As far as I can see, quiver does not have the option to rotate about the midpoint. Would be a very useful addition though!
But it can be done manually. The trick is to turn off AutoScaling and then move the quivers to rotate around the midpoint.
This does mean that autoscaling is no longer used.
myfig = figure(123);
clf; hold all;
%%generate data
[x,y] = meshgrid(0:pi/2:9*pi, 0:pi/2:9*pi);
theta = 0.1*x; %theta = -0.1*x; for the second plot
theta_nematic = mod(theta,pi); %limit the angle to the interval 0 to pi
u=cos(theta_nematic); %for plotting, convert angle into components of a unit vector
v=sin(theta_nematic);
%% plot original quiver (rotated about endpoint)
myquiv= quiver(x,y,u,v);
myquiv.ShowArrowHead = 'off'; %to represent nematic orientation
myquiv.AutoScale = 'on'; % turn off autoscaling
myquiv.Color=[0.9 0.9 0.9];
%% plot modified quiver (rotated about midpoint)
% Quiver absolute size
ScaleF=2;
%calculate arrow starting points (when rotated about midpoint)
x_tail = x - ScaleF/2*cos(theta_nematic);
y_tail = y - ScaleF/2*sin(theta_nematic);
% scale quiver accordingly
u=ScaleF*u; %for plotting, convert angle into components of a unit vector
v=ScaleF*v;
myquiv= quiver(x_tail,y_tail,u,v,'b');
myquiv.ShowArrowHead = 'off'; %to represent nematic orientation
myquiv.AutoScale = 'off'; % turn off autoscaling
% plot midpoints
plot(x,y,'.r');
red: x,y points
grey: original quiver rotating about endpoint
blue: quivers rotating about midpoint
