Animation of a 3D graph: animate3d

### 7.21.2 Animation of a 3D graph: animate3d

The animate3d command creates three-dimensional animations using graphs of functions depending on a parameter. (See also Section 7.4.2.)

- 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:

animate3d(x^2+a*y^2,[x=-2..2,y=-2..2],a=-2..2, frames=10,display=red+filled)

Output:
The output is an animation beginning with: