How to make an angled line in a meshgrid

I need to make an angled line (ultimately an angled square) in a meshgrid, but my matlab skills are low to non-excistent, sorry.

Suppose i have a 500x500 meshgrid with all values as 0. I need to make some rotated squares inside this meshgrid. Right now i can only make straight squares, so [y1:y2, x1:x2] = 1. However, i cannot figure out how to make rotated squares, i dont even know if this is possible in a meshgrid.

I know the length of the squares and the required angle, but how do i then make the line between two corner points of the square (and ultimately fill in the whole square). It doesn't matter if the lines are 'blocky', (then ill just increase the size of the meshgrid and the squares), or if the square isn't exactly the length needed (because there is no point in the meshgrid at that exact angle and squarewidth).

This is the code i am using so far (mostly copied from this thread https://nl.mathworks.com/matlabcentral/answers/329166-plotting-random-points-within-boundary) imageHeight and Width are the height and width of the meshgrid (in the case of the example 500), the squarewidth is the width of the square im making.

The xlim and ylim at the bottom are just there because thats the only part I need.

I hope someone understands my question and can help me further

% M-file to place multiple small squares inside a big circle where no squares overlap, though they might touch.
% Clean up
close all;
clc;
fontSize = 15;
% Initialize some parameters.
numberOfsquares = 150000; % Number of small squares
squareInsideValue = 0; % black squares
circleOutsideValue = 1; % white circle 
circleInsideValue = 1; % white circle
squareWidth = 12; 
imageWidth = 500;
imageHeight =  500; % square area 0f 500*500
circleRadius = 250;    % big circle radius
% Initialize an image to hold one single big circle.
ourImage = circleOutsideValue * ones(imageHeight, imageWidth);
[x, y] = meshgrid(1:imageWidth, 1:imageHeight);
ourImage((x - imageWidth/2).^2 + (y - imageHeight/2).^2 <= circleRadius.^2) = circleInsideValue;
% Display it in the upper left plot.
%subplot(2, 1, 1);
%imshow(ourImage, []);
%title('Circle Mask', 'FontSize', fontSize);
%set(gcf, 'Position', get(0,'Screensize')); % Maximize figure.
% Place the small squares inside one by one.
for k = 1 : numberOfsquares
  % Get a random row, column location
  y1 = randi(imageHeight, 1);
  x1 = randi(imageWidth, 1);
  y2 = y1 + squareWidth - 1;
  x2 = x1 + squareWidth - 1;
  
  % See if any of those corners are outside the circle.  Skip this square if so.
  if sqrt((x1 - imageWidth/2)^2 + (y1 - imageHeight/2)^2) > circleRadius
    continue;
  end
  if sqrt((x1 - imageWidth/2)^2 + (y2 - imageHeight/2)^2) > circleRadius
    continue;
  end
  if sqrt((x2 - imageWidth/2)^2 + (y1 - imageHeight/2)^2) > circleRadius
    continue;
  end
  if sqrt((x2 - imageWidth/2)^2 + (y2 - imageHeight/2)^2) > circleRadius
    continue;
  end
  % If you get to here it's inside the circle. 
  % Now make sure no corner is inside any square that has already been placed.
  if ourImage(y1, x1) == squareInsideValue
    continue;
  end
  if ourImage(y1, x2) == squareInsideValue
    continue;
  end
  if ourImage(y2, x1) == squareInsideValue
    continue;
  end
  if ourImage(y2, x2) == squareInsideValue
    continue;
  end
  % If we get here, we're free to place the square.
  ourImage(y1:y2, x1:x2) = squareInsideValue;
end
% Display it in the lower left plot.
%subplot(2, 1, 2);
figure(2), clf(2);
imshow(ourImage);
%caption = sprintf('Now with %d Squares Added', numberOfsquares);
%title(caption, 'FontSize', fontSize);
xlim([170 195])
ylim([330 342.5])
% Note: squares might not be overlapping but they might be touching.

