FIRST you get the angle between white and blue (it does not matter which angle, the procedure is the same, you just have to adjust the rotation later on)
METHOD1:
create vectors using points belonging to either white or blue lines
vector1 = [x2,y2,0] - [x1,y1,0];
vector2 = [x3,y3,0] - [x1,y1,0];
Theta = atan2d(norm(cross(vector1, vector2)), dot(vector1, vector2));
METHOD2 (less robust):
poly1=polyfit(x_values_blue,y_values_blue,1); % get coefficient of line passing through the points you have in one line
x=-20:20; % or another range, doesn't matter
y1=poly1(1)*x+poly1(2); % calculate line based on the coefficients found
% repeat the same for the white line
poly2=polyfit(x_values_white,y_values_white,1);
y2=poly2(1)*x+poly2(2);
% here you have the two slopes, calculate the difference to get their angle
beta=atand(poly1(1));
theta=atand(poly2(1));
SECOND you need to create a rotated vector using the angle you just found (to create the red lines)
% define the x- and y-data for the original line we would like to rotate
x = L1_x_values;
y = L1_y_values;
% create a matrix of these points, which will be useful in future calculations
v = [x;y];
% choose a point which will be the center of rotation (in this case the
% origin)
x_center = 0;
y_center = 0;
% create a rotation matrix
center = repmat([x_center; y_center], 1, length(x));
% define a counter-clockwise rotation matrix
theta = Theta ; % the angle you found previously in degrees, using the first method
theta = theta ; % angle measured using the second method, just comment the one you won't use
R = [cos(theta) -sin(theta); sin(theta) cos(theta)];
% rotate
s = v - center; % shift points in the plane so that the center of rotation is at the origin
so = R*s; % apply the rotation about the origin
vo = so + center; % shift again so the origin goes back to the desired center of rotation
% pick out the vectors of rotated x- and y-data
x_rotated = vo(1,:);
y_rotated = vo(2,:);
