How to solve a plotting problem regarding straight lines

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Giuseppe
Giuseppe on 1 Dec 2019
Edited: Giuseppe on 3 Dec 2019
How can I make the two lines meet in their intersection point as shown in the figure below ?
(I want to obtain the two lines that I've drawn using red dots!)
clc ;clear all; close all;
%Profilo
gamma = 1.4;
xdorso = [0 0.7 1]; xventre = [0 0.45 1];
ydorso = [0 0.03 0]; yventre = [0 -0.05 0];
delta1 = atand(0.03/0.44);
delta2 = atand(0.05/0.45);
delta3 = atand(0.03/0.56);
delta4 = atand(0.05/0.55);
n = 1000;
x = linspace(0,1,n);
alfa = -8:2:8;
deviazionedorso = delta1 + abs(alfa(1:4));
deviazioneventre = delta2 + alfa(5:end);
mach1 = 1.01:0.001:1.6;
lunghezza = length(mach1);
massimo = mach1;
for i = 1:lunghezza
m1 = mach1(i);
epsmin = asin(1/m1)*57.3;
eps = linspace(epsmin,90,30);
delta = abaco(eps,m1,gamma);
massimo(i)= max(delta);
figure(1)
plot(eps,delta);
hold on
end
machcriticodorso = deviazionedorso;
for i = 1:length(deviazionedorso)
calcolod = deviazionedorso(i);
for j = 1:lunghezza
if abs(massimo(j)-calcolod)<0.1
machcriticodorso(i) = mach1(j);
end
end
end
machcriticoventre = deviazioneventre;
for i = 1:length(deviazioneventre)
calcolov = deviazioneventre(i);
for j = 1:lunghezza
if abs(massimo(j)-calcolov)<0.1
machcriticoventre(i) = mach1(j);
end
end
end
machcriticosuperiore = [machcriticodorso machcriticoventre];
figure(4);
plot(alfa,machcriticosuperiore,'k-o');
xlabel('\alpha'); ylabel('M_{cr_{sup}}');
axis([-8 8 1 1.6])

Accepted Answer

Turlough Hughes
Turlough Hughes on 1 Dec 2019
We don't really need all that code to answer the question. It would be much more preferable to just post some sample data. Anyway, I've tried to replicate your data as follows:
x=linspace(-8,8,9);
y=[linspace(0.5,0.28,4) linspace(0.29,0.59,5)];
Where x and y correspond to the data in alfa,machcriticosuperiore.
You could use a linear fit to the "two lines" and then solve for the point of intersection as follows:
idx=x<=-1;
l1=polyfit(x(idx),y(idx),1); % l1 is coefficient m, c, of a linear fit to the data
l2=polyfit(x(~idx),y(~idx),1);
xi=(l2(2)-l1(2))/(l1(1)-l2(1)); % When y of line 1 = y of line 2, you get xi=(c2-c1)/(m1-m2)
yi=l1(1)*xi+l1(2);
plot(x,y,'ok')
hold on, plot(xi,yi,'or')
You could also insert the intersection point into your original data and then plot with the line:
x=[x(idx) xi x(~idx)];
y=[y(idx) yi y(~idx)];
xlabel('\alpha'); ylabel('M_{cr_{sup}}');
plot(x,y,'-ok');
  1 Comment
Giuseppe
Giuseppe on 3 Dec 2019
It works very well! Thank you, Thurlough Hughes!
Edit. The second part of your prompt (plotting with the intersection) seems to not work !
I obtain this:
pb.PNG
Can you help me ?
EDIT: I've solved plotting two vectors of 10 elements by simply adding the extrapolated value!

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