MuPAD Pro Computing Essentials - Examples 

Example 7.11 - Plotting in spherical coordinates

Let us consider a family of surfaces in spherical coordinates: 

For various values of a and b we can obtain quite interesting surfaces similar to sea shells. Let us plot one of them.

export(plot, spherical):
h:=(x,y,z)->[abs(sin(x)),abs(sin(y)),abs(sin(z))]:
 
B:=3:
 
shell:=spherical(
   [(1.3^(phi))*sin(B*theta),phi,theta],
   phi=-1..2*PI, theta=0..PI,
   Grid = [30,30],
   Style = [ColorPatches, AndMesh],
   Color = [Function,h]
):
 
plot(
   shell,
   Scaling=Constrained,
   BackGround=[0.8,0.8,1],
   CameraPoint=[100,70,20],
   FocalPoint=[0,0,0],
   ViewingBox=Automatic,
   Axes=None
)

Try the same program for different values of B, e.g. B=1, 2, 4, 5, ....