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<h3><a name="s03_04_05">3.4.5 </a>Parametric Object</h3>
<a name="s03_04_05_i1"><a name="parametric"></a><a name="s03_04_05_i2"><a name="parametric, keyword"></a><a name="s03_04_05_i3"><a name="s03_04_05_i4"><a name="function, parametric"></a><a name="s03_04_05_i5"><a name="s03_04_05_i6"><a name="contained_by, parametric"></a><a name="s03_04_05_i7"><a name="s03_04_05_i8"><a name="max_gradient, parametric"></a><a name="s03_04_05_i9"><a name="s03_04_05_i10"><a name="accuracy, parametric"></a><a name="s03_04_05_i11"><a name="s03_04_05_i12"><a name="precompute, parametric"></a><a name="s03_04_05_i13">
<p>
Where the isosurface object uses implicit surface functions, F(x,y,z)=0, the parametric object is a set of
equations for a surface expressed in the form of the parameters that locate points on the surface, x(u,v), y(u,v),
z(u,v). Each pair of values for u and v gives a single point <code><x,y,z></code> in 3d space
</p>
<p>
The parametric object is not a solid object it is "hollow", like a thin shell.
</p>
<p>
Syntax:
</p>
<pre>
parametric {
function { FUNCTION_ITEMS },
function { FUNCTION_ITEMS },
function { FUNCTION_ITEMS }
<u1,v1>, <u2,v2>
[contained_by { SPHERE | BOX }]
[max_gradient FLOAT_VALUE]
[accuracy FLOAT_VALUE]
[precompute DEPTH, VarList]
}
</pre>
<p>
Parametric default values: <a name="s03_04_05_i14">
</p>
<pre>
accuracy : 0.001
</pre>
<p>
The first function calculates the <code>x</code> value of the surface, the second <code>y</code> and the third the <code>z</code>
value. Allowed is any function that results in a float.
</p>
<p>
<code><u1,v1>,<u2,v2></code> boundaries of the <code>(u,v)</code> space, in which the surface has to be
calculated<a name="s03_04_05_i15">
</p>
<p>
<code>contained_by { ... }</code> The contained_by 'object' limits the area where POV-Ray samples for the surface
of the function. This container can either be a sphere or a box, both of which use the standard POV-Ray syntax. If not
specified a <code>box {<-1,-1,-1>, <1,1,1>}</code> will be used as default.<a name="s03_04_05_i16">
</p>
<p>
<code>max_gradient</code>, It is not really the maximum gradient. It's the maximum magnitude of all six partial
derivatives over the specified ranges of u and v. That is, if you take <code>dx/du</code>, <code>dx/dv</code>, <code>dy/du</code>,
<code>dy/dv</code>, <code>dz/du</code>, and <code>dz/dv</code> and calculate them over the entire range, the <code>max_gradient</code>
is the maximum of the absolute values of all of those values. <a name="s03_04_05_i17">
</p>
<p>
<code>accuracy</code> The default value is 0.001. Smaller values produces more accurate surfaces, but take longer
to render.<a name="s03_04_05_i18"><a name="precompute"></a>
</p>
<p>
<code>precompute</code> can speedup rendering of parametric surfaces. It simply divides parametric surfaces into
small ones (2^depth) and precomputes ranges of the variables(x,y,z) which you specify after depth. The maximum depth
is 20. High values of depth can produce arrays that use a lot of memory, take longer to parse and render faster. If
you declare a parametric surface with the precompute keyword and then use it twice, all arrays are in memory only
once.
</p>
<p>
Example, a unit sphere:
</p>
<pre>
parametric {
function { sin(u)*cos(v) }
function { sin(u)*sin(v) }
function { cos(u) }
<0,0>, <2*pi,pi>
contained_by { sphere{0, 1.1} }
max_gradient ??
accuracy 0.0001
