can any body find the mistake here? I am rotating the coordinates of the arc and then bringing it to its original position. but it is not coming back to its original position ????!!!!

clear, clc

% the  arc coordinates
a=2:0.001:3;
b=sqrt((16-a.^2));

plot(a,b,'k')
axis equal 
grid on
hold on 


% the new coordinate axis  origin and rotating angle from the first
% coordinate

x_origin= 1;
y_origin= 1;

rot_angle= -45;

% 1- calculating the coordinate of the arc according to the new coordinates
% translating
a11=a-x_origin;
b11=b-y_origin;

% rotating
a1=a.*cosd(-1*rot_angle)-b.*sind(-1*rot_angle);
b1=a.*sind(-1*rot_angle)+b.*cosd(-1*rot_angle);

plot(a1,b1,'r')

% 2- re_transformating the axis to the first one
% rotating
a22=a1.*cosd(rot_angle)-b1.*sind(rot_angle);
b22=a1.*sind(rot_angle)+b1.*cosd(rot_angle);

% translating
a2=a22+x_origin;
b2=b22+y_origin;


plot(a2,b2,'--g')

Answer 1

[Matt J]

Some observations,

1. You never use a11,b11 anywhere.
2. After rotating back, you perform a translation by x_origin, y_origin. In other words, it did come back to its original position, but then you shifted it.

[nezir elali]

Dear Matt j

thanks for your answer.

I noticed that after I submitted the question ..... when I was very sleepy and tired ..... and barely I could hold my eyes open..... really, I solved this small problem ..... here is the codes:

clear, clc

% the main arc coordinates

a=2:0.001:3;

b=sqrt((16-a.^2));

plot(a,b,'k')

axis equal

grid on

hold on

% the new coordinate axis origin and rotating angle from the first

% coordinate

x_origin= 1;

y_origin= 1;

rot_angle= -45;

% 1- calculating the coordinate of the arc according to the new coordinates

% translating

a11=a-x_origin;

b11=b-y_origin;

% rotating

a1=a11.*cosd(-1*rot_angle)-b11.*sind(-1*rot_angle);

b1=a11.*sind(-1*rot_angle)+b11.*cosd(-1*rot_angle);

plot(a1,b1,'r')

% 2- re_transformating the axis to the first one

% rotating

a22=a1.*cosd(rot_angle)-b1.*sind(rot_angle);

b22=a1.*sind(rot_angle)+b1.*cosd(rot_angle);

% translating

a2=a22+x_origin;

b2=b22+y_origin;

plot(a2,b2,'o')