% Copyright The Numerical Algorithms Group Limited 1991.
% Certain derivative-work portions Copyright (C) 1988 by Leslie Lamport.
% All rights reserved

% Title: 3-D Graphics
 
% Address comments and questions to the
%   Computer Algebra Group, Mathematical Sciences Department
%   IBM Thomas J. Watson Research Center, Box 218
%   Yorktown Heights, New York  10598  USA
 
%  Author: Clifton J. Williamson
%  Date created: Memorial Day 1990
%  Date last updated: same
 
\begin{page}{ExPlot3DFunctions}{Plotting Functions of Two Variables}
\beginscroll
To plot a function {\em z = f(x,y)}, you need only specify the function and the
intervals over which the dependent variables will range.
For example, here's how you plot the function {\em z = cos(x*y)} as the 
variables {\em x} and {\em y} both range between -3 and 3:
\graphpaste{draw(cos(x*y),x = -3..3,y = -3..3)}
\endscroll
\autobuttons\end{page}
 
\begin{page}{ExPlot3DParametricSurface}{Plotting Parametric Surfaces}
\beginscroll
To plot a parametric surface defined by {\em x = f(u,v)}, 
{\em y = g(u,v)}, {\em z = h(u,v)}, specify the functions
{\em f(u,v)}, {\em g(u,v)}, and {\em h(u,v)}
as arguments of the function `surface', then give
the intervals over which {\em u} and {\em v} are to range.
With parametric surfaces, we can create some interesting graphs.
Here's an egg:
\graphpaste{draw(surface(5*sin(u)*cos(v),4*sin(u)*sin(v),3*cos(u)),u=0..\%pi,v=0..2*\%pi)}
Here's a cone:
\graphpaste{draw(surface(u*cos(v),u*sin(v),u),u=0..4,v=0..2*\%pi)}
\endscroll
\autobuttons\end{page}
 
\begin{page}{ExPlot3DParametricCurve}{Plotting Parametric Curves}
\beginscroll
To plot a parametric curve defined by {\em x = f(t)}, 
{\em y = g(t)}, {\em z = h(t)}, specify the functions
{\em f(t)}, {\em g(t)}, and {\em h(t)}
as arguments of the function `curve', then give
the interval over which {\em t} is to range.
Here is a spiral:
\graphpaste{draw(curve(cos(t),sin(t),t),t=0..6)}
Here is the {\em twisted cubic curve}:
\graphpaste{draw(curve(t,t**2,t**3),t=-3..3)}
\endscroll
\autobuttons\end{page}