8.21.2  Animation of a 3D graph: animate3d

The animate3d command creates three-dimensional animations using graphs of functions depending on a parameter. (See also Section 8.4.2.)

• animate takes three mandatory arguments and two optional arguments:
  • expr, an expression involving three variables, one of which will be regarded as the parameter.
  • vars a list of the the (non-parameter) variables in the expression, which can also specify ranges of values var=a..b.
  • param the name of the parameter, which can also specify a range of values.
  • Optionally, frames=n, where n is an integer specifying the number of frames.
  • Optionally, xstep, which can be xstep=n to specify the discretization step in the x direction.
  • Optionally, ystep, which can be ystep=m to specify the discretization step in the y direction.
  • Instead of xstep and ystep, you could use the option nstep=n to specify the number of points used to graph.
• animate3d(expr,vars,param,frames=n ⟨opt,xstep=n, ystep=m ⟩) draws an animation consisting of graph of the function as the parameter varies.

Example.
Input:

Output:
The output is an animation beginning with: