/usr/share/doc/axiom-doc/hypertex/graph3dparametric.xhtml

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 <body>
  <div align="center"><img align="middle" src="doctitle.png"/></div>
  <hr/>
  <div align="center">Parametric Space Curves</div>
  <hr/>
This page describes the plotting in three dimensional space of a curve
defined by the parametric equations x=f(t), y=g(t), z=h(t), where f,g, and
h are functions of the parameter t which ranges over a specified interval.
The basic draw command for this function utilizes either the uncompiled
functions or compiled functions format and uses the 
<a href="dbopcurve.xhtml">curve</a> command to specify the three
functions for the x, y, and z components of the curve. The general format
for uncompiled functions is:
<pre>
   draw(curve(f(t),g(t),h(t)), t=a..b)
</pre>
where a..b is the segment defining the interval [a,b] over which the
parameter t ranges. In this case the functions are not compiled until
the draw command is executed. Here is an example:
<ul>
 <li>
  <input type="submit" id="p1" class="subbut" 
    onclick="makeRequest('p1');"
    value="draw(curve(cos(t),sin(t),t),t=-12..12)" />
  <div id="ansp1"><div></div></div>
 </li>
</ul>
In the case of compiled functions, the functions are named and compiled
independently. This is useful if you intend to use the functions often,
or if the functions are long and complex. The following lines show 
functions whose parameters are of the type SmallFloat. The functions
are compiled and stored by Axiom when entered.
<ul>
 <li>
  <input type="submit" id="p2" class="noresult" 
    onclick="makeRequest('p2');"
    value="i1(t:SF):SF==sin(t)*cos(3*t/5)" />
  <div id="ansp2"><div></div></div>
 </li>
 <li>
  <input type="submit" id="p3" class="noresult" 
    onclick="makeRequest('p3');"
    value="i2(t:SF):SF==cos(t)*cos(3*t/5)" />
  <div id="ansp3"><div></div></div>
 </li>
 <li>
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    onclick="makeRequest('p4');"
    value="i3(t:SF):SF==cos(t)*sin(3*t/5)" />
  <div id="ansp4"><div></div></div>
 </li>
</ul>
Once the functions are compiled the draw command only needs the names of
the functions to execute. Here is a compiled functions example:
<ul>
 <li>
  <input type="submit" id="p5" class="subbut" 
    onclick="handleFree(['p2','p3','p4','p5']);"
    value="draw(curve(i1,i2,i3),0..15*%pi)" />
  <div id="ansp5"><div></div></div>
 </li>
</ul>
Note that the parameter range does not take the variable name as in the
case of uncompiled functions. It is understood that the indicated range
applies to the parameter of the functions, which in this case is t.
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axiom-hypertex-data 20120501-8 / usr / share / doc / axiom-doc / hypertex / graph3dparametric.xhtml
