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Line Segment - equation of a straight line in Matlab


A line segment is a straight line which links two points without extending beyond them. In this article we’re going to develop three functions to work out equations of straight lines in Matlab with different approaches.



At the end, we’re going to wrap those three functions in a menu, so that the user can choose the appropriate one, according to known data.

In two dimensions, the equation is often given by the slope-intercept form

y = mx + b


where:

m is the slope of the line (y2 – y1)/(x2 – x1)
b is the y-intercept of the line
x is the independent variable of the function y = f(x)

basic information of a straight line

Our first function assumes you enter points (x1, y1) and (x2, y2), and the function returns the slope m and the intersect b.

function [m, b] = str_lin1(x1, y1, x2, y2)
m = (y2-y1) / (x2-x1);
b = y1 - m*x1;


Now, the following video shows you how to use the concepts of point and slope to find linear equations. After the video, we show you how to implement a function to easily achieve the equivalent results.

Our second function in this task, assumes you enter point (x, y) and the slope. It returns the intercept.

function b = str_lin2(x1, y1, m)
b = y1 - m*x1;

The third function interpolates an entered value. You enter the slope, the intercept and the value. The function returns the interpolated values.

function [x, y] = str_lin3(m, b, val)
y = m*val + b;
x = (val - b) / m;

Now, we’re going to wrap those three functions using a menu and a switch structure:

% Functions on straight lines
clear all, clc, format compact, close all

option = menu('Choose your case: y = mx + b',...
'Enter (x1, y1) and (x2, y2); get m and b',...
'Enter (x1, y1) and m; get b',...
'Enter m, b and a value; get interpolated (val, y) and (x, val)');

switch option
case 1
x1 = input(
'Enter x1 = ');
y1 = input(
'Enter y1 = ');
x2 = input(
'Enter x2 = ');
y2 = input(
'Enter y2 = ');
[m, b] = str_lin1(x1, y1, x2, y2)

case 2
x1 = input(
'Enter x1 = ');
y1 = input(
'Enter y1 = ');
m = input(
'Enter m = ');
b = str_lin2(x1, y1, m)

case 3
m = input(
'Enter m = ');
b = input(
'Enter b = ');
v = input(
'Enter val = ');
[x, y] = str_lin3(m, b, v);
str = [
'(' num2str(v) ', ' num2str(y) ')'];
disp(str)
str = [
'(' num2str(x) ', ' num2str(v) ')'];
disp(str)
end


Let’s assume that the script above is called line_segment. We can run some examples from the command window, like this...

>>line_segment

Example 1: enter two points


Matlab displays the following menu:

menu in Matlab to work with equations of straight lines


If we click on the first option, the flow is like this:

Enter x1 = 0
Enter y1 = -2
Enter x2 = 2/3
Enter y2 = 0

and the results are

m = 3
b = -2

Example 2: enter one point and slope


Let's run again our code, but this time we select the second button. The scirpt works like this...

Enter x1 = 2/3
Enter y1 = 0
Enter m = 3

and the result is

b = -2

Example 3: enter slope, intercept and one value to be interpolated


Finally, the third option can be used for a simple linear interpolation. Let's run it, and we get...

Enter m = -4
Enter b = 1
Enter val = 0

(0, 1)
(0.25, 0)

From 'Line Segment' to home

From 'Line Segment' to Flow Control

Top

Online Calc for straight lines




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