Avoiding drift while creating angular rotation with variable degree increments

Hello,

With the following code, I am trying to create a variable "deg" which should have small degree increments (ddeg_min) for deg<=angle and large increments (ddeg_max) for rest of a complete revolution. I want to repeat the same increments after completion of each revolution. For example, the increment should be 0.1 for 0<=deg<=16.0 and it should repeat the same thing after 360 degrees i.e. incr should be 0.1 for 360.1<=deg<=316.0. But, I am getting a drift in values e.g. 16.1 for first revolution and 366.1 for next revolution and so on.

It was hard to explain but I tried to make it as comprehendible as possible. Waiting for your kind suggestions, Thx.

close all
clear all
clc
phi=90;
angle=16;
ddeg_min=0.1; 
ddeg_max=10; 
deg(1)=0;
d_deg(1)=ddeg_min;
i=1; 
while (1)
    i=i+1;
    revol_n=floor(deg(i-1)/360);
    kkk=deg(i-1)-revol_n*360;
    if (kkk >= 0 && kkk < angle)
        d_deg(i)=ddeg_min;
        deg(i)=deg(i-1)+d_deg(i);
    else
        d_deg(i)=ddeg_max;
        deg(i)=deg(i-1)+d_deg(i);
    end
    if deg(i)>=1070
        break
    end
end

Answer 1

[Jan]

Let's start with a simplification of the code:

phi      = 90;
angle    = 16;
ddeg_min = 0.1; 
ddeg_max = 10; 
deg(1)   = 0;
d_deg(1) = ddeg_min;
i        = 1; 
while deg(i) < 1070
    kkk = rem(deg(i), 360);
    if kkk < angle
        deg(i + 1) = deg(i) + ddeg_min;
    else
        deg(i + 1) = deg(i) + ddeg_max;
    end
    i = i + 1;
end

Or:

phi   = 90;
angle = 16;
ddeg  = [0.1, 10];
deg   = 0;
i     = 1; 
while deg(i) < 1070
    deg(i + 1) = deg(i) + ddeg(1 + rem(deg(i), 360) < angle);
    i = i + 1;
end

What is the problem now?

"the increment should be 0.1 for 0<=deg<=16.0"

"I am getting a drift in values e.g. 16.1"

Yes, of course. Welcome to the world of numerical maths.

0.1 + 0.1 + 0.1 == 0.3   % FALSE !!!
0.1 + 0.1 + 0.1 - 0.3    % This is 5.551115123125783e-17

Most floating point values cannot be represented accurately as binary numbers. Therefore you have to consider a rounding effekt. Your loop does not stop at the wanted value, because it does not reach 16, but 15.99999999999996. This must be considered either by using a specific range:

if abs(kkk - angle) < 100 * eps(angle)

But in ypour case it is easier to create the output by a constructive apporach:

deg = [0:0.1:16, 26:10:360];
deg = [deg, deg + 360, deg + 720];
deg = deg(deg < 1070);

[Waseem Akhtar]

@Jan Thank you for your reply. I think you got to the root of the problem!

The constructive appraoch you gave seems simple and better. I am trying to implement it for the real case in which I have four 90 degree intervals of small increments in each revoltion i.e. 0:0.1:16, 90:0.1:106, 180:0.1:196 and 270:0.1:286

At the same time, I would love to know how this problem can be addressed the other way i.e. by controling the numerical variations (as you highlighted). It would be great if you could correct my code. tbh I'm not a computational expert, I would like to learn handling such situations.

Thank you once again!

Answer 2

[Mathieu NOE]

hello

why make things so complicated ?

this way you can generate the pattern for the first revolution . if you want to have it for multiple revolutions simply add 360 for each rev

close all
clear all
clc
phi=90;
angle=16;
ddeg_min=0.1; 
ddeg_max=10; 

% one revolution pattern
deg1 = (0:ddeg_min:angle);
deg2 = (angle+ddeg_max:ddeg_max:360);
deg = [deg1 deg2];

[Waseem Akhtar]

@Mathieu NOE Thanks for your answer.

In actual, there would be more than 1 intervals of small increments in each revolution e.g. 4 at 0,90,180 and 270. I am looking for a generalized approach, I'm not sure if it can be better than this one.

Thanks once again!

[Mathieu NOE]

hello

you mean in the 0 - 360 range there would be 4 sectors with low increment and 4 sectors with large increment ?

this can be easily adapted using my code example

[Waseem Akhtar]

Yes exactly. Also, I want to keep it generalized i.e. the code should accept the number of sectors as an input.

Thank you.

[Mathieu NOE]

as simple as this :

ddeg_min=0.1; 
ddeg_max=10; 

start_points = [0 90 180 270];
angle=16;   % angular amplitude for refined resolution


deg = [];
% one revolution pattern
sectors = length(start_points);
for ci = 1:sectors
    deg_fine = (start_points(ci):ddeg_min:start_points(ci)+angle);
    if ci <= sectors-1
        deg_coarse = (start_points(ci)+angle:ddeg_max:start_points(ci+1));
    else % last sector (xx to 360)
        deg_coarse = (start_points(ci)+angle:ddeg_max:360);
    end
    tmp = unique([deg_fine deg_coarse]); % remove duplicates
    deg = [deg tmp]; % concatenate results for all sectors
end

plot(deg)
    

[Waseem Akhtar]

@Mathieu NOE that's great, thank you!

[Mathieu NOE]

My pleasure !