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

Question

Bera 2024-6-4

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评论： Bera 2024-6-5

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!

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Answer 1

Amish 2024-6-5

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https://ww2.mathworks.cn/matlabcentral/answers/2125336-creating-a-grid-on-an-image-at-an-angle-with-a-specific-spacing#answer_1467731

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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:

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;