Find Intersection coordinates of Contour and line plot

Hello,

I am trying to output the x-values for where the efficiency contour plot intersects the red and blue line. I have used the getContourLineCoordinates function to get the x and y values of the contour plot. I was then trying to find where the the x values of the lines matched those of the contour but ran into some issues. Any help would be much appreciated. Thanks!

clear
clc
clf()
% Motor data from specification
raw_peak=[0 462;2000 462;4000 462;6000 462;8000 462;10000 462;12000 462;14000 399;16000 315];
raw_cont=[0 440;2000 440;4000 440;6000 440;8000 440;10000 440;12000 440;14000 380;16000 300];
N=linspace(0,16000,60); % [rpm]%
Tq=linspace(0,462, 50); % [Nm]%
N_p_rpm_X=raw_peak(:,1); % [rpm]%
Tq_p_Nm_Y=raw_peak(:,2); % [Nm]%
N_c_rpm_X=raw_cont(:,1); % [rpm]%
Tq_c_Nm_Y=raw_cont(:,2); % [Nm]%
kc=0.1; % [W/Nm^2]%
ki=0.0; % [W/(rad/s)]%
kw=1.0e-5; % [W/(rad/s)^3]%
C=500; % [W]%
effMin=0.89; % [-]%
omega=N*pi/30; % [rad/s]
for i=1:length(omega)
    for j=1:length(Tq)
        Pout(i,j)=(omega(i)*Tq(j)); % [W]
        Ploss(i,j)=kc*Tq(j)^2+ki*omega(i)+kw*omega(i)^3+C; % [W]
    end
end
eff=max(effMin,Pout./(Pout+Ploss))*100; % [-]
eff_trans=eff';
V=[70,85,90,91,92,93,94,95,96,97,98,99];
hold on
[C,h]=contour(N,Tq,eff_trans,V);
plot(N_p_rpm_X,Tq_p_Nm_Y,'b','LineWidth', 2);
plot(N_c_rpm_X,Tq_c_Nm_Y,'r','LineWidth', 2);
clabel(C)
contourTable = getContourLineCoordinates(C);
x2=table2array(contourTable(1:end,3));
y2=table2array(contourTable(1:end,4));
N_p_rpm_X_new = [N_p_rpm_X, zeros(size(N_p_rpm_X, 1), size(x2, 2)-size(N_p_rpm_X, 2)); zeros(size(x2, 1)-size(N_p_rpm_X, 1), size(x2, 2))];
Tq_p_Nm_Y_new = [Tq_p_Nm_Y, zeros(size(Tq_p_Nm_Y, 1), size(y2, 2)-size(Tq_p_Nm_Y, 2)); zeros(size(y2, 1)-size(Tq_p_Nm_Y, 1), size(y2, 2))];
Tq_c_Nm_Y_new = [Tq_c_Nm_Y, zeros(size(Tq_c_Nm_Y, 1), size(y2, 2)-size(Tq_c_Nm_Y, 2)); zeros(size(y2, 1)-size(Tq_c_Nm_Y, 1), size(y2, 2))];
x_cord_c = N_p_rpm_X_new(abs(Tq_p_Nm_Y_new - y2)<0.1);
hf=gcf();
ha=gca();
xlim([0 16500]);
ylim([0 500]);
grid on; 
xlabel('Motor Speed [rpm]');
ylabel('Motor Torque [Nm] & Motor efficiency [%]');
title('Motor Efficiency')

Answer 1

[Adam Danz]

Jackson Foley, I've just updated the getContourLineCoordinates function, please download the latest version (1.1.0). The (x,y) coordinates in the latest version are in order of proximity which is required to solve this problem easily. You'll also need the intersections() function from the file exchange.

Then, the intersections are as easy as,

[xi,yi] = intersections(contourTable.X, contourTable.Y, N_p_rpm_X, Tq_p_Nm_Y); 
plot(xi, yi, 'ko')

You can repeat that for the red line.

[Jackson Foley]

Hello Adam, that has seemed to work. Just curious what the other selections points are since there doesnt seem to be any visual intersection on the graph?

[Adam Danz]

The incorrect intersections are due to a small mistake in my answer. My answer treates all (x,y) coordinates as if they are from the same line. You can imagine that all of the contours are connected by a line and the incorrect intersections are intersecting the connector line.

Instead, the interesections should be performed separately for each contour line.

