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How to rotate points on 2D coordinate systems

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I have some points on a 2D Cartesian coordinate system. I want to rotate all these points 90 degrees counterclockwise. What is the best solution? (When I work with 3D coordinates, I use “view” to change the view direction, but apparently, it doesn’t work with 2D coordinates)

Accepted Answer

John Chilleri
John Chilleri on 6 Feb 2017
Hello,
You can rotate your points with a rotation matrix:
Here's a simple implementation,
% Create rotation matrix
theta = 90; % to rotate 90 counterclockwise
R = [cosd(theta) -sind(theta); sind(theta) cosd(theta)];
% Rotate your point(s)
point = [3 5]'; % arbitrarily selected
rotpoint = R*point;
The rotpoint is the 90 degree counterclockwise rotated version of your original point.
Hope this helps!
  4 Comments
Ria
Ria on 12 Feb 2024
Hello, if you needed the rotation clockwise, could you just reverse each sign of cosd and sind?
George Abrahams
George Abrahams on 12 Feb 2024
@Ria You have two options. First option, set theta, the angle of rotation, to -90. Second option, the inverse of a rotation matrix is its transpose, , so transpose the matrix. In MATLAB this is typically achieved with the .' syntax.
R = [cosd(-90) -sind(-90); sind(-90) cosd(-90)]
R = 2×2
0 1 -1 0
R = [cosd(90) -sind(90); sind(90) cosd(90)].'
R = 2×2
0 1 -1 0

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More Answers (3)

Amit
Amit on 29 Mar 2023
Write and execute a MATLAB program for geometric modeling of a parametric circle with center at any point {xc,yc}, radius R and lying in the X-Y plane. Test your program with R=40 mm and center at both the origin and at {10,10} for estimating the point and tangent vector at any given parameter value 0<=u<=1.

Amit
Amit on 29 Mar 2023
Write and execute a MATLAB program for geometric modeling of a parametric circle with center at any point {xc,yc}, radius R and lying in the X-Y plane. Test your program with R=40 mm and center at both the origin and at {10,10} for estimating the point and tangent vector at any given parameter value 0<=u<=1.
Write the Matlab code for both the original parametric equation and computationally efficient parametric equation. Compare the computational times.

Amit
Amit on 29 Mar 2023
a) Write and execute a MATLAB program to plot a planar parametric curve whose x- and y- axis modeled using cubic polynomial of the form: X(u) =A*u^3+B*u+C Y(u) =E*u^3+F* u^2+G Where 0 ≤ u ≤ 1 is the parameter, and A, B, C, E, F, G are the polynomial coefficients. Your program should work for any user supplied input of these polynomial coefficients.
b) Write Matlab program to generate and plot a the Hermite cubic curve for any set of two control points and two tangent vectors. Validate your code with sample data given below: P0 = [1, 1], P’0 = [0.6, 0.8], P1= [8, 2] and P’1 = [-0.4472, -0.8944].
Also include in the program the facility of putting point at the specified u-value and an arrow for the tangent vector at that point.

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