IIRC in another question, your said your Point class actually uses float x,y; for the coordinates. So one thing that can help is to shift the centers (the "zeros") over to the edge of the pixel, like:
int xi = pt.x + 0.5;
int yi = pt.y + 0.5;
And use those integers in calls the GLUT line drawing api.
I think this change would go inside your drawLine() function.