T = contourTable;  % this is just for simpliciy; you can replace T with contourTable

% Loop through each contour level
groups = unique(T.Group);
xy = cell(numel(groups),2); 
for i = groups'
    groupIdx = T.Group == i; 
    [xy{i,1},xy{i,2}] = intersections(T.X(groupIdx), T.Y(groupIdx), N_c_rpm_X, Tq_c_Nm_Y);
end
% Convert (x,y) values into a matrix
xyMat = cell2mat(arrayfun(@(i){[xy{i,:}]},1:size(xy,1))'); 

plot(xyMat(:,1), xyMat(:,2), 'ko')

[Jackson Foley]

Amazing, that works! Thank you so much for your help Adam.

[Leilane Passos]

Hi, is there a way to pick the indeces as well?

Answer 2

[KSSV]

You can use this: https://in.mathworks.com/matlabcentral/fileexchange/22441-curve-intersections?focused=5165138&tab=function

[Jackson Foley]

So I was able to get a matrix of intersection points but its outputting 175 values. From my graph I can visually only see 2 for each efficiency contour curve. Am I missing something?

clear
clc
clf()
% Motor data from specification
raw_peak=[0 462;2000 462;4000 462;6000 462;8000 462;10000 462;12000 462;14000 399;16000 315];
raw_cont=[0 440;2000 440;4000 440;6000 440;8000 440;10000 440;12000 440;14000 380;16000 300];
N=linspace(0,16000,60); % [rpm]%
Tq=linspace(0,462, 50); % [Nm]%
N_p_rpm_X=raw_peak(:,1); % [rpm]%
Tq_p_Nm_Y=raw_peak(:,2); % [Nm]%
N_c_rpm_X=raw_cont(:,1); % [rpm]%
Tq_c_Nm_Y=raw_cont(:,2); % [Nm]%
kc=0.1; % [W/Nm^2]%
ki=0.0; % [W/(rad/s)]%
kw=1.0e-5; % [W/(rad/s)^3]%
C=500; % [W]%
effMin=0.89; % [-]%
omega=N*pi/30; % [rad/s]
for i=1:length(omega)
    for j=1:length(Tq)
        Pout(i,j)=(omega(i)*Tq(j)); % [W]
        Ploss(i,j)=kc*Tq(j)^2+ki*omega(i)+kw*omega(i)^3+C; % [W]
    end
end
eff=max(effMin,Pout./(Pout+Ploss))*100; % [-]
eff_trans=eff';
V=[70,85,90,91,92,93,94,95,96,97,98,99];
hold on
[C,h]=contour(N,Tq,eff_trans,V);
plot(N_p_rpm_X,Tq_p_Nm_Y,'b','LineWidth', 2);
plot(N_c_rpm_X,Tq_c_Nm_Y,'r','LineWidth', 2);
clabel(C)
contourTable = getContourLineCoordinates(C);
x2=table2array(contourTable(1:end,3))';
y2=table2array(contourTable(1:end,4))';
N_p_rpm_X_new = [N_p_rpm_X, zeros(size(N_p_rpm_X, 1), size(x2', 2)-size(N_p_rpm_X, 2)); zeros(size(x2', 1)-size(N_p_rpm_X, 1), size(x2', 2))]';
N_c_rpm_X_new = [N_c_rpm_X, zeros(size(N_c_rpm_X, 1), size(x2', 2)-size(N_c_rpm_X, 2)); zeros(size(x2', 1)-size(N_c_rpm_X, 1), size(x2', 2))]';
Tq_p_Nm_Y_new = [Tq_p_Nm_Y, zeros(size(Tq_p_Nm_Y, 1), size(y2', 2)-size(Tq_p_Nm_Y, 2)); zeros(size(y2', 1)-size(Tq_p_Nm_Y, 1), size(y2', 2))]';
Tq_c_Nm_Y_new = [Tq_c_Nm_Y, zeros(size(Tq_c_Nm_Y, 1), size(y2', 2)-size(Tq_c_Nm_Y, 2)); zeros(size(y2', 1)-size(Tq_c_Nm_Y, 1), size(y2', 2))]';
Peak_cords=[N_p_rpm_X_new;Tq_p_Nm_Y_new];
Cont_cords=[N_c_rpm_X_new;Tq_c_Nm_Y_new];
Contour_cords=[x2;y2];
P=InterX(Cont_cords,Contour_cords);
hf=gcf();
ha=gca();
xlim([0 16500]);
ylim([0 500]);
grid on; 
xlabel('Motor Speed [rpm]');
ylabel('Motor Torque [Nm] & Motor efficiency [%]');
title('Motor Efficiency')

[KSSV]

You need to run InterX for each contour line and for each line.