Plotting and finding the intersection of 2 curves

Question

Aizaz Anwer 2020-12-17

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此问题的直接链接

https://ww2.mathworks.cn/matlabcentral/answers/696730-plotting-and-finding-the-intersection-of-2-curves

评论： Image Analyst 2020-12-21

i want to plot two curves and find the intersection point of them. Please help me with the code or link to where i can find the answer

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Paul Hoffrichter 2020-12-17

编辑：Paul Hoffrichter 2020-12-17

Is this what you want? Scenario 1: Someone gives you a .fig file. You get it into Matlab and now you have two curves. (How these curves were created by the sender can be considered unknown.) Now you want to know how to get the (x1, x2) coordinates of the intersection point.

Or is this what you want? Scenario 2:You have two functions, f(x) and g(x). When you plot them, you notice that they interesect. You want a function that gives the intersection point. That is: (x1, x2) = Intersection( x, f, g).

Image Analyst 2020-12-17

在 MATLAB Online 中打开

Sell = [12,22,28]
Price1 = [15,30,50]
Buy = [10,18,29]
Price2 = [25,42,50]
plot(Sell, Price1, 'b.-', 'LineWidth', 2, 'MarkerSize', 20);
grid on;
hold on;
plot(Buy, Price2, 'r.-', 'LineWidth', 2, 'MarkerSize', 20);
legend('Sell', 'Buy', 'location', 'southeast');

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Answer 1

Paul Hoffrichter 2020-12-17

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链接

此回答的直接链接

https://ww2.mathworks.cn/matlabcentral/answers/696730-plotting-and-finding-the-intersection-of-2-curves#answer_578560

If you have two vectors, x1, y1 that form the curve (x1, y1), and likewise, another curve (x2, y2), then you can get the intersection points using the function by Douglas Schwarz.

https://www.mathworks.com/matlabcentral/fileexchange/11837-fast-and-robust-curve-intersections

or from this function by NS.

https://www.mathworks.com/matlabcentral/fileexchange/22441-curve-intersections

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Answer 2

Image Analyst 2020-12-18

0
链接

此回答的直接链接

https://ww2.mathworks.cn/matlabcentral/answers/696730-plotting-and-finding-the-intersection-of-2-curves#answer_578755

在 MATLAB Online 中打开

For the specific case at hand:

Sell = [12,22,28]
Price1 = [15,30,50]
Buy = [10,18,29]
Price2 = [25,42,50]
plot(Sell, Price1, 'b.-', 'LineWidth', 2, 'MarkerSize', 20);
grid on;
hold on;
plot(Buy, Price2, 'r.-', 'LineWidth', 2, 'MarkerSize', 20);
legend('Sell', 'Buy', 'location', 'southwest');	
xlabel('Sell or Buy Price in $', 'FontSize', 20);
ylabel('Price1 or Price2 in $', 'FontSize', 20);
% Get equations for the last two line segments.
coeff1 = polyfit(Sell(2:3), Price1(2:3), 1)
coeff2 = polyfit(Buy(2:3), Price2(2:3), 1)
% Find out where the lines are equal.
% ax + b = cx + d.  Find x
% x = (d-b) / (a-c)
matchPrice = (coeff2(2) - coeff1(2)) / (coeff1(1) - coeff2(1))
y = coeff1(1) * matchPrice + coeff1(2)
caption = sprintf('Match at x = $%.2f, y = $%.2f', matchPrice, y);
title(caption, 'FontSize', 20);
% Draw lines in dark green color.
darkGreen = [0, 0.5, 0];
line([matchPrice, matchPrice], [0, y], 'Color', darkGreen, 'LineWidth', 2);
line([0, matchPrice], [y, y], 'Color', darkGreen, 'LineWidth', 2);
fprintf('Done running %s.m ...\n', mfilename);

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Image Analyst 2020-12-20

在 MATLAB Online 中打开

If your data is linear, this works:

data = readmatrix('sample data.xlsx');
Sell = data(:, 3);
Price1 = data(:, 2);
Buy = data(:, 1);
Price2 = data(:, 4);
plot(Sell, Price1, 'b-', 'LineWidth', 2, 'MarkerSize', 20);
grid on;
hold on;
plot(Buy, Price2, 'r-', 'LineWidth', 2, 'MarkerSize', 20);
legend('Sell', 'Buy', 'location', 'east');	
xlabel('Sell or Buy Price in $', 'FontSize', 20);
ylabel('Price1 or Price2 in $', 'FontSize', 20);
% Get equations for the last two line segments.
coeff1 = polyfit(Sell, Price1, 1)
coeff2 = polyfit(Buy, Price2, 1)
% Find out where the lines are equal.
% ax + b = cx + d.  Find x
% x = (d-b) / (a-c)
matchPrice = (coeff2(2) - coeff1(2)) / (coeff1(1) - coeff2(1))
y = coeff1(1) * matchPrice + coeff1(2)
caption = sprintf('Match at x = $%.2f, y = $%.2f', matchPrice, y);
title(caption, 'FontSize', 20);
% Draw lines in dark green color.
darkGreen = [0, 0.5, 0];
line([matchPrice, matchPrice], [0, y], 'Color', darkGreen, 'LineWidth', 2);
line([0, matchPrice], [y, y], 'Color', darkGreen, 'LineWidth', 2);
fprintf('Done running %s.m ...\n', mfilename);

What do you normally plot on the x and y axes?

