Animation of a 3D graph

### 19.10.2 Animation of a 3D graph

The animate3d command creates 3D animations using graphs of functions depending on a parameter. (See also Section 19.2.2.)

- 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

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

The output is an animation beginning with: