fig01
  #                                                                           
  # Astronomy 505: Homework #3, Problem 1 (Ideal Ball-and-String Pendulum)    
  # 1 September, 2002                                                         
  # Nicole P. Vogt                                                            
  #                                                                           
  # This macro creates a diagram of a pendulum of length l which is held such 
  # that the string is horizontal (ready to drop).  There are four physical   
  # elements:                                                                 
  #                                                                           
  #   the ball   of the pendulum                                              
  #   the string of the pendulum, of length l (runs to center of ball)        
  #   the base point where the pendulum is secured, around which it rotates   
  #   a nail, located a distance d = 0.6 x l below the base point             
  #                                                                           
  # The path of the ball is traced out.  It falls in a circular arc of radius 
  # l for 90 degrees, and then the string catches on the nail.  The ball then 
  # traces out a second arc of radius (l - d), for an additional 155 degrees. 
  #                                                                           
  # The nail and the lengths l and d are labeled, and a dashed vertical line  
  # runs from the base point through the nail and down to the edge of the     
  # figure.  The ball, base point, and nail are filled with colour.           
  #                                                                           
  # n.b. The length l is written as R within the macro, for ease of reading.  
  #                                                                           
  macro read fig01.sm                # read macros into memory;  then type    
                                     # fig01 on sm command line to draw figure
 #dev postencap :SY :OFfig01.eps     # comment this line out to draw on screen
                                     # rather than writing postscript to /tmp 
  # 
  # Set up figure.  
  # 
  era
  ctype black  ptype 20 3  expand 0.901  ltype 0  # initialize drawing format
  set R = 100                                     # length of string
  set d =   R * 0.6                               # distance from base to nail
  set w =   R / 15                                # width of pendulum ball
  lim $(-1.15*R) $(0.50*R) $(-1.15*R) $(0.50*R)   # local coordinate limits - 
                                                  # keep figure a square, so 
                                                  # that circles are not oval
  # 
  # Draw arc of path of pendulum ball, starting at edge of ball.
  # 
  ltype 1                                         # dotted lines
  set r0 =  180 + 180/pi * atan(w/R)              # find edge of ball
  draw_circ   0    0        $(R)  $(r0) 270       # arc of radius  R
  draw_circ   0 $(-d)       $(R-d) 270   425      # arc of radius (R - d)
  relocate    0    0    draw    0 $(-1.15*R)      # line from base through nail
  # 
  # Draw labels and string
  # 
  ltype 0                                         # solid lines
  relocate    0    0    draw $(-R+w) 0            # string to edge of ball
  relocate    5    0    draw   15    0            # label string (ends)
  relocate    5 $(-d)   draw   15 $(-d)
  relocate    0   10    draw    0   20            # label nail position (ends)
  relocate $(-R)  10    draw $(-R)  20
  # 
  # Draw ball (fill with yellow, edge with black).
  # 
  set a = 0, 2.1*pi, 0.01                         # use angular variable to 
  set x = -R + cos(a) * w                         # define x and y coordinates
  set y =  0 + sin(a) * w
  ctype yellow angle 45 shade 100 x y             # fill with yellow
  ctype black  angle  0 connect   x y             # edge with black
  # 
  # Draw base point (fill with blue, edge with black).
  # 
  set x =      cos(a) * w / 6
  set y =      sin(a) * w / 6
  ctype blue   angle 45 shade 100 x y
  ctype black  angle  0
  connect x y
  # 
  # Draw nail (fill with blue, edge with black).
  # 
  set x =      cos(a) * w / 3
  set y = -d + sin(a) * w / 3
  ctype blue   angle 45 shade 100 x y
  ctype black  angle  0
  connect x y
  # 
  # Label figure elements.
  # 
  expand 1.501  label_arrow  $(-R)  15   0  15 15 "l"
  expand 1.501  label_arrow2   10 $(-d) 10   0 15 "d"
  expand 1.501  relocate  -5 $(-d)  putlabel 4 Nail
  # 
  # Return to screen display, if creating postscript figure.
  # 
  dev x11

draw_circ 5
  # 
  # Draw circle at ($1,$2) of radius ($3) between angles ($4) to ($5), 
  # input in degrees.  
  # 
  set i = $4*pi/180, $5*pi/180, 0.001   # supermongo works in radians
  set x = $1 + $3*cos(i)
  set y = $2 + $3*sin(i)
  connect x y

draw_circle 8
  # 
  # Draw circle at ($1,$2) of radius ($3) between angles ($4) to ($5), 
  # input in degrees.  Align label at midpoint of arc,  with offsets 
  # ($6,$7) and content ($8).
  # 
  draw_circ $1 $2 $3 $4 $5
  relocate $(x[dimen(x)/2] + $6) $(y[dimen(y)/2] + $7)
  putlabel 5 $8

label_arrow 6
  # 
  # Draw a two-headed horizontal arrow from ($1,$2) to ($3,$4).
  # Form a gap at the center of width ($5) to place label ($6).
  # 
  set _x1 = ($1 + $3)/2
  set _y1 = ($2 + $4)/2
  relocate $(_x1) $(_y1) putlabel 5 $6
  expand 0.601
  draw_arrow $(($1 + $3)/2 - $5/2) $(_y1) $1 $2
  draw_arrow $(($1 + $3)/2 + $5/2) $(_y1) $3 $4

label_arrow2 6
  # 
  # Draw a two-headed vertical arrow from ($1,$2) to ($3,$4).
  # Form a gap at the center of width ($5) to place label ($6).
  # 
  set _x1 = ($1 + $3)/2
  set _y1 = ($2 + $4)/2
  relocate $(_x1) $(_y1) putlabel 5 $6
  expand 0.601
  draw_arrow $(_x1) $(($2 + $4)/2 - $5/2) $1 $2
  draw_arrow $(_x1) $(($2 + $4)/2 + $5/2) $3 $4