A00_basic_engine2.txt

# Filename: A00_basic_engine.py
# Author: James D. Miller; Gustavus Adolphus College.

import time, sys, textwrap
from timeit import default_timer

def px_from_m( x_m):
    return int(round( x_m * env['m_to_px']))
        
def move( car):
    v_i = car['v_mps']
    car['v_mps'] +=  car['a_mps2'] * dt_s
    
    if env['exact_solution']:
        #car['x_m'] += ((v_i + car['v_mps'])/2.0)  * dt_s
        car['x_m'] += v_i * dt_s + (car['a_mps2'] * (dt_s ** 2.0))/2.0
    
    else:
        # Normal Euler's method (using v at the beginning of the frame).
        #car['x_m'] += v_i * dt_s
        
        # Backward Euler's method (using v at the end of the frame).
        car['x_m'] += car['v_mps'] * dt_s
    
def debug_print(name_string):
    # Print out the values for a set of global names contained in
    # a string and separated by commas.
    
    names = name_string.split(",")
    print_string = ''
    for name in names:
        print_string += name + ":" + str(eval(name)) + ", "
    print print_string

def dp(variable, variable_name):
    print variable_name + "=" + str(variable)
    
def x_corrected_exact( car, x_overlap):
    # Inputs are conditions at time of collision detection. These
    # values have signs. For example x_overlap is positive for penetration
    # on the right end of the track.    
    
    if (env['stickiness_correction']):
        
        x_coll_m = car['x_m']
        v_coll_mps = car['v_mps']
        
        # Determine the car state as it passes through the wall.
        # v_coll_mps**2 = v_wall_mps**2 + 2*a*x_overlap
        v_wall_mps = (v_coll_mps**2.0 - 2.0 * car['a_mps2'] * x_overlap)**0.5
        if track['collision_state'] == 'left':
            v_wall_mps = -1.0 * abs(v_wall_mps)
        
        # Might have to consider the case where it reverses direction during the
        # collision (at the top of the track).
                
        # The time expended penetrating the wall.
        # x_coll_m = x_wall_m + ((v_wall_mps + v_coll_mps)/2.0) * t_pen   
        t_pen = 2.0 * x_overlap/(v_wall_mps + v_coll_mps)
        
        # The distance covered bouncing back from the wall in time t_pen. Change
        # the sign (direction) of v_wall.
        v_wall_afterbounce_mps = v_wall_mps * -1.0 * env['CR']
        x_bounce_pen = v_wall_afterbounce_mps * t_pen + (car['a_mps2'] * t_pen**2.0)/2.0
        if track['collision_state'] == 'left':
            if x_bounce_pen < 0.0: x_bounce_pen = 0.0
        else:
            if x_bounce_pen > 0.0: x_bounce_pen = 0.0
        
        # The corrected position, that is, where it would be if it had bounced off the wall.
        car['x_m'] = (x_coll_m - x_overlap) + x_bounce_pen
        
        # Also need to determine the velocity at the corrected position.
        car['v_mps'] = v_wall_afterbounce_mps + t_pen * car['a_mps2']
    
        if False:
            dp(x_coll_m, "x_coll_m")
            dp(v_coll_mps, "v_coll_mps")
            dp(t_pen, "t_pen")
            dp(v_wall_mps, "v_wall_mps")
            dp(v_wall_afterbounce_mps, "v_wall_afterbounce_mps")
            dp(x_bounce_pen, "x_bounce_pen")
            dp(car['x_m'], "car['x_m']")
            dp(car['v_mps'], "car['v_mps']")
        
    else:
        # If no position correction, simply reverse the direction of the car.
        car['v_mps'] *= -1.0 * env['CR']
    
def check_for_wall_collisions( car):
        
    # Check for a collision.
    if (car['x_m'] < track['left_edge_m']):
        x_overlap = car['x_m'] - track['left_edge_m']
        track['collision_state'] = 'left'

    elif (car['x_m'] > track['right_edge_m']): 
        x_overlap = car['x_m'] - track['right_edge_m']
        track['collision_state'] = 'right'
    
    else:
        track['collision_state'] = 'none'
                            
