Calculate perpendicular line to an 3rd order polynomial

Hi all,

I have been trying to calculate the perpendicular line to an 3rd order (or higher) polynomial line.

I found a way to do it with an 2nd order polynomial, however, can't work out how to do it for any higher.

This calcualtion would make my data analysis a lot quicker, but is not essential. I've tried a bunch of stuff and I think this is my last hope.

Thanks in advance for any help.

Answer 1

[Torsten]

For a general function f, the formula for the perpendicular line to the function through (x0,f(x0)) is

y = f(x0) + (x-x0)* ( -1/f'(x0) )

[Adam]

Thanks mate.

Helped me figure it out.

For people looking for something similar I have written this basic script that should help.

It could probably be done better and more efficient, but I am a bit of a Matlab rookie.

Hopefully this is a good start for anyone looking. See below.

pow = 4; % power of the poly can be between 3 and 5. 
              % It could be more, but it is constrained by the if function in the script.
x = linspace(0,1,5);
y = 1./(1+x);
scatter(x,y);
  p = polyfit(x,y,pow);
    hold on 
  yy = polyval(p,x); 
  plot(x,yy) 
   k2 = polyder(p);
if pow==3
    y2 = k2(1)*x.^2 + k2(2)*x + k2(3);
elseif pow==4
    y2 = k2(1)*x.^3 + k2(2)*x.^2 + k2(3)*x + k2(4);
elseif pow==5
    y2 = k2(1)*x.^4 + k2(2)*x.^3 + k2(3)*x.^2 + k2(4)*x + k2(5);
end

for i = 2:4
 y3 = y2(i);
 pe = -1/y3;
 X1 = x(i); 
 Y1 = y(i);  
 X2 = X1+.2;  
 Y2 = pe*(X2 - X1)+Y1;
 plot([X2, X1], [Y2, Y1],':','LineWidth', 2); 
 X3 = X1-.2;  
 Y3 = pe*(X3 - X1)+Y1;  
 plot([X3, X1], [Y3, Y1],'--', 'LineWidth', 2);
end
axis equal