> 
# Plotting a sphere     Math II    18 September 1996
# 
# 
# We plot a sphere x**2+y**2+z**2=1 in three different manners.
# 
--------------------------------------------------------------------------------
> with(plots):
--------------------------------------------------------------------------------
# First, we express z as a function of x and y
# The first argument in plot3d gives the value of z.
# We look at both the positive and negative values of z.
# Notice that we need to restrict the range of y to depend on x.
# 
> top:=plot3d(sqrt(1-x*x-y*y),x=-1..1,y=-sqrt(1-x*x)..sqrt(1-x*x),color=blue):
> bottom:=plot3d(-sqrt(1-x*x-y*y),x=-1..1,y=-sqrt(1-x*x)..sqrt(1-x*x),color=blue):
> display3d({top,bottom},title=`Sphere using z=...`);
--------------------------------------------------------------------------------
# 
# Now, we parametrize. We still use rectangular coordinates.
# 
> x1 := cos(t); y1:= sin(t)*sin(s); z1:= sin(t)*cos(s);

                                  x1 := cos(t)

                               y1 := sin(t) sin(s)

                               z1 := sin(t) cos(s)
--------------------------------------------------------------------------------
> plot3d([x1,y1,z1],t=0..2*Pi,s=0..Pi,title=`Sphere using parametrization`,color=blue);
--------------------------------------------------------------------------------
# 
# We now represent the sphere using spherical coordinates
# 
> sphereplot(1,theta=0..2*Pi,phi=0..Pi,title=`Plot in spherical coordinates`,color=blue);
--------------------------------------------------------------------------------
> \

# 
# Notice that the first representation is far worse than the other 
# two.
# 
# 
# 
# 
# 
# 
# 
# 
# 
--------------------------------------------------------------------------------
>