    # Resolve the collision.
    if track['collision_state'] != 'none':
        track['collision_mark_px'] = px_from_m( car['x_m'])
    
        if env['exact_solution']:
            x_corrected_exact( car, x_overlap)
        
        else:
            if (env['stickiness_correction']):
            
                if (env['correction_version_2']):
                    # Move the car back to the surface and then an additional
                    # equal amount but reduced by the CR coefficient.
                    car['x_m'] -= x_overlap * (1 + env['CR'])
                
                else:
                    # Simple stickiness correction. Move it back by the amount of the overlap.
                    # This puts the car at the surface.
                    if track['collision_state'] == 'left': 
                        car['x_m'] = track['left_edge_m']
                    else:
                        car['x_m'] = track['right_edge_m']
                    
            # loss of (1-CR)*100% on each bounce.
            car['v_mps'] *= -1 * env['CR']  
    
    else:
        track['collision_mark_px'] = -999

def build_airtrack_string( car):
    left_edge_px  = px_from_m( track['left_edge_m'])
    right_edge_px = px_from_m( track['right_edge_m'])
    display_width_px = 135
    car_location_px = px_from_m( car['x_m'])
    
    string = ''
    for j in range(0, display_width_px + 1):
        if (j == car_location_px):
            string += '*'
        elif (j == left_edge_px) or (j == right_edge_px):
            string += '|'
        elif (track['show_start_mark'] and (j == track['track_mark_px'])):
            string += "."
        elif (track['show_collision_mark'] and (j == track['collision_mark_px'])):
            string += "0"
        else:
            string += ' '
    return string            
            
def render( car):   
    display_string = build_airtrack_string( car)
    if cl['details']:
        print display_string + 'x=' + "%6.3f" % car['x_m'] + ', v=' + "% .2f" % car['v_mps'] + ", F=" + "%3.0f" % fps_observed
    else:
        print display_string

def pos_avg_10( car):
    x_list.append( car['x_m'])
    if len(x_list) > 10: x_list.pop(0)
    return sum(x_list)/float(len(x_list))
    
def pretty_paragraphs( text_string, n_blanklines):
    paragraph_list = text_string.split('||')
    for paragraph in paragraph_list:    
        dedented_text = textwrap.dedent( paragraph).strip()
        print textwrap.fill(dedented_text, initial_indent='    ', subsequent_indent=' ')
        print ""
    for j in range( n_blanklines): print "\n"
  
def print_delay( string):
    print string
    time.sleep( 0.10)
  
def try_sleep( seconds):
    # If you don't want to wait. Press control-c to break out of the sleep.
    try:
        time.sleep( seconds)
    except KeyboardInterrupt:
        print_delay("               *      ")
        print_delay("              * *     ")
        print_delay("             *   *    ")
        print_delay("              * *     ")
        print_delay("               *      ")
        print "\n\n\n"

def print_header(car):
    print "\n\n\n\n"
    print " Example #" + str(cl['example_index'])
    print " ---------------------"
    print " Initial x = " + str(car['x_m'])
    print " Initial v = " + str(car['v_mps'])
    print " a = " + str(car['a_mps2'])
    print " Coefficient of Restitution = " + str(env['CR'])
    print ""
    print " Stickiness correction = " + str(env['stickiness_correction'])
    if env['stickiness_correction'] and not env['exact_solution']:
        print " Correction (version 2) = " + str(env['correction_version_2'])
    print " Exact solution = " + str(env['exact_solution'])
    print " Use observed dt in next frame = " + str(env['use_observed_dt'])
    print ""
    print " Show starting mark (\".\") = " + str(track['show_start_mark'])
    print " Show collision mark (\"0\") = " + str(track['show_collision_mark'])
    print " Show physics-engine output = " + str(cl['details'])
    print ""
    print " FPS target = " + str(env['fps_target'])
    print " Auto-Off = " + str(env['auto_off'])
    print " Zoom (meters to px factor) = " + str(env['m_to_px'])
    print " "
        
