Trying to plot a vertical line that stops at the intersection of a curved line in Matlab.

Here is my code that i used to plot my data and it works! On the plot, i have 2 red lines and a black curve. I need help figuring out how to get the red lines to stop at the intersection of the black curved line.

clc
close all
clearvars
phi =0:10:80;
intstep = (phi(2)-phi(1))/10;  %interpolation step
phiint = phi(1):intstep:phi(end); %intepolated phi, to get a smoother curve

GZ =    [0    0.3475    0.7315    1.2363    1.6167    1.6898    1.3167    0.8303    0.1829;
         0    0.2195    0.4828    0.8705    1.1448    1.1302    0.6840    0.1426   -0.5377;
         0    0.2304    0.5596    0.9949    1.1924    1.1046    0.7462    0.2743   -0.1829;
         0    0.1034    0.3094    0.6291    0.7222    0.5442    0.1126   -0.4131   -0.9033];

KG = 10.97;

m_disp =  1.0e+04 *2.0118; %mass displacement

cargo = 1.0e+03 * [3.3    1.1    2.3059]; %weigth cargo

cg = [13.2   10.8   12.12]; %VCG cargo
GZ(5,:)=GZ(4,:)-0.597*cosd(phi);
GGprim=(1100*10.92)/m_disp(end);
leg_1 = {'-k'};
figure
for n=1:size(GZ(5,:),1)
    GZint(n,:)=interp1(phi,GZ(5,:),phiint,'spline'); %interpolate to get a smoother curve
    plot(phiint,GZint(n,:),leg_1{n})
    hold on
    leg_1{n} = strcat('KG = ', num2str(KG(n)), 'm \Delta =  ', num2str(m_disp(n)) , ' MT');
end
%plot([0,60],[0,0],'linewidth',2)
%plot([57.4,57.4],[-0.6,-0.08068],'linewidth',2)
xline(57.3,'color','red','linewidth',2);
yline(0,'color','red','linewidth',2);

grid on
ylabel('GZ [m]','Interpreter','latex')
title('Figure 2b')
xlabel( ['Angle of Heel, ' '$\varphi\circ$'],'Interpreter','latex')
xlim([0 60]) %Hint if you graph doesn't fit within these axis something is wrong
ylim([-0.6 0.3])
legend(leg_1, 'location','northwest')

Answer 1

[Star Strider]

Try something like this —

% clc
% close all
% clearvars
phi =0:10:80;
intstep = (phi(2)-phi(1))/10;  %interpolation step
phiint = phi(1):intstep:phi(end); %intepolated phi, to get a smoother curve

GZ =    [0    0.3475    0.7315    1.2363    1.6167    1.6898    1.3167    0.8303    0.1829;
         0    0.2195    0.4828    0.8705    1.1448    1.1302    0.6840    0.1426   -0.5377;
         0    0.2304    0.5596    0.9949    1.1924    1.1046    0.7462    0.2743   -0.1829;
         0    0.1034    0.3094    0.6291    0.7222    0.5442    0.1126   -0.4131   -0.9033];

KG = 10.97;

m_disp =  1.0e+04 *2.0118; %mass displacement

cargo = 1.0e+03 * [3.3    1.1    2.3059]; %weigth cargo

cg = [13.2   10.8   12.12]; %VCG cargo
GZ(5,:)=GZ(4,:)-0.597*cosd(phi);
GGprim=(1100*10.92)/m_disp(end);
leg_1 = {'-k'};
figure
for n=1:size(GZ(5,:),1)
    GZint(n,:)=interp1(phi,GZ(5,:),phiint,'spline'); %interpolate to get a smoother curve
    plot(phiint,GZint(n,:),leg_1{n})
    hold on
    leg_1{n} = strcat('KG = ', num2str(KG(n)), 'm \Delta =  ', num2str(m_disp(n)) , ' MT');
end
%plot([0,60],[0,0],'linewidth',2)
%plot([57.4,57.4],[-0.6,-0.08068],'linewidth',2)

