How to obtain and plot perpedicular lines using the gradient of a function

Question

KostasK 2022-9-27

0
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https://ww2.mathworks.cn/matlabcentral/answers/1813240-how-to-obtain-and-plot-perpedicular-lines-using-the-gradient-of-a-function

评论： KostasK 2022-9-27

Hi all,

I have a simple function (quadratic in this case) where I would like to plot the lines perpedicular to its tangent for every point. As a first step I define the function and take the gardient to draw the tangent:

clear ; clc

x = (0:100)' ;

y1 = 5*x.^2 + 3*x - 4 ;

% Obtain tangent: y - y1 = slope*(x - x1)

dy1 = gradient(y1, x) ;

b1 = y1 - dy1.*x ;

y1tan = dy1'.*x + b1' ;

% Plot tangent at 50th point to demonstrate

figure ; plot(x, [y1 y1tan(:,50)]) ; legend('y1', 'tangent') ; grid on

The above works perfectly, so I proceed to use the similar method to obtain the perpendicular line to the tangent I just drew:

% Obtain perpendicular

dy1p= -1./dy1 ;

b1p = y1 - dy1p.*x ;

y1perp = dy1p'.*x + b1p' ;

% Plot

figure ; plot(x, [y1 y1tan(:,50) y1perp(:,50)]) ; legend('y1', 'tangent', 'perpendicular') ; grid on

As you can see, for some reason I am unable to get the perpendicular line which I do not understand why. Similar posts in the past that I have looked, don't seem to be doing anything radically different so I am struggling to understand why I can't accomplish this.

Thanks for your help in advance.