def modify( car, env):
        
    if cl['example_index'] == 1:
        car['x_m'] = 2.0; car['v_mps'] = 0.0; car['a_mps2'] = -1.5
        track['show_collision_mark'] = False
        env['CR'] = 0.7

        print_header(car)
        explaination = ''' 
        This first example has the car (represented by a "*") starting from rest and accelerating to the left. Stickiness
        correction is ON. There is energy loss (fractional reduction in v) after each wall collision.
        ||
        Control-s pauses (and restarts) the run. Control-s can be used to give additional time (pause) for reading the descriptions
        at the beginning. Control-c stops the run. Control-c can also be used to skip
        the reading-wait at the beginning.
        ||
        For starters, remember that this is 1-D motion! The history of this motion moves vertically, one step at a time,
        as the program renders each new single-line snapshot. An effective way to view this 1-D motion (animation) is to focus
        your attention at the bottom row. The YouTube video will provide some training wheels (an annotation rectangle) to help
        you do this. Another approach
        is to place a sheet of paper over everything on the screen except the bottom row.
        ||
        If the "d" option is given at the command line, the details of the physics calculation are printed with each
        frame. This outputs, position, velocity, and frame rate.
        '''
        pretty_paragraphs( explaination, 1) 
        try_sleep(5.0)
        
    elif cl['example_index'] == 2:
        car['x_m'] = 1.65; car['v_mps'] = 2.7; car['a_mps2'] =  0.0
        env['stickiness_correction'] = False
        track['show_collision_mark'] = False
        env['CR'] = 1.0
        
        print_header(car)
        explaination = ''' 
        Stickiness correction is turned off which allows the overlap (penetration) to be seen. These are
        elastic collisions (CR=1), meaning this will run until a keyboard stop or the loop counter hits its limit.
        ||
        Control-s pauses the run. Control-c stops the run.
        '''
        pretty_paragraphs( explaination, 1) 
        try_sleep(3.0)        
        
        
    elif cl['example_index'] == 3:
        car['x_m'] = 2.0; car['v_mps'] = 0.0; car['a_mps2'] = -1.5
        env['stickiness_correction'] = False
        track['show_collision_mark'] = False
        env['auto_off'] = False
        env['fps_target'] = 30
        env['CR'] = 0.6
        
        print_header(car)
        explaination = ''' 
        All parameters are identical to example 1 except that stickiness
        correction is OFF.
        ||
        Watch the wall collision. With stickiness correction turned off, the car will be allowed to render in the state of
        collision (on the other side of the wall). But with the first bounce, due to
        gravity and the collision-related energy losses, the car does not recover from the state of penetration (the car sticks to the wall),
        that is, the ball does not bounce back
        far enough to get back to the other side.
        This leads to a state of perpetual collisions,
        with gravity dragging the car to the left.
        ||
        Control-s pauses the run. Control-c stops the run.      
        '''
        pretty_paragraphs( explaination, 1) 
        try_sleep(4.0)        
        
    elif cl['example_index'] == 4:
        car['x_m'] = 0.2; car['v_mps'] = 10.0; car['a_mps2'] =  -10.0
        env['CR'] = 0.8
        env['fps_target'] = 300
        track['show_collision_mark'] = False

        print_header(car)
        explaination = ''' 
        The target frame rate is set high to give an interesting display of the time-series tail. The car
        loses speed from each
        wall collision. Acceleration (set high) to the left (negative).
        ||
        Control-s pauses the run. Control-c stops the run.
        '''
        pretty_paragraphs( explaination, 1) 
        try_sleep(3.0)        

        
    elif cl['example_index'] == 5:
        car['x_m'] = 2.0; car['v_mps'] = 3.0; car['a_mps2'] =  2.0
        env['CR'] = 0.7
        
        print_header(car)
        explaination = ''' 
        Acceleration is to the right (opposite direction from other examples).
        ||
        A collision mark (0) is displayed at the original collision position (before stickiness correction).
        ||
        Control-s pauses the run. Control-c stops the run.      
        '''
        pretty_paragraphs( explaination, 1) 
        try_sleep(3.0)        
        
