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Swati Umamaheshwaran on 17 Sep 2017
Answered: Preetham Manjunatha on 8 Feb 2022
I need to plot the lines x+y=3 and x-y= -1 and find their point of intersection. I know that to plot the lines I could use 'fplot'. How can I find the coordinates of their intersection and plot it? Please help.
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Answers (5)
Star Strider on 17 Sep 2017
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Another approach:
xymtx = [1 1; 1 -1];
cv = [3; -1];
xy = xymtx\cv; % Calculate Intercept
xint = xy(2); % X-Value Of Intercept
yint = xy(1); % Y-Value Of Intercept
xyind = [xint - 1, xint + 1]'; % X-Values For Plot
xydep = [cv -xyind.*xymtx(:,2)]; % Y-Values For Plot
figure(1)
plot(xyind, xydep(1,:), xyind, xydep(2,:), '-r')
hold on
plot(xint, yint, 'pg', 'MarkerFaceColor','g', 'MarkerSize',10)
hold off
This is straightforward and relatively simple linear algebra. The ‘xydep’ variable calculates the y-values corresponding to the arbitrary values in ‘xydep’, and is the result of solving ‘[X + Y] = C’ for ‘Y’.
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Tutku Oztel on 9 Jan 2019
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Hello,
I'm sharing the function that I wrote to find the intersection points of two lines with their given slope and constant values:
function [x0 y0] = intersectPoints(m1,m2,b1,b2)
% Insersection point of two lines with known slope and constant
% parameters.
% [x0 y0] = intersectPoints(m1,m2,b1,b1)
% where m's are slope, and b's are constants.
% written by Tutku Öztel in 06.01.2019
x0 = (b2-b1)/(m1-m2); %find the x point
y0 = m1*x0+b1;
end
Late though, but still.. Hope it will be helpful! :)
Tutku
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José Luis Sandoval on 7 Jun 2020
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https://www.mathworks.com/matlabcentral/answers/357026-how-to-plot-2-lines-and-find-the-coordinates-of-their-intersection#comment_887846
Usefuil, thanks.
Wai Keong Bryce Wong on 12 Oct 2020
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https://www.mathworks.com/matlabcentral/answers/357026-how-to-plot-2-lines-and-find-the-coordinates-of-their-intersection#comment_1052126
This is super useful. Thanks for your help!
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Simon Kölbl on 17 Sep 2017
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I would do it like this:
% define x Axis and evaluate functions
x_points = -5:0.1:5;
function1 = -x+1;
function2 = x+1;
index_intersection = find(function1 == function2);
x_value_intersection = x_points(index_intersection);
y_value_intersection = function1(index_intersection);
% plot functions and intersection point:
curve1 = plot(x_points, function1);
hold on
curve2 = plot(x_points, function2);
intersection = plot(x_value_intersection, y_value_intersection,...
'Marker', '+', 'MarkerSize', 6, 'Color', 'r');
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Cyril Okhio on 13 Nov 2018
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https://www.mathworks.com/matlabcentral/answers/357026-how-to-plot-2-lines-and-find-the-coordinates-of-their-intersection#comment_636946
Sorry it did not work. There are errors in Line 9.
Image Analyst on 5 Jun 2021
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https://www.mathworks.com/matlabcentral/answers/357026-how-to-plot-2-lines-and-find-the-coordinates-of-their-intersection#comment_1565965
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@Cyril Okhio, I think @Simon Kölbl meant this:
clc;% Clear command window.
fprintf('Running %s.m ...\n', mfilename);
clear;% Delete all variables.
close all;% Close all figure windows except those created by imtool.
workspace;% Make sure the workspace panel is showing.
% Define x Axis and evaluate functions
x_points = -5:0.1:5;
function1 = -x_points+1;
function2 = x_points+1;
index_intersection = find(function1 == function2);
x_value_intersection = x_points(index_intersection)
y_value_intersection = function1(index_intersection)
% Plot functions and intersection point:
curve1 = plot(x_points, function1);
hold on
curve2 = plot(x_points, function2);
intersection = plot(x_value_intersection, y_value_intersection,...
'Marker', '+', 'MarkerSize', 20, 'Color', 'r', 'LineWidth', 2);
grid on
caption = sprintf('At intersection, x = %f, y = %f', x_value_intersection, y_value_intersection);
fontSize = 15;
title(caption, 'FontSize', 15);
xlabel('x', 'FontSize', 15);
ylabel('y', 'FontSize', 15);
fprintf('Done running %s.m\n', mfilename);
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Matt J on 5 Jun 2021
Edited: Matt J on 5 Jun 2021
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Using this File Exchange submission,
https://www.mathworks.com/matlabcentral/fileexchange/93470-intersections-of-multiple-2d-lines-or-line-segments
xy=linexlines2D( [1,1,-3].' , [1,-1,1] ); %the intersection point
hold on
fimplicit(@(x,y) x+y-3);
fimplicit(@(x,y) x-y+1);
plot(xy(1),xy(2),'or','MarkerFaceColor','r')
hold off
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Preetham Manjunatha on 8 Feb 2022
Here is the link to find the intersection point of two line segments/lines. A fast two line intersection point finder based on the line parametric space. Finds the intersection point between two lines if it exists or else submits NaN. if you need to find the intersection of the multiple line segments, MATLAB's Mapping Toolbox has function polyxpoly - that finds the intersection points for lines or polygon edges.
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