Problem 194. Clockwise or Counterclockwise

Created by Alfonso Nieto-Castanon

Solve Later

Given a list of 2-d points defining the vertices of a polygon, determine whether these points are sorted clockwise.

The inputs to this function are two vectors x and y (with equal size) containing the x- and y- coordinates of the polygon vertices, respectively.

The function should return true when sorted clockwise, and false when sorted counterclockwise (the polygon vertices will always be sorted either way).

Example:

x = [-1,-1,1,1];
y = [-1,1,1,-1];

defines a square, the vertices are listed clockwise

d_correct = true;

Solve

Solution Stats

529 Solutions
104 Solvers

Last Solution submitted on Jun 27, 2020

Last 200 Solutions

Problem Comments

3 Comments

3 Comments

Alfonso Nieto-Castanon on 2 Feb 2012

added more samples to the test

David Verrelli on 21 Jun 2018

Hello, Alfonso Nieto-Castanon. This is a very nice problem. It was interesting to see the variety of approaches used to solve it. It was also interesting to notice a few submissions failed your added test cases from circa Dec 2017. Do you allow for self-intersecting polygons, as per https://en.wikipedia.org/wiki/Polygon ?
I suspect a common solution tactic will fail badly when faced with self-intersecting polygons. —DIV

David Verrelli on 21 Jun 2018

...On second thought, maybe there's no consistent definition of CW/CCW for self-intersecting polygons, such as figure-eight or bow-tie ("cross-quadrilateral") shapes.

Solution Comments

Solution 1739929

1 Comment

1 Comment

Karl Ezra Pilario on 1 Mar 2019

I don't understand why the vector sizes of x and y for the last test case are both 100x15. The problem strictly says that the points are 2-dimensional. Can someone explain this?

Solution 1234357

1 Comment

1 Comment

David Verrelli on 21 Jun 2018

I like the readability of this submission. However the logic of the if statement is curious to me: it seems that after setting tf to false, tf can be reset back to true. Would it be more robust to either (i) initialise tf before your loop, or (ii) include a "break" command?

Solution 1212705

1 Comment

1 Comment

Chris Cleveland on 15 Jun 2017

Simply beautiful!

Solution 136517

1 Comment

1 Comment

James on 6 Sep 2012

Didn't realize ispolycw was in the Mapping Toolbox, and not Cody friendly.

Solution 55985

2 Comments

2 Comments

yurenchu on 15 Aug 2017

This method (as well as several others) would fail in a more extensive test suite; for example, when x = [1,1,2] and y = [2,1,1]; or when x = [-2,-2,-4,-4] and y = [1,3,1,-1]; or when x = [-1,-1,3] and y = [-3,1,1].

Alfonso Nieto-Castanon on 4 Dec 2017

@yurenchu, Thanks for pointing this out, I have added a few more test cases now

Problem Recent Solvers104

Problem Tags

math polygon