    elif cl['example_index'] == 6:
        car['x_m'] = 2.0; car['v_mps'] = 3.0; car['a_mps2'] =  2.0
        env['CR'] = 0.7
        env['m_to_px'] = 30.0
        
        print_header(car)
        explaination = ''' 
        The scaling factor between the physics engine and the renderer has decreased from the level used in example 5.
        This effectively zooms out the view of the
        track and the car on it. The output from the physics engine is unchanged by this;
        all characteristics of the movement is identical to example 5.
        ||
        Control-s pauses the run. Control-c stops the run.
        '''
        pretty_paragraphs( explaination, 1) 
        try_sleep(3.0)   

    elif cl['example_index'] == 7:
        car['x_m'] = 2.0; car['v_mps'] = 0.0; car['a_mps2'] = -2.0
        env['CR'] = 1.0
        env['fps_target'] = 240
        track['show_start_mark'] = True
        
        print_header(car)
        explaination = '''
        The CR value of unity yields elastic collisions. The frame rate is set high so to give
        the highest precision in the physics predictions. Note the car consistently returns to the initial starting point
        as marked by the period symbol on the track.
        ||
        Control-s pauses the run. Control-c stops the run.    
        '''
        pretty_paragraphs( explaination, 1) 
        try_sleep(3.0)        
        
    elif cl['example_index'] == 8:
        car['x_m'] = 2.0; car['v_mps'] = 0.0; car['a_mps2'] = -2.0
        env['CR'] = 1.0
        env['fps_target'] = 10
        track['show_start_mark'] = True
        
        print_header(car)
        explaination = '''
        This is like the previous example (7), except the target frame rate is reduced to give
        the lower precision in the physics predictions.
        Note the car does NOT return to the initial starting point (as marked on the track by column of period symbols).
        ||
        The "0"s are very visible in this example. As mentioned before, these are marks to indicate the
        position of the car at the time of collision detection (before stickiness correction
        is applied to resolve the state of overlap).
        ||
        Control-s pauses the run. Control-c stops the run.    
        '''
        pretty_paragraphs( explaination, 1) 
        try_sleep(3.0)        
        
    elif cl['example_index'] == 9:
        car['x_m'] = 2.0; car['v_mps'] = 0.0; car['a_mps2'] = -2.0
        env['CR'] = 1.0
        env['fps_target'] = 10
        env['use_observed_dt'] = True
        track['show_start_mark'] = True
        
        print_header(car)
        explaination = '''
        The observed dt is used in the subsequent frame to calculate the
        physics engine motions.
        All other settings are identical to those in example 8.
        Note the car, again, does NOT return to the initial starting point (as marked on the track by column of period symbols).
        But here the return behavior is more variable.
        ||
        Control-s pauses the run. Control-c stops the run.    
        '''
        pretty_paragraphs( explaination, 1) 
        try_sleep(3.0)        
        
    elif cl['example_index'] == 10:
        car['x_m'] = 2.0; car['v_mps'] = 0.0; car['a_mps2'] = -2.0
        env['CR'] = 1.0
        env['fps_target'] = 10
        track['show_start_mark'] = True
        env['exact_solution'] = True
        
        print_header(car)
        explaination = '''
        The Euler-method calculation has been replaced
        with an exact calculation method in this example. The calculation uses physics kinematics equations
        to model the motion between the ends of the track and also the motion in the collision frames. The frame rate is set low to give
        the most severe test for this exact method. Note the car consistently returns to the initial starting point.
        ||
        Control-s pauses the run. Control-c stops the run.   
        '''
        pretty_paragraphs( explaination, 1) 
        try_sleep(3.0)        
        
    elif cl['example_index'] == 11:
        car['x_m'] = 2.0; car['v_mps'] = 0.0; car['a_mps2'] = -2.0
        env['CR'] = 1.0
        env['fps_target'] = 10
        track['show_start_mark'] = True
        env['exact_solution'] = True
        env['use_observed_dt'] = True
        
