How to calculate the area between two curves separately based on being below or above.

Question

Wolfgang McCormack 2021-4-17

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https://ww2.mathworks.cn/matlabcentral/answers/804721-how-to-calculate-the-area-between-two-curves-separately-based-on-being-below-or-above

回答： Star Strider 2021-4-17

Hi Alll

how can I seperate calculate all the area difference when the orange line is below the black line and vice versa. In other words, calculating A1 and A3 seprately from A2.

Thanks

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Austin Thai 2021-4-17

What does your data look like? Are these curves analytic functions or discrete datapoints? Are they equally spaced in x?

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Answer 1

Star Strider 2021-4-17

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https://ww2.mathworks.cn/matlabcentral/answers/804721-how-to-calculate-the-area-between-two-curves-separately-based-on-being-below-or-above#answer_677601

在 MATLAB Online 中打开

Try something like this:

t = linspace(0, 10*pi, 500);                                    % Create Data
y1 = exp(-0.1*t) .* sin(t);                                     % Create Data
y2 = exp(-0.2*t) .* cos(t);                                     % Create Data
icptidx = find(diff(sign(y1 - y2)));                            % Approximate Indices Of Intersections
icptidx = [1, icptidx, numel(t)]; 
areavct = cumtrapz(t, y1 - y2);                                 % Cumulative Areas
for k = 1:numel(icptidx)-1
    areas(k) = areavct(icptidx(k+1)) - areavct(icptidx(k));
    xtxt(k) = (t(icptidx(k+1))+t(icptidx(k)))/2;                % Used in ‘text’ To Label Areas
    ytxt(k) = (y1(icptidx(k+1))+y2(icptidx(k)))/2;              % Used in ‘text’ To Label Areas
end
figure
plot(t, y1)
hold on
plot(t,y2)
hold off
grid
text(xtxt, ytxt, compose('$\\leftarrow Area = %.3f$', areas), 'Interpreter','latex', 'Rotation',60)
ylim([min(ylim) max(ylim)+0.2])