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How to plot 2 lines and find the coordinates of their intersection?

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Swati Umamaheshwaran
Swati Umamaheshwaran 2017 年 9 月 17 日
回答済み: Preetham Manjunatha 2022 年 2 月 8 日
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.

回答 (5 件)

Star Strider
Star Strider 2017 年 9 月 17 日
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’.

Tutku Oztel
Tutku Oztel 2019 年 1 月 9 日
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
  2 件のコメント
José Luis Sandoval
José Luis Sandoval 2020 年 6 月 7 日
Usefuil, thanks.
Wai Keong Bryce Wong
Wai Keong Bryce Wong 2020 年 10 月 12 日
This is super useful. Thanks for your help!

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Simon Kölbl
Simon Kölbl 2017 年 9 月 17 日
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');
  2 件のコメント
Cyril Okhio
Cyril Okhio 2018 年 11 月 13 日
Sorry it did not work. There are errors in Line 9.
Image Analyst
Image Analyst 2021 年 6 月 5 日
@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
Matt J 2021 年 6 月 5 日
編集済み: Matt J 2021 年 6 月 5 日
Using this File Exchange submission,
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

Preetham Manjunatha
Preetham Manjunatha 2022 年 2 月 8 日
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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