0 100644 --- a/README.markdown +++ b/README.markdown @@ -109,6 +109,7 @@ Bad sorting algorithms (don't use these!): - [Karatsuba Multiplication](Karatsuba%20Multiplication/). Another take on elementary multiplication. - [Haversine Distance](HaversineDistance/). Calculating the distance between 2 points from a sphere. - [Strassen's Multiplication Matrix](Strassen%20Matrix%20Multiplication/). Efficient way to handle matrix multiplication. +- [CounterClockWise](/CounterClockWise/). Determining the area of a simple polygon. ### Machine learning From e48117cd2cd5efaec539eb83c44d47089edc5054 Mon Sep 17 00:00:00 2001 From: TaeJoong Yoon Date: Wed, 17 Oct 2018 04:22:34 +0900 Subject: [PATCH 2/2] Update README.md --- CounterClockWise/README.md | 14 +++++++------- 1 file changed, 7 insertions(+), 7 deletions(-) diff --git a/CounterClockWise/README.md b/CounterClockWise/README.md index 6b6c1a1da..2d15eba53 100644 --- a/CounterClockWise/README.md +++ b/CounterClockWise/README.md @@ -70,9 +70,9 @@ var p3 = Point(x: 3, y: 6) print(ccw(points: [p1,p2,p3])) // -1 means ClockWise ``` -![triangle](/Users/taejoongyoon/Developer/Swift/swift-algorithm-club/CounterClockWise/Images/Triangle_img.jpg) +![triangle](./Images/Triangle_img.jpg) -![triangleExpression](/Users/taejoongyoon/Developer/Swift/swift-algorithm-club/CounterClockWise/Images/triangle.png) +![triangleExpression](./Images/triangle.png) @@ -87,9 +87,9 @@ var p7 = Point(x: 9, y: 3) print(ccw(points: [p4,p5,p6,p7])) // 1 means CounterClockWise ``` -![Quadrilateral](/Users/taejoongyoon/Developer/Swift/swift-algorithm-club/CounterClockWise/Images/Quadrilateral_img.jpg) +![Quadrilateral](./Images/Quadrilateral_img.jpg) -![triangleExpression](/Users/taejoongyoon/Developer/Swift/swift-algorithm-club/CounterClockWise/Images/quadrilateral.png) +![triangleExpression](./Images/quadrilateral.png) @@ -105,9 +105,9 @@ var p12 = Point(x: 12, y: 8) print(ccw(points: [p8,p9,p10,p11,p12])) // 1 means CounterClockWise ``` -![triangle](/Users/taejoongyoon/Developer/Swift/swift-algorithm-club/CounterClockWise/Images/Pentagon_img.png) +![triangle](./Images/Pentagon_img.png) -![triangleExpression](/Users/taejoongyoon/Developer/Swift/swift-algorithm-club/CounterClockWise/Images/pentagon.png) +![triangleExpression](./Images/pentagon.png) @@ -115,4 +115,4 @@ You probably won't need to use the CCW in any real-world problems, but it's cool -*Written for Swift Algorithm Club by TaeJoong Yoon* \ No newline at end of file +*Written for Swift Algorithm Club by TaeJoong Yoon*