Tangent line on a curve. From a peak down the "unload curve" (in each case the bottom curve)

Hi guys :)

I'm pretty confused how i can plot tanget lines onto my 3 curves.

my current plot looks like this:

Now i want to insert 3 tangent lines each starting at the 3 peaks and going down the bottom curves. Should look like this (cause i need the values "h_c"):

THANKS a lot for your help!!!

Current Code:

A_04 = readmatrix("AlCrMoN_04.xlsx"); % Excelfile consist of 2 columns with 41 rows
ersteSpalte04 = [A_04(:,1)];
zweiteSpalte04 = [A_04(:,2)];

A_13 = readmatrix("AlCrMoN_13.xlsx"); % Excelfile consist of 2 columns with 41 rows
ersteSpalte13 = [A_13(:,1)];
zweiteSpalte13 = [A_13(:,2)];

A_29 = readmatrix("AlCrMoN_29.xlsx"); % Excelfile consist of 2 columns with 41 rows
ersteSpalte29 = [A_29(:,1)];
zweiteSpalte29 = [A_29(:,2)];

%% Plots
figure("Name","load displacement");
hold on
grid on
plot(ersteSpalte04,zweiteSpalte04,"LineWidth",1.5,"DisplayName","AlCrMoN 04");
plot(ersteSpalte13,zweiteSpalte13,"LineWidth",1.5,"DisplayName","AlCrMoN 13");
plot(ersteSpalte29,zweiteSpalte29,"LineWidth",1.5,"DisplayName","AlCrMoN 29");
xlim([0 0.23])
xlabel("Eindringtiefe (ht) in µm"); ylabel("Kraft (P) in mN");
legend("show", "Location", "northwest");
hold off

Answer 1

[chicken vector]

The approach is to find the index of the maximum point in the curve:

[~,idx] = max(yData{j});

Then we can compute the derivative from that point until the end of the data, such that we perform the evluation on a continous curve:

dydt = gradient(yData{j}(idx:end))./gradient(xData{j}(idx:end));

Or:

dydt = diff(yData{j}(idx:end))./diff(xData{j}(idx:end));
% In general I suggest you to use "gradient", but for the derivative 
% on the first point using "diff" makes no difference.

Finally we can find the intersection with the X axis as follows:

hC(j) = -yData{j}(idx)/dydt(1) + xData{j}(idx);

If you like to keep graphics code seprated from computational code:

material = "AlCrMoN";
IDs = {"04","13","29"};
N = length(IDs);
xData = cell(N,1);
yData = cell(N,1);
hC = zeros(N,1);

for j = 1 : N
    data = readmatrix(material + "_" + IDs{j} + ".xlsx");
    xData{j} = data(:,1);
    yData{j} = data(:,2);
    [~,idx] = max(yData{j});
    dydt = gradient(yData{j}(idx:end))./gradient(xData{j}(idx:end));
    hC(j) = -yData{j}(idx)/dydt(1) + xData{j}(idx);
end

figure("Name","load displacement");
hold on;
for j = 1 : N
    plot(xData{j}, yData{j}, "LineWidth",1.5, "DisplayName", material + " " + IDs{j});
    plot([hC(j) xData{j}(idx)],[0 yData{j}(idx)],'k', "HandleVisibility", "Off");
end
hold off;
grid on;
xlim([0 0.23])
xlabel("Eindringtiefe (ht) in µm");
ylabel("Kraft (P) in mN");
legend("Show", "Location", "NorthWest");

[chicken vector]

Shorter version:

material = "AlCrMoN";
IDs = {"04","13","29"};
N = length(IDs);

figure("Name","load displacement");
hold on;
for j = 1 : N
    data = readmatrix(material + "_" + IDs{j} + ".xlsx");
    xData = data(:,1);
    yData = data(:,2);
    [~,idx] = max(yData);
    dydt = gradient(yData(idx:end))./gradient(xData(idx:end));
    hC = -yData(idx)/dydt(1) + xData(idx);
    plot(xData, yData, "LineWidth",1.5, "DisplayName", material + " " + IDs{j});
    plot([hC xData(idx)],[0 yData(idx)],'k', "HandleVisibility", "Off");
end
hold off;
grid on;
xlim([0 0.23])
xlabel("Eindringtiefe (ht) in µm");
ylabel("Kraft (P) in mN");
legend("Show", "Location", "NorthWest");

[moinmoinnoob69]

Thanks a lot!!

You saved my day <3