plotting half an ellipse, a linear line and the interceptions between

Hi all

i would like to plot an ellipse that will grow in a for loop.

i also have a linear line that doesnt change.

i would like to find the interceptions between the linear line and the ongrowing ellipses.

the code looks like that:

x1 = p0/OCR:0.1:x_int;

yeta=+3*x1-3*p;

t=0:0.01:pi;

plot(p0/2+p0/2*cos(t),p0/2*M*sin(t), 'k')

and then i change the p0 value with a for loop, giving me a bigger ellipse.

plot(p(i),q(i),'ko','MarkerFaceColor', 'k', 'MarkerSize', 4)

how do i shoe the interceptions, and not the p value? (attached pic, the 1st subplot)

Answer 1

[Hassaan]

% Parameters
p0 = 400; % Initial p0 value
M = 1.5; % Ratio for the ellipse equation

% Linear line equation
x1 = 400:0.1:600;
yeta = 3 * x1 - 1200;

% Plot the static linear line
figure;
subplot(2, 2, 1);
plot(x1, yeta, 'r', 'LineWidth', 1.5); 
hold on;

% Initial plot for the first ellipse
t = 0:0.01:pi;
p_values = p0/2 + p0/2 * cos(t);
q_values = p0/2 * M * sin(t);
plot(p_values, q_values, 'k', 'LineWidth', 1.5);
hold on;

% Plot ellipse and calculate intersections in a loop
for k = 1:5
    p0 = p0 + 10; % Increase p0 for the growing ellipse
    p_values = p0/2 + p0/2 * cos(t);
    q_values = p0/2 * M * sin(t);
    
    % Plot the growing ellipse
    plot(p_values, q_values, 'k', 'LineWidth', 1.5);
    
    % Find intersections
    for i = 1:length(x1)
        % Intersection condition
        idx = find(abs(p_values - x1(i)) < 1e-1 & abs(q_values - yeta(i)) < 1e-1);
        if ~isempty(idx)
            plot(p_values(idx), q_values(idx), 'ko', 'MarkerFaceColor', 'k', 'MarkerSize', 4);
        end
    end
end

% Set axis properties
axis equal;
xlim([350 650]);
ylim([0 250]);
xlabel('p [kPa]');
ylabel('q [kPa]');
title('Intersections of Ellipses and Linear Line');
grid on;
hold off;

[Yuval]

Hassan thanks.

in your code, only the first line gets a markercolor, why? and how can we show on every ellipse?

is it possible to do so with an array? so the interceptions will help in other subplots as well?

[Yuval]

UPDATE

i used the code you suggested, im not recieving all interceptions, please advise