% xline(57.3,'color','red','linewidth',2);
% yline(0,'color','red','linewidth',2);

ixx = find(phiint>57.3,1,'first')+(-1:1).';                 % Index Range For Vertical Line
ixy = find(diff(sign(GZint)))+(-1:1).';                     % Index Range For Horizontal Line
y1 = interp1(phiint(ixx),GZint(ixx),57.3);                  % Y-Limit Of Vertical Line
x1 = interp1(GZint(ixy(:,2)),phiint(ixy),0);                % X-Limit Of Horizontal Line
plot([1 1]*57.3, [min(ylim) y1], '-r', 'LineWidth',2)       % Plot Vertical Line
plot([min(xlim) x1(2)], [0 0], '-r', 'LineWidth',2)         % Plot Horizontal Line

grid on
ylabel('GZ [m]','Interpreter','latex')
title('Figure 2b')
xlabel( ['Angle of Heel, ' '$\varphi\circ$'],'Interpreter','latex')
xlim([0 60]) %Hint if you graph doesn't fit within these axis something is wrong
ylim([-0.6 0.3])
legend(leg_1, 'location','northwest')

I’m not certain which intersection you want for the horizontal line. This extends it to the second intersection, to stop at the first intersection change the ‘x1’ subscript to 1 in the plot call using it (’Plot Horizontal Line’).

.

[Michael Thiel]

Thank you for your help. I tried to change the intersection for the horizontal line and it doesn't inersect the curve.

i played with your code and couldn't figure it out.

How can i plot the horizontal line inbetween the curve? from the first point to the second? sorry i wasn't clear in my initial question.

[Star Strider]

My pleasure!

I wasn’t certain what you wanted with respect to the intersections. To do that requires one minor adjustment to the code, since ‘x1(1)’ is the first intersection and ‘x1(2)’ is the second intersection.

Change that plot call to:

plot([x1(1) x1(2)], [0 0], '-r', 'LineWidth',2) % Plot Horizontal Line

and it should do what you want —

% clc
% close all
% clearvars
phi =0:10:80;
intstep = (phi(2)-phi(1))/10;  %interpolation step
phiint = phi(1):intstep:phi(end); %intepolated phi, to get a smoother curve

GZ =    [0    0.3475    0.7315    1.2363    1.6167    1.6898    1.3167    0.8303    0.1829;
         0    0.2195    0.4828    0.8705    1.1448    1.1302    0.6840    0.1426   -0.5377;
         0    0.2304    0.5596    0.9949    1.1924    1.1046    0.7462    0.2743   -0.1829;
         0    0.1034    0.3094    0.6291    0.7222    0.5442    0.1126   -0.4131   -0.9033];

KG = 10.97;

m_disp =  1.0e+04 *2.0118; %mass displacement

cargo = 1.0e+03 * [3.3    1.1    2.3059]; %weigth cargo

cg = [13.2   10.8   12.12]; %VCG cargo
GZ(5,:)=GZ(4,:)-0.597*cosd(phi);
GGprim=(1100*10.92)/m_disp(end);
leg_1 = {'-k'};
figure
for n=1:size(GZ(5,:),1)
    GZint(n,:)=interp1(phi,GZ(5,:),phiint,'spline'); %interpolate to get a smoother curve
    plot(phiint,GZint(n,:),leg_1{n})
    hold on
    leg_1{n} = strcat('KG = ', num2str(KG(n)), 'm \Delta =  ', num2str(m_disp(n)) , ' MT');
end
%plot([0,60],[0,0],'linewidth',2)
%plot([57.4,57.4],[-0.6,-0.08068],'linewidth',2)

