ParametricPlot3D
 Usage
• ParametricPlot3D[{ ,  ,  }, {u,  ,  }] produces a three-dimensional space curve parametrized by a variable u which runs from  to  .
• ParametricPlot3D[{ ,  ,  }, {u,  ,  }, {v,  ,  }] produces a three-dimensional surface parametrized by u and v.
• ParametricPlot3D[{ ,  ,  , s}, ... ] shades the plot according to the color specification s.
• ParametricPlot3D[{{ ,  ,  }, { ,  ,  }, ... }, ... ] plots several objects together.
Notes
• ParametricPlot3D evaluates its arguments in a non-standard way (see Section A.4.2). You should use Evaluate to evaluate the function to be plotted if this can safely be done before specific numerical values are supplied. • At positions where the  etc. do not evaluate to real numbers, holes are left in surfaces. • ParametricPlot3D has the same options as Graphics3D, with the following additions:
| Compiled | True | whether to compile the function to plot | | PlotPoints | Automatic | the number of sample points for each parameter |
• ParametricPlot3D has the default option setting Axes -> True. • With the default setting PlotPoints -> Automatic, ParametricPlot3D uses PlotPoints -> 75 for curves and PlotPoints -> {30, 30} for surfaces. • ParametricPlot3D returns a Graphics3D object. • New in Version 2.
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