electrostatics.py 文件源码

def line(self, x0):
        """Returns the field line passing through x0.
        Refs: http://folk.uib.no/fcihh/seminar/lec1.pdf and lect2.pdf
              http://numbercrunch.de/blog/2013/05/visualizing-streamlines/
        and especially: "Electric field lines don't work",
        http://scitation.aip.org/content/aapt/journal/ajp/64/6/10.1119/1.18237
        """

        if None in [XMIN, XMAX, YMIN, YMAX]:
            raise ValueError('Domain must be set using init().')

        # Set up integrator for the field line
        streamline = lambda t, y: list(self.direction(y))
        solver = ode(streamline).set_integrator('vode')

        # Initialize the coordinate lists
        x = [x0]

        # Integrate in both the forward and backward directions
        dt = 0.008

        # Solve in both the forward and reverse directions
        for sign in [1, -1]:

            # Set the starting coordinates and time
            solver.set_initial_value(x0, 0)

            # Integrate field line over successive time steps
            while solver.successful():

                # Find the next step
                solver.integrate(solver.t + sign*dt)

                # Save the coordinates
                if sign > 0:
                    x.append(solver.y)
                else:
                    x.insert(0, solver.y)

                # Check if line connects to a charge
                flag = False
                for c in self.charges:
                    if c.is_close(solver.y):
                        flag = True
                        break

                # Terminate line at charge or if it leaves the area of interest
                if flag or not (XMIN < solver.y[0] < XMAX) or \
                  not YMIN < solver.y[1] < YMAX:
                    break

        return FieldLine(x)