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.
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!
