# 3D implicit surface

### 7.13.2 3D implicit surface

For an implicit plot in ℝ2:

- plotimplicit takes four mandatory arguments and three optional arguments:
  - expr, an expression of three variables implicitly defining a curve by expr=0.
  - xvar, yvar and zvar, the first, second and third variables,optionally with their ranges var=a..b.
  - 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.
  - Optionally, zstep, which can be zstep=p to specify the discretization step in the y direction.
  - Optionally, unfactored.
- plotimplicity(expr,xvar,yvar,zvar ⟨xstep,ystep,zstepunfactored⟩) draws the graphic representation of the surface defined by the implicit equation expr=0 over the given ranges of the variables.

#### Examples.

- Input:
  plotimplicit(x^2+y^2+z^2-1,x,y,z, xstep=0.2,ystep=0.1,zstep=0.3)
  or:
  plotimplicit(x^2+y^2+z^2-1,x,y,z, xstep=0.2,ystep=0.1,zstep=0.3,unfactored)
  Output:
- Input:
  plotimplicit(x^2+y^2+z^2-1,x=-1..1,y=-1..1,z=-1..1)
  Output: