/usr/share/doc/axiom-doc/hypertex/graph3dsurfaces.xhtml

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 <body>
  <div align="center"><img align="middle" src="doctitle.png"/></div>
  <hr/>
  <div align="center">Parametric Surfaces</div>
  <hr/>
Graphing a surface defined by x=f(u,v), y=g(u,v), z=h(u,v). This page
describes plotting of surfaces defined by the parametric equations of two
variables, x=f(u,v), y=g(u,v), and z=h(u,v), for which the ranges of u and
v are explicitly defined. The basic draw command for this function utilizes
either the uncompiled function or compiled function format and uses the
<a href="dbopsurface.xhtml">surface</a> command to specify the three 
functions for the x, y, and z components of the surface. The general 
format for uncompiled functions is:
<pre>
    draw(surface(f(u,v),g(u,v),h(u,v)), u=a..b, v=c..d)
</pre>
where a..b and c..d are segments defining the intervals [a,b] and [c,d]
over which the parameters u and v span. In this case the functions are 
not compiled until the draw command is executed. Here is an example of a
surface plotted using the parabolic cylindrical coordinate system option:
<ul>
 <li>
  <input type="submit" id="p1" class="subbut" 
    onclick="makeRequest('p1');"
    value="draw(surface(u*cos(v),u*sin(v),v*cos(u)),u=-4..4,v=0..2*%pi,coordinates==parabolicCylindrical)" />
  <div id="ansp1"><div></div></div>
 </li>
</ul>
In the case of compiled functions, the functions are named and compiled
independentlyh. 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="n1(u:SF,v:SF):SF == u*cos(v)" />
  <div id="ansp2"><div></div></div>
 </li>
 <li>
  <input type="submit" id="p3" class="noresult" 
    onclick="makeRequest('p3');"
    value="n2(u:SF,v:SF):SF == u*sin(v)" />
  <div id="ansp3"><div></div></div>
 </li>
 <li>
  <input type="submit" id="p4" class="noresult" 
    onclick="makeRequest('p4');"
    value="n3(u:SF,v:SF):SF == u" />
  <div id="ansp4"><div></div></div>
 </li>
</ul>
Once the function is compiled the draw command only needs the names of
the functions to execute. Here is a compiled functions example plotted
using the toroidal coordinate system option:
<ul>
 <li>
  <input type="submit" id="p5" class="subbut" 
    onclick="handleFree(['p2','p3','p4','p5']);"
    value="draw(surface(n1,n2,n3),1.0..4.0,1.0..4*%pi,coordinates==toroidal(1$SF))" />
  <div id="ansp5"><div></div></div>
 </li>
</ul>
Note that the parameter ranges do not take the variable names as in the case
of uncompiled functions. The variables are entered in the order in which 
they are defined in the function specification. In this case the first
range specifies the u-variable and the second range specifies the v-variable.
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axiom-hypertex-data 20120501-8 / usr / share / doc / axiom-doc / hypertex / graph3dsurfaces.xhtml