% xline(57.3,'color','red','linewidth',2);
% yline(0,'color','red','linewidth',2);

ixx = find(phiint>57.3,1,'first')+(-1:1).';                 % Index Range For Vertical Line
ixy = find(diff(sign(GZint)))+(-1:1).';                     % Index Range For Horizontal Line
y1 = interp1(phiint(ixx),GZint(ixx),57.3);                  % Y-Limit Of Vertical Line
x1 = interp1(GZint(ixy(:,2)),phiint(ixy),0);                % X-Limit Of Horizontal Line
plot([1 1]*57.3, [min(ylim) y1], '-r', 'LineWidth',2)       % Plot Vertical Line
plot([x1(1) x1(2)], [0 0], '-r', 'LineWidth',2)             % Plot Horizontal Line
dx1 = diff(x1)                                              % Difference Between 'x1(1)' And 'x1(2)'

dx1 = 29.0000

grid on
ylabel('GZ [m]','Interpreter','latex')
title('Figure 2b')
xlabel( ['Angle of Heel, ' '$\varphi\circ$'],'Interpreter','latex')
xlim([0 60]) %Hint if you graph doesn't fit within these axis something is wrong
ylim([-0.6 0.3])
legend(leg_1, 'location','northwest')

Other intersections are also possible, depending on what you want.

I added ‘dx1’ in the event you want to calculate the difference between those intersections. Delete it if you don’t need it.

.

[Michael Thiel]

The intersection on the left side doesn't end on the curve like it does on the right. Is there a way to fix it?

[Star Strider]

That has to do more with the plot function and the chosen line width than the precision of the calculations. One option could be to ‘fudge’ ‘x1(1)’ by multiplying it by a small constant —

% clc
% close all
% clearvars
phi =0:10:80;
intstep = (phi(2)-phi(1))/10;  %interpolation step
phiint = phi(1):intstep:phi(end); %intepolated phi, to get a smoother curve

GZ =    [0    0.3475    0.7315    1.2363    1.6167    1.6898    1.3167    0.8303    0.1829;
         0    0.2195    0.4828    0.8705    1.1448    1.1302    0.6840    0.1426   -0.5377;
         0    0.2304    0.5596    0.9949    1.1924    1.1046    0.7462    0.2743   -0.1829;
         0    0.1034    0.3094    0.6291    0.7222    0.5442    0.1126   -0.4131   -0.9033];

KG = 10.97;

m_disp =  1.0e+04 *2.0118; %mass displacement

cargo = 1.0e+03 * [3.3    1.1    2.3059]; %weigth cargo

cg = [13.2   10.8   12.12]; %VCG cargo
GZ(5,:)=GZ(4,:)-0.597*cosd(phi);
GGprim=(1100*10.92)/m_disp(end);
leg_1 = {'-k'};
figure
for n=1:size(GZ(5,:),1)
    GZint(n,:)=interp1(phi,GZ(5,:),phiint,'spline'); %interpolate to get a smoother curve
    plot(phiint,GZint(n,:),leg_1{n})
    hold on
    leg_1{n} = strcat('KG = ', num2str(KG(n)), 'm \Delta =  ', num2str(m_disp(n)) , ' MT');
end
%plot([0,60],[0,0],'linewidth',2)
%plot([57.4,57.4],[-0.6,-0.08068],'linewidth',2)

% xline(57.3,'color','red','linewidth',2);
% yline(0,'color','red','linewidth',2);

ixx = find(phiint>57.3,1,'first')+(-1:1).';                 % Index Range For Vertical Line
ixy = find(diff(sign(GZint)))+(-1:1).';                     % Index Range For Horizontal Line
y1 = interp1(phiint(ixx),GZint(ixx),57.3);                  % Y-Limit Of Vertical Line
x1 = interp1(GZint(ixy(:,2)),phiint(ixy),0);                % X-Limit Of Horizontal Line
plot([1 1]*57.3, [min(ylim) y1], '-r', 'LineWidth',2)       % Plot Vertical Line
plot([x1(1)*1.02 x1(2)], [0 0], '-r', 'LineWidth',2)             % Plot Horizontal Line
dx1 = diff(x1)                                              % Difference Between 'x1(1)' And 'x1(2)'

dx1 = 29.0000

grid on
ylabel('GZ [m]','Interpreter','latex')
title('Figure 2b')
xlabel( ['Angle of Heel, ' '$\varphi\circ$'],'Interpreter','latex')
xlim([0 60]) %Hint if you graph doesn't fit within these axis something is wrong
ylim([-0.6 0.3])
legend(leg_1, 'location','northwest')

I chose the constant (1.02) arbitrarily, and it appears to work. Change it to give the result you want.

.