# Orientation of 3 ordered points

Orientation of an ordered triplet of points in the plane can be

• counterclockwise
• clockwise
• colinear

The following diagram shows different possible orientations of (a,b,c) If orientation of (p1, p2, p3) is collinear, then orientation of (p3, p2, p1) is also collinear.
If orientation of (p1, p2, p3) is clockwise, then orientation of (p3, p2, p1) is counterclockwise and vice versa is also true.

Given three points p1, p2 and p3, find orientation of (p1, p2, p3).
Example:

```Input:   p1 = {0, 0}, p2 = {4, 4}, p3 = {1, 2}
Output:  CounterClockWise

Input:   p1 = {0, 0}, p2 = {4, 4}, p3 = {1, 1}
Output:  Colinear
```

How to compute Orientation?

```The idea is to use slope. Slope of line segment (p1, p2): σ = (y2 - y1)/(x2 - x1)
Slope of line segment (p2, p3): τ = (y3 - y2)/(x3 - x2)

If  σ > τ, the orientation is clockwise (right turn)

Using above values of σ and τ, we can conclude that,
the orientation depends on sign of  below expression:

(y2 - y1)*(x3 - x2) - (y3 - y2)*(x2 - x1)

Above expression is negative when σ < τ, i.e.,  counterclockwise```

Below is the implementation of above idea.

## C++

 `// A C++ program to find orientation of three points ` `#include ` `using` `namespace` `std; ` ` `  `struct` `Point ` `{ ` `    ``int` `x, y; ` `}; ` ` `  `// To find orientation of ordered triplet (p1, p2, p3). ` `// The function returns following values ` `// 0 --> p, q and r are colinear ` `// 1 --> Clockwise ` `// 2 --> Counterclockwise ` `int` `orientation(Point p1, Point p2, Point p3) ` `{ ` `    ``// See 10th slides from following link for derivation ` `    ``// of the formula ` `    ``int` `val = (p2.y - p1.y) * (p3.x - p2.x) - ` `              ``(p2.x - p1.x) * (p3.y - p2.y); ` ` `  `    ``if` `(val == 0) ``return` `0;  ``// colinear ` ` `  `    ``return` `(val > 0)? 1: 2; ``// clock or counterclock wise ` `} ` ` `  `// Driver program to test above functions ` `int` `main() ` `{ ` `    ``Point p1 = {0, 0}, p2 = {4, 4}, p3 = {1, 2}; ` `    ``int` `o = orientation(p1, p2, p3); ` `    ``if` `(o==0)         cout << ``"Linear"``; ` `    ``else` `if` `(o == 1)  cout << ``"Clockwise"``; ` `    ``else`              `cout << ``"CounterClockwise"``; ` `    ``return` `0; ` `} `

## Java

 `// JAVA Code to find Orientation of 3 ` `// ordered points ` `class` `Point ` `{ ` `    ``int` `x, y; ` `    ``Point(``int` `x,``int` `y){ ` `        ``this``.x=x; ` `        ``this``.y=y; ` `    ``} ` `} ` ` `  `class` `GFG { ` `     `  `    ``// To find orientation of ordered triplet  ` `    ``// (p1, p2, p3). The function returns  ` `    ``// following values  ` `    ``// 0 --> p, q and r are colinear ` `    ``// 1 --> Clockwise ` `    ``// 2 --> Counterclockwise ` `    ``public` `static` `int` `orientation(Point p1, Point p2, ` `                                         ``Point p3) ` `    ``{ ` `        ``// See 10th slides from following link  ` `        ``// for derivation of the formula ` `        ``int` `val = (p2.y - p1.y) * (p3.x - p2.x) - ` `                  ``(p2.x - p1.x) * (p3.y - p2.y); ` `      `  `        ``if` `(val == ``0``) ``return` `0``;  ``// colinear ` `      `  `        ``// clock or counterclock wise ` `        ``return` `(val > ``0``)? ``1``: ``2``;  ` `    ``} ` `     `  `    ``/* Driver program to test above function */` `    ``public` `static` `void` `main(String[] args)  ` `    ``{ ` `            ``Point p1 = ``new` `Point(``0``, ``0``); ` `            ``Point p2 = ``new` `Point(``4``, ``4``); ` `            ``Point p3 = ``new` `Point(``1``, ``2``); ` `             `  `            ``int` `o = orientation(p1, p2, p3); ` `             `  `            ``if` `(o==``0``)      ` `            ``System.out.print(``"Linear"``); ` `            ``else` `if` `(o == ``1``)   ` `            ``System.out.print(``"Clockwise"``); ` `            ``else`               `            ``System.out.print(``"CounterClockwise"``); ` `         `  `    ``} ` `} ` ` `  `//This code is contributed by Arnav Kr. Mandal. `

## C#

 `// C# Code to find Orientation of 3 ` `// ordered points ` `using` `System; ` `public` `class` `Point ` `{ ` `    ``public` `int` `x, y; ` `    ``public` `Point(``int` `x,``int` `y) ` `    ``{ ` `        ``this``.x = x; ` `        ``this``.y = y; ` `    ``} ` `} ` ` `  `class` `GFG  ` `{ ` `     `  `    ``// To find orientation of ordered triplet  ` `    ``// (p1, p2, p3). The function returns  ` `    ``// following values  ` `    ``// 0 --> p, q and r are colinear ` `    ``// 1 --> Clockwise ` `    ``// 2 --> Counterclockwise ` `    ``public` `static` `int` `orientation(Point p1, Point p2, ` `                                        ``Point p3) ` `    ``{ ` `        ``// See 10th slides from following link  ` `        ``// for derivation of the formula ` `        ``int` `val = (p2.y - p1.y) * (p3.x - p2.x) - ` `                ``(p2.x - p1.x) * (p3.y - p2.y); ` `     `  `        ``if` `(val == 0) ``return` `0; ``// colinear ` `     `  `        ``// clock or counterclock wise ` `        ``return` `(val > 0)? 1: 2;  ` `    ``} ` `     `  `    ``/* Driver program to test above function */`` ` `    ``public` `static` `void` `Main(String[] args)  ` `    ``{ ` `            ``Point p1 = ``new` `Point(0, 0); ` `            ``Point p2 = ``new` `Point(4, 4); ` `            ``Point p3 = ``new` `Point(1, 2); ` `             `  `            ``int` `o = orientation(p1, p2, p3); ` `             `  `            ``if` `(o == 0)      ` `                ``Console.WriteLine(``"Linear"``); ` `            ``else` `if` `(o == 1)  ` `                ``Console.WriteLine(``"Clockwise"``); ` `            ``else`             `                ``Console.WriteLine(``"CounterClockwise"``); ` `         `  `    ``} ` `} ` ` `  `/* This code contributed by PrinciRaj1992 */`

Output:

`CounterClockwise`

The concept of orientation is used in below articles:
Find Simple Closed Path for a given set of points
How to check if two given line segments intersect?
Convex Hull | Set 1 (Jarvis’s Algorithm or Wrapping)
Convex Hull | Set 2 (Graham Scan)

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Improved By : princiraj1992

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