atan2 & mod number not converges to correct value???

Hi All,

I am calculating principle axis values using eigen values and calculating the angles ang1 & ang2 as below.

clear all; clc;
Ix0 = 1.3562e+08;
Iy0 = 3.3113e+06;
Ixy0 = 2.9802e-07;

I = [ Ix0  -Ixy0 ;
     -Ixy0   Iy0 ];
[ eig_vec, eig_val ] = eig(I);
I1 = eig_val(1,1);
I2 = eig_val(2,2);
ang1 = atan2( eig_vec(2,1), eig_vec(1,1) );
ang2 = atan2( eig_vec(2,2), eig_vec(1,2) );
ang1_d = ang1*180/pi;
ang2_d = ang2*180/pi;
ang1_ = mod(abs(ang1_d), 90);
ang2_ = mod(abs(ang2_d), 90)

ang2_ =

   90.0000

ang2_ = mod(abs(ang2_d), 90) shoud be ~= 0, but it is not. What's wrong in here?

Answer 1

[Steven Lord]

First, if you want angles in degrees use atan2d directly.

But as for what you're seeing with ang2_ being 90.0000? Your angle is not exactly ninety but is very slightly less than ninety, small enough that mod(..., 90) returns the number itself but close enough that to four decimal places it is 90.0000. See how far away it is from ninety.

difference = 90-ang2_

The value of difference will not be 0, but it will be a very small number.

[Baha411]

Thanks for your answer. Yeah very close

vpa(90-ang2_)
ans =
0.00000000000014210854715202003717422485351562

I use both radian and degrees in my code.

I am trying to determine if the mod 90 of those angles are very close to zero.

For that, is there any other way than this code below?

ang1_01 = mod(abs(ang1_d), 90);
ang1_02 = mod(90-abs(ang1_d), 90);
ang2_01 = mod(abs(ang2_d), 90);
ang2_02 = mod(90-abs(ang2_d), 90);
%%% 
if ang1_01<1e-3 || ang1_02<1e-3 || ang2_01<1e-3 || ang2_02<1e-3
disp('yes');
else
disp('no');
end