File:Transmission line pulse reflections.gif

"""
(C) Steven Byrnes, 2014-2016. This code is released under the MIT license
http://opensource.org/licenses/MIT

This code runs in Python 2.7 or 3.3. It requires imagemagick to be installed;
that's how it assembles images into animated GIFs.
"""

# Use Python 3 style division: a/b is real division, a//b is integer division
from __future__ import division

import subprocess, os
directory_now = os.path.dirname(os.path.realpath(__file__))

import pygame as pg
from numpy import linspace
from math import erf, exp

frames_in_anim = 240
animation_loop_seconds = 12 #time in seconds for animation to loop one cycle

bgcolor = (255,255,255) #background is white
ecolor = (0,0,0) #electrons are black
wire_color = (200,200,200) # wire color is light gray
split_line_color = (0,0,0) #line down the middle is black
arrow_color = (140,0,0)

# pygame draws pixel-art, not smoothed. Therefore I am drawing it
# bigger, then smoothly shrinking it down

img_height = 330
img_width = 900

final_height = 110
final_width = 300

# ~23 megapixel limit for wikipedia animated gifs
assert final_height * final_width * frames_in_anim < 22e6

# transmission line wire length and thickness, and y-coordinate of the top of
# each wire
tl_length = int(img_width * .9)
tl_thickness = 27
tl_open_top_y = 30
tl_open_bot_y = tl_open_top_y + 69
tl_short_top_y = 204
tl_short_bot_y = tl_short_top_y + 69

tl_open_center_y = int((tl_open_top_y + tl_open_bot_y + tl_thickness) / 2)
tl_short_center_y = int((tl_short_top_y + tl_short_bot_y + tl_thickness) / 2)

wavelength = 1.1 * tl_length

e_radius = 4

# dimensions of triangular arrow head (this is for the longest arrows; it's
# scaled down when the arrow is too small)
arrowhead_base = 9
arrowhead_height = 15
# width of the arrow line
arrow_width = 6

# number of electrons spread out over the transmission line (top plus bottom)
num_electrons = 130
# max_e_displacement is defined here as a multiple of the total electron path length
# (roughly twice the width of the image, because we're adding top + bottom)
max_e_displacement = 0.0194

num_arrows = 30
max_arrow_halflength = 24

def tup_round(tup):
    """round each element of a tuple to nearest integer"""
    return tuple(int(round(x)) for x in tup)

def draw_arrow(surf, x, tail_y, head_y):
    """
    draw a vertical arrow. Coordinates do not need to be integers
    """
    # calculate dimensions of the triangle; it's scaled down for short arrows
    if abs(head_y - tail_y) >= 1.5 * arrowhead_height:
        h = arrowhead_height
        b = arrowhead_base
    else:
        h = abs(head_y - tail_y) / 1.5
        b = arrowhead_base * h / arrowhead_height

    if tail_y < head_y:
        # downward arrow
        triangle = [tup_round((x, head_y)),
                    tup_round((x - b, head_y - h)),
                    tup_round((x + b, head_y - h))]
        triangle_middle_y = head_y - h/2
    else:
        # upward arrow
        triangle = [tup_round((x, head_y)),
                    tup_round((x - b, head_y + h)),
                    tup_round((x + b, head_y + h))]
        triangle_middle_y = head_y + h/2
    pg.draw.line(surf, arrow_color, tup_round((x, tail_y)),
                 tup_round((x, triangle_middle_y)), arrow_width)
    pg.draw.polygon(surf, arrow_color, triangle, 0)

def pulse(c, t, open_or_short):
    """
    c is a coordinate, c=0 is the left side of the image, c=1 is the terminal
    t is time, with t=0 at the beginning of the animation, t=1 at the end
    This calculates two things:
     * Displacement of an electron in the top wire relative to its equilibrium
       position (i.e., integral of I(x,t') from t'=-infty to t'=t), in
       arbitrary units.
     * Charge on the top wire at that location, in arbitrary units.
    """
    assert c <= 1
    # We imagine that c>1 is a "mirror-world" beyond the terminal, which will
    # not be actually drawn. Then we can add up a leftward-traveling pulse and
    # a rightward-traveling pulse, using the superposition principle
    pulse_speed = 3
    pulse_width = 0.2
    if open_or_short == 'open':
        pulses = [{'center': 1 + pulse_speed * (t - 0.5), 'sign': +1},
                  {'center': 1 - pulse_speed * (t - 0.5), 'sign': +1}]
    else:
        pulses = [{'center': 1 + pulse_speed * (t - 0.5), 'sign': +1},
                  {'center': 1 - pulse_speed * (t - 0.5), 'sign': -1}]

    displacement = 0
    charge = 0
    for pulse in pulses:
        center, sign = pulse['center'], pulse['sign']
        displacement += erf((c - center) / pulse_width) * sign
        charge += exp(-(c - center)**2 / pulse_width**2) * sign
    return {'displacement': displacement, 'charge': charge/2}

def e_path_open(param, time):
    """
    "param" is an abstract coordinate that goes from 0 to 1 as the electron
    position goes right across the top wire then left across the bottom wire.
    "time" goes from 0 to 1 over the course of the animation.
    This returns a dictionary: 'pos' is (x,y), the
    coordinates of the corresponding point on the electron
    dot path; 'displacement' is the displacement of an electron at this point
    relative to its equilibrium position (between -1 and -1); and 'charge' is
    the net charge at this point (between -1 and +1)

    This is for the open-circuit line.
    """
    # d is a vertical offset between the electrons and the wires
    d = e_radius + 2
    # pad is how far to extend the transmission line beyond the image borders
    # (since those electrons may enter the image a bit)
    pad = 120
    path_length = 2 * (tl_length + pad)
    howfar = param * path_length