Image Analyst 2020-12-21

Why are there two Sell prices at 49 (elements 25 and 26) yet two different prices for those? It will take extra code to get rid of duplicates and average them.

Image Analyst 2020-12-21

在 MATLAB Online 中打开

sample data.xlsx

OK, I had to put in some lines to repair bad data, like your duplicated Sell prices at 49 (elements 25 and 26). That data repair is in between the --------- lines. Not only does the data repair make it more robust, but the final result does not depend on the curve having a linear relationship. The buy/sell/price plots could be curved. Yay!

Here is the final code and it will be accurate to 1/1000th of a cent.

clc;    % Clear the command window.
close all;  % Close all figures (except those of imtool.)
clear;  % Erase all existing variables. Or clearvars if you want.
workspace;  % Make sure the workspace panel is showing.
format long g;
format compact;
data = readmatrix('sample data.xlsx');
Sell = data(:, 3);
Price1 = data(:, 2);
Buy = data(:, 1);
Price2 = data(:, 4);
p1 = plot(Sell, Price1, 'b-', 'LineWidth', 2, 'MarkerSize', 20);
grid on;
hold on;
p2 = plot(Buy, Price2, 'r-', 'LineWidth', 2, 'MarkerSize', 20);
legend([p1, p2], 'Sell', 'Buy', 'location', 'east');	
xlabel('Sell or Buy Price in $', 'FontSize', 20);
ylabel('Price1 or Price2 in $', 'FontSize', 20);
%------------------------------------------------------------------------
% DATA REPAIR - FIX BAD DATA
% Now we have a problem with the supplied "Sell" data and need to fix it.
% If some of the "x" arrays have the same price more than once, 
% the interpolation step will fail.  So we need to average together any duplicates.
[Sell, sortOrder] = sort(Sell, 'Ascend'); % first sort from least to greatest.
% Now sort Price1 the same way.
Price1 = Price1(sortOrder);
% Now we can average all Price1 that have the same Sell price.
Price1 = splitapply(@mean, Price1, findgroups(Sell));
Sell = unique(Sell);
% Now fix Buy and Price2 the same way: (Actually in the supplied data, these arrays were OK.)
[Buy, sortOrder] = sort(Buy, 'Ascend'); % first sort from least to greatest.
% Now sort Price1 the same way.
Price2 = Price2(sortOrder);
% Now we can average all Price1 that have the same Sell price.
Price2 = splitapply(@mean, Price2, findgroups(Buy));
Buy = unique(Buy);
%------------------------------------------------------------------------
% Find the overall range
minPrice = min([Sell; Price1; Buy; Price2])
maxPrice = max([Sell; Price1; Buy; Price2])
% Interpolate extra points to get more accuracy for non-linear curves.
% We'll get to the nearest 1/1000 of a cent.
numPoints = (maxPrice - minPrice) * 1000;
% Get all possible "x" values.
x = linspace(minPrice, maxPrice, numPoints);
% Interpolate the other arrays at the new x points.
Price1a = interp1(Sell, Price1, x);
Price2a = interp1(Buy , Price2, x);
% Find differences at every x value.
priceDifference = abs(Price2a - Price1a);
% Find there the difference is minimum
[minDiff, indexOfMinDiff] = min(priceDifference)
% Get the x value there.
xMatch = x(indexOfMinDiff);
% Find out where the lines are equal.
% ax + b = cx + d.  Find x
% x = (d-b) / (a-c)
matchPrice1 = Price1a(indexOfMinDiff)
matchPrice2 = Price2a(indexOfMinDiff)
yMatch = mean([matchPrice1, matchPrice2])
caption = sprintf('Match at x = $%.2f, y = $%.2f', xMatch, yMatch);
title(caption, 'FontSize', 20);
% Draw lines in dark green color.
darkGreen = [0, 0.5, 0];
line([xMatch, xMatch], [0, yMatch], 'Color', darkGreen, 'LineWidth', 2);
line([0, xMatch], [yMatch, yMatch], 'Color', darkGreen, 'LineWidth', 2);
% Legend will update to show these lines but we don't want them.
% so tell legend to only have the two plot lines.
legend([p1, p2], 'Sell', 'Buy', 'location', 'east');	
fprintf('Done running %s.m ...\n', mfilename);