Answer 1

[darova]

Here is an idea:

• create 4 points (corners of your rectangle) and some background

x = [...]
y = [...]
A = ones(50);       % background (empty image)

• rotate your data using rotation matrix

• create mask of rectangle region using impoly

p = impoly(gca,[x y]);
imshow(p.createMask)

[Stef Kuiper]

First of all, thank you for your answer, but to be honest i have no idea what you are doing.

I tried something myself in matlab, but using the rotation matrix, it rotates the square about the 0.0 point and i have no idea how to rotate it around its centre (i guess i need to do something translate it towards 0.0, then rotate it and then translate it back somehow?).

x = [20 20 35 35];
y = [20 35 35 20];


theta = 20  ;
R = [cosd(theta) -sind(theta);
     sind(theta) cosd(theta)];
point_1 = R*[x(1),y(1)]'
point_2 = R*[x(2),y(2)]'
point_3 = R*[x(3),y(3)]'
point_4 = R*[x(4),y(4)]'

figure(1), clf(1), hold on
hSquare = fill(x,y,'y');
plot([point_1(1),point_2(1), point_3(1), point_4(1), point_1(1)],[point_1(2),point_2(2), point_3(2), point_4(2), point_1(2)])
xlim([0 50])
ylim([0 50])
hold off

Also, i can only rotate the square in a normal plot, it doesn't work in the 'mesh plot', since after a (for example) 20 degree rotation, the point [20, 20] becomes [11.9534, 25.6343].

The only thing i know how to plot in such a 'mesh plot' are different scales of grey. So how did you plot the blue circles and the lines of the rotated square?

A = ones(50);
A(x(1),y(1)) = 0;
A(x(2),y(2)) = 0;
A(x(3),y(3)) = 0;
A(x(4),y(4)) = 0;

imshow(A, [])
h = gca;
h.Visible = 'On';

Also, the impoly is part of an add-on i have never used. I downloaded it, but i have no idea how to use it.

In short, i only know how to rotate the square around the plot centre [0, 0]. And i have no idea how to do it in such a 'mesh plot'

[darova]

Rotate it this way

v = R*[x(:)-mean(x) y(:)-mean(y)]';     % rotate all points together
    % extract new coordinates and move them back to original position
x1 = v(1,:) + mean(x);                  
y1 = v(2,:) + mean(y);

What is just rotate image themself?

I = zeros(100);                 % background
mask = ones(20,30);             % rectangle
I1 = imrotate(mask,25);         % rotate rectangle
[m,n] = size(I1);
I(20+(1:m),30+(1:n)) = I1;      % insert rectangle
imshow(I)

[Stef Kuiper]

thank you for your fast answer, this one really helped me out!

I have one last question, i changed the code a bit to show the original and rotated image in the same plot

I = zeros(100);                 % background
mask = ones(20,20)-0.4;             % rectangle
I1 = imrotate(mask,45)-0.2;         % rotate rectangle
[m,n] = size(I1);
I(20+(1:m),20+(1:n)) = I1;      % insert rectangle
I(20+(1:20),20+(1:20)) = mask   % insert original rectangle
figure(2), clf(2)
imshow(I)

I also looked up the imrotate command in the help part of matlab. There it says that imrotate rotates the image around its centre. However, as you can see in the picture below, it (i believe) didn't rotate the image around its centre. Is this a mistake from my side or did i misunderstand the command somehow?

[darova]

It's because the imaged changed it's size after rotation

I = zeros(100);                % background
mask = ones(20,20)-0.4;        % rectangle
I1 = imrotate(mask,45)-0.2;    % rotate rectangle
[m,n] = size(I1);
ii = -(m-1)/2:(m-1)/2;
jj = -(n-1)/2:(n-1)/2;
I(20+ii,20+jj) = I1;     % insert rectangle
I(20+(-10:9),20+(-10:9)) = mask; % insert original rectangle
imshow(I)

[Stef Kuiper]

thank you so very much!

[darova]