%!

% - procedures -------------------------------------

/pi 3.141593 def

% t in radians ==> [cos(t) -sin(t)] = [y(t) y'(t)]

/cosine {
4 dict begin
/t exch def
% change to degrees 
/T t 180 mul pi div def
[
T cos
T sin neg
]
end
} def

% - picture ----------------------------------------

gsave

% change scale to inches
72 dup scale
1 1 translate
0.01 setlinewidth

% centre the coordinates
3.25 1.5 translate

% for magnification:
1 1 scale

% - put in the grid -----------------------------

/top 1.5 def
/bottom -1.5 def
/left -3.25 def
/right 3.25 def

newpath
1 0.75 0.75 setrgbcolor
% 0.5 setgray
/x -3.2 def
65 {
x bottom moveto
x top lineto
/x x 0.1 add def
} repeat

/y -1.4 def
30 {
left y moveto
right y lineto
/y y 0.1 add def
} repeat
stroke

% - put in some axes ----------------------------

1 0 0 setrgbcolor
newpath
left 0 moveto
right 0 lineto
0 bottom moveto
0 top lineto
stroke

% - now do the graph --------------------------

% try once with 2 curves ----------------------

% choose the number of Bezier curves
/N 2 def
/t pi neg def
% set the step size
/h 2 pi mul N div def

0 1 0 setrgbcolor
newpath
% start the graph
/x t def
t cosine aload pop
/slope exch def
/y exch def
x y moveto
N {
% x1 y1 
x h 3 div add 
y h 3 div slope mul add

/t t h add def
/x t def
t cosine aload pop
/slope exch def
/y exch def
% x2 y2
x h 3 div sub 
y h 3 div slope mul sub
% x3 y3
x y
curveto
} repeat
stroke

% choose again the number of Bezier curves
/N 4 def
/t pi neg def
% set the step size
/h 2 pi mul N div def

0 0 1 setrgbcolor
newpath
% start the graph
/x t def
t cosine aload pop
/slope exch def
/y exch def
x y moveto
N {
% x1 y1 
x h 3 div add 
y h 3 div slope mul add

/t t h add def
/x t def
t cosine aload pop
/slope exch def
/y exch def
% x2 y2
x h 3 div sub 
y h 3 div slope mul sub
% x3 y3
x y
curveto
} repeat
stroke

% try again with 4 curves ----------------------

0 setgray
% choose the number of Bezier curves
/N 8 def
/t pi neg def
% set the step size
/h 2 pi mul N div def

newpath
% start the graph
/x t def
t cosine aload pop
/slope exch def
/y exch def
x y moveto
N {
% x1 y1 
x h 3 div add 
y h 3 div slope mul add

/t t h add def
/x t def
t cosine aload pop
/slope exch def
/y exch def
% x2 y2
x h 3 div sub 
y h 3 div slope mul sub
% x3 y3
x y
curveto
} repeat
stroke

% draw the box and clip to it
newpath
-3.25 -1.5 moveto
6.5 0 rlineto
0 3 rlineto
-6.5 0 rlineto
closepath
stroke

grestore

showpage

gsave

% change scale to inches
72 dup scale
1 1 translate
0.01 setlinewidth

% centre the coordinates
3.25 1.5 translate

% for magnification:
4 4 scale

% - put in the grid -----------------------------

/top 1.5 def
/bottom -1.5 def
/left -3.25 def
/right 3.25 def

newpath
1 0.75 0.75 setrgbcolor
% 0.5 setgray
/x -3.2 def
65 {
x bottom moveto
x top lineto
/x x 0.1 add def
} repeat

/y -1.4 def
30 {
left y moveto
right y lineto
/y y 0.1 add def
} repeat
stroke

% - put in some axes ----------------------------

1 0 0 setrgbcolor
newpath
left 0 moveto
right 0 lineto
0 bottom moveto
0 top lineto
stroke

% - now do the graph --------------------------

% try once with 2 curves ----------------------

% choose the number of Bezier curves
/N 2 def
/t pi neg def
% set the step size
/h 2 pi mul N div def

0 1 0 setrgbcolor
newpath
% start the graph
/x t def
t cosine aload pop
/slope exch def
/y exch def
x y moveto
N {
% x1 y1 
x h 3 div add 
y h 3 div slope mul add

/t t h add def
/x t def
t cosine aload pop
/slope exch def
/y exch def
% x2 y2
x h 3 div sub 
y h 3 div slope mul sub
% x3 y3
x y
curveto
} repeat
stroke

% choose again the number of Bezier curves
/N 4 def
/t pi neg def
% set the step size
/h 2 pi mul N div def

0 0 1 setrgbcolor
newpath
% start the graph
/x t def
t cosine aload pop
/slope exch def
/y exch def
x y moveto
N {
% x1 y1 
x h 3 div add 
y h 3 div slope mul add

/t t h add def
/x t def
t cosine aload pop
/slope exch def
/y exch def
% x2 y2
x h 3 div sub 
y h 3 div slope mul sub
% x3 y3
x y
curveto
} repeat
stroke

% try again with 4 curves ----------------------

0 setgray
% choose the number of Bezier curves
/N 8 def
/t pi neg def
% set the step size
/h 2 pi mul N div def

newpath
% start the graph
/x t def
t cosine aload pop
/slope exch def
/y exch def
x y moveto
N {
% x1 y1 
x h 3 div add 
y h 3 div slope mul add

/t t h add def
/x t def
t cosine aload pop
/slope exch def
/y exch def
% x2 y2
x h 3 div sub 
y h 3 div slope mul sub
% x3 y3
x y
curveto
} repeat
stroke

% draw the box and clip to it
newpath
-3.25 -1.5 moveto
6.5 0 rlineto
0 3 rlineto
-6.5 0 rlineto
closepath
stroke

grestore

showpage