    #go right along top transmission line
    if howfar < tl_length + pad:
        x = howfar - pad
        y = tl_open_top_y + tl_thickness - d
        temp = pulse(x / tl_length, time, 'open')
        displacement = temp['displacement']
        charge = temp['charge']
        return {'pos':(x,y), 'displacement': displacement, 'charge': charge}

    #go left along bottom transmission line
    x = path_length - howfar - pad
    y = tl_open_bot_y + d
    temp = pulse(x / tl_length, time, 'open')
    displacement = temp['displacement']
    charge = -temp['charge']
    return {'pos':(x,y), 'displacement': displacement, 'charge': charge}

def e_path_short(param, time):
    """Same as e_path_open(...) above, but for the short-circuit line."""
    # d is a vertical offset between the electrons and the wires
    d = e_radius + 2
    # pad is how far to extend the transmission line beyond the image borders
    # (since those electrons may enter the image a bit)
    pad = 120
    path_length = (2 * (tl_length + pad) + 4*d
                   + (tl_short_bot_y - tl_short_top_y - tl_thickness))
    howfar = param * path_length

    #at the beginning, go right along top wire
    if howfar < tl_length + pad:
        x = howfar - pad
        y = tl_short_top_y + tl_thickness - d
        temp = pulse(x / tl_length, time, 'short')
        displacement = temp['displacement']
        charge = temp['charge']
        return {'pos':(x,y), 'displacement': displacement, 'charge': charge}

    #at the end, go left along bottom wire
    if (path_length - howfar) < tl_length + pad:
        x = path_length - howfar - pad
        y = tl_short_bot_y + d
        temp = pulse(x / tl_length, time, 'short')
        displacement = temp['displacement']
        charge = -temp['charge']
        return {'pos':(x,y), 'displacement': displacement, 'charge': charge}

    #in the middle...
    temp = pulse(1, time, 'short')
    charge = temp['charge']
    assert abs(charge) < 1e-9
    displacement = temp['displacement']

    #top part of short...
    if tl_length + pad < howfar < tl_length + pad + d:
        x = howfar - pad
        y = tl_short_top_y + tl_thickness - d
    #bottom part of short...
    elif tl_length + pad < (path_length - howfar) < tl_length + pad + d:
        x = path_length - howfar - pad
        y = tl_short_bot_y + d
    #vertical part of short...
    else:
        x = tl_length + d
        y = (tl_short_top_y + tl_thickness - d) + ((howfar-pad) - (tl_length + d))
    return {'pos': (x,y), 'displacement': displacement, 'charge': charge}

def e_path(param, time, which):
    return e_path_open(param, time) if which == 'open' else e_path_short(param, time)

def main():
    #Make and save a drawing for each frame
    filename_list = [os.path.join(directory_now, 'temp' + str(n) + '.png')
                         for n in range(frames_in_anim)]

    for frame in range(frames_in_anim):
        time = frame / frames_in_anim

        #initialize surface
        surf = pg.Surface((img_width,img_height))
        surf.fill(bgcolor);

        #draw transmission line
        pg.draw.rect(surf, wire_color, [0, tl_open_top_y, tl_length, tl_thickness])
        pg.draw.rect(surf, wire_color, [0, tl_open_bot_y, tl_length, tl_thickness])
        pg.draw.rect(surf, wire_color, [0, tl_short_top_y, tl_length, tl_thickness])
        pg.draw.rect(surf, wire_color, [0, tl_short_bot_y, tl_length, tl_thickness])
        pg.draw.rect(surf, wire_color, [tl_length,
                                        tl_short_top_y,
                                        tl_thickness,
                                        tl_short_bot_y - tl_short_top_y + tl_thickness])

        #draw line down the middle
        pg.draw.line(surf,split_line_color, (0,img_height//2),
                     (img_width,img_height//2), 12)

        #draw electrons. Remember, "param" is an abstract coordinate that goes
        #from 0 to 1 as the electron position goes right across the top wire
        #then left across the bottom wire
        equilibrium_params = linspace(0, 1, num=num_electrons)
        for which in ['open', 'short']:
            for eq_param in equilibrium_params:
                temp = e_path(eq_param, time, which)
                param_now = eq_param + max_e_displacement * temp['displacement']
                xy_now = e_path(param_now, time, which)['pos']
                pg.draw.circle(surf, ecolor, tup_round(xy_now), e_radius)

        #draw arrows
        arrow_params = linspace(0, 0.49, num=num_arrows)
        for which in ['open', 'short']:
            center_y = tl_open_center_y if which == 'open' else tl_short_center_y
            for i in range(len(arrow_params)):
                a = arrow_params[i]
                arrow_x = e_path(a, time, which)['pos'][0]
                charge = e_path(a, time, which)['charge']
                head_y = center_y + max_arrow_halflength * charge
                tail_y = center_y - max_arrow_halflength * charge
                draw_arrow(surf, arrow_x, tail_y, head_y)

        #shrink the surface to its final size, and save it
        shrunk_surface = pg.transform.smoothscale(surf, (final_width, final_height))
        pg.image.save(shrunk_surface, filename_list[frame])

    seconds_per_frame = animation_loop_seconds / frames_in_anim
    frame_delay = str(int(seconds_per_frame * 100))
    # Use the "convert" command (part of ImageMagick) to build the animation
    command_list = ['convert', '-delay', frame_delay, '-loop', '0'] + filename_list + ['anim.gif']
    subprocess.call(command_list, cwd=directory_now)
    # Earlier, we saved an image file for each frame of the animation. Now
    # that the animation is assembled, we can (optionally) delete those files
    if True:
        for filename in filename_list:
            os.remove(filename)

main()