Creating a grid on an image at an angle with a specific spacing

Hey All

The summary is it all. Basically I have an image and a code that draws two "axes" lines a red and blue line. I basically want to form a grid using lines parellel to those in order to find their intersects and plot other circles where they intersect.

I have provided an image for clarification!

Answer 1

[Amish]

Hi Bera,

Assuming that your axes could be at an angle from the default x-y axes, you can follow the following approach to plot the required grid pattern:

1. Plot the original axes (Red and Blue line)

% Original line equations: y = m1*x + b1 and y = m2*x + b2
m1 = 1; 
b1 = 0; 
m2 = -1; 
b2 = 0; 

% Define plot range for x
x_range = linspace(-10, 10, 400);

% Calculate y values based on the line equations
y1 = m1 * x_range + b1;
y2 = m2 * x_range + b2;

% Plot the lines
figure;
hold on;
plot(x_range, y1, 'r'); 
plot(x_range, y2, 'b'); 
axis equal;

2. Generate parallel lines at a fixed distance away from the original lines. For this, use a method that shifts the lines by adjusting the intercept (b).

% Define the number of parallel lines and their separation
num_lines = 5; % Num lines on each side of the original line
sep = 1; % Separation distance

% Generate and plot parallel lines for the first line
for i = -num_lines:num_lines
    b_shift = b1 + i * sep;
    y_shift = m1 * x_range + b_shift;
    plot(x_range, y_shift, 'LineStyle', '-', 'Color', [0.8, 0.5, 0.5]);
end

% Generate and plot parallel lines for the second line
for i = -num_lines:num_lines
    b_shift = b2 + i * sep;
    y_shift = m2 * x_range + b_shift;
    plot(x_range, y_shift, 'LineStyle', '-', 'Color', [0.5, 0.5, 0.8]);
end

3. Finally, to find intersections between two sets of lines, you can use the fact that at the intersection, the values are equal. So, (), which can be solved for . These can then be plotted.

% Find intersections between sets of parallel lines
for i = -num_lines:num_lines
    for j = -num_lines:num_lines
        % Calculate new intercepts
        b1_shift = b1 + i * sep;
        b2_shift = b2 + j * sep;
        
        % Solve for x and y to find intersection
        x_intersect = (b2_shift - b1_shift) / (m1 - m2);
        y_intersect = m1 * x_intersect + b1_shift;
        
        % Plot circle at intersection
        viscircles([x_intersect, y_intersect], 0.2, 'Color', 'k', 'LineWidth', 0.5);
    end
end

hold off;

The final graphs might look like:

Hope this helps!

[Bera]

Thank you