        print_header(car)
        explaination = '''
        The observed dt is used in subsequent frames. Note that in contrast to example 9, the car consistently returns to the initial starting point.
        ||
        Control-s pauses the run. Control-c stops the run.   
        '''
        pretty_paragraphs( explaination, 1) 
        try_sleep(3.0)        
        
    elif cl['example_index'] == 12:
        car['x_m'] = 2.0; car['v_mps'] = 0.0; car['a_mps2'] = -2.0
        env['CR'] = 0.8
        env['fps_target'] = 10
        track['show_start_mark'] = True
        env['exact_solution'] = True
        env['use_observed_dt'] = True
        
        print_header(car)
        explaination = '''
        Same as example 11 but with a CR of less than 1.0.
        ||
        Control-s pauses the run. Control-c stops the run.    
        '''
        pretty_paragraphs( explaination, 1) 
        try_sleep(3.0)        
        
    else:
        cl['example_index'] = "--> Defaults"
        print_header(car)
        explaination = ''' 
        No command line arguments were supplied or there was no match for the mode value. Default parameters will be used.
        ||
        Control-s pauses the run. Control-c stops the run.
        '''
        pretty_paragraphs( explaination, 1) 
        try_sleep(3.0)
        
def at_rest( car):
    avg_car_position = pos_avg_10( car)
    rest_tolerance = 0.001
    if  ( (abs(avg_car_position - track['left_edge_m'])  < rest_tolerance) or
          (abs(avg_car_position - track['right_edge_m']) < rest_tolerance) ):
        return True
    else:
        return False
        
def cl_args_init():
    cl['n_args'] = len(sys.argv) - 1
    
    if cl['n_args'] >= 1:
        cl['example_index'] = int(sys.argv[1])
     
    cl['details'] = False     
    if cl['n_args'] == 2:
        if sys.argv[2] == "d":
            cl['details'] = True
    
def main():  
    global env, dt_s, track, fps_observed, x_list, cl
    
    # A list to support calculating a running average of the position.
    x_list = []
    
    # Initialize the general parameters that control the environment.
    env = {'stickiness_correction':True, 'correction_version_2':True ,
           'm_to_px':55.0, 'CR':0.80, 'auto_off':True, 'fps_target':30,
           'exact_solution':False, 'use_observed_dt':False}
    
    # Characteristics of the air track (the 1-D range of space that the car moves along).
    track = {'left_edge_m':0.25 , 'right_edge_m':2.2,
             'show_start_mark':False, 
             'collision_state':'none', 
             'collision_mark_px':-999, 'show_collision_mark':True}
    
    car = {'x_m':1.1, 'v_mps':0.0, 'a_mps2':0.0}

    # Use the command-line arguments if provided. Put them in a dictionary.
    cl = {'details':False, 'n_args':0}
    cl_args_init()
    
    # Modify the initial conditions for the car and environment if command line parameters 
    # were provided.
    if (cl['n_args'] > 0):
        modify( car, env)  
    
    fps_observed = env['fps_target']
    dt_target_s = 1.0/env['fps_target']
    dt_s = dt_target_s
    dt_observed_s = dt_target_s
    
    # A mark on the track where the car started at (optionally displayed)
    track['track_mark_px'] = px_from_m(car['x_m'])
    
    t_now_s = default_timer()
    
    for j in range( 50000):
        try:        
            t_previous_s = t_now_s
            
            if (dt_observed_s < 0.15):
                move( car)
                check_for_wall_collisions( car)
                render( car)
            
            if env['auto_off']:
                if at_rest( car):
                    break
          
            time.sleep( dt_target_s)
            
            t_now_s = default_timer()
            dt_observed_s = t_now_s - t_previous_s
            
            if env['use_observed_dt']:
                dt_s = dt_observed_s
            fps_observed = 1/dt_observed_s
        
        except KeyboardInterrupt:
            # You pressed control-c.
            print "Stopped by keyboard."
            break
        
        except:
            print "There is a problem in the TRY block above: \n"
            # The following "raise" will print out the traceback.
            raise
            break
            
main()