This is documentation for Mathematica 3, which was
based on an earlier version of the Wolfram Language.
View current documentation (Version 11.2)
 Documentation / Mathematica / Add-ons / Standard Packages / Graphics  /


ParametricPlot3D is a built-in function for producing three-dimensional space curves and surfaces, parameterized by one or two coordinates respectively. The option PlotPoints allows you to specify the number of sample points used. This package extends ParametricPlot3D by providing an alternative to the PlotPoints option where the sampling may be specified by giving a step size in each coordinate. The package also introduces PointParametricPlot3D for plotting either one- or two-parameter sets of points in space.

Parametric plots in three dimensions.

  • This loads the package.
  • In[1]:= <<Graphics`ParametricPlot3D`

  • This gives the plot of a sphere using a mesh of long, thin rectangles.
  • In[2]:= ParametricPlot3D[
    {Cos[u] Cos[v], Sin[u] Cos[v], Sin[v]},
    {u, 0, 2Pi, Pi/20},
    {v, -Pi/2, Pi/2, Pi/10}]

  • Only a collection of points is shown when you use PointParametricPlot3D.
  • In[3]:= PointParametricPlot3D[
    {Cos[u] Cos[v], Sin[u] Cos[v], Sin[v]},
    {u, 0, 2Pi }, {v, -Pi/2, Pi/2 }]

    CylindricalPlot3D and SphericalPlot3D plot functions given in cylindrical and spherical coordinates, respectively. The names given to the variables in spherical coordinates vary in the literature. The convention used here is that the angle theta is measured from the positive axis, and the angle phi is measured in the plane from the positive


    Functions for plotting in three dimensions.

  • Here is a sphere of radius 2. It is very simple to represent in spherical coordinates.
  • In[4]:= SphericalPlot3D[ 2,
    {theta, 0, Pi}, {phi, 0, 2Pi}]

  • In this plot the height is given by (1+Sin[phi])r^2. Polar coordinates are used in the plane.
  • In[5]:= CylindricalPlot3D[ (1 + Sin[phi]) r^2,
    {r, 0, 1}, {phi, 0, 2Pi}]

  • You can use any option that can be given for Graphics3D.
  • In[6]:= CylindricalPlot3D[ (1 + Sin[phi]) r^2,
    {r, 0, 1}, {phi, 0, 2Pi},
    Boxed -> False, Axes -> False,
    ViewPoint -> {1.5, -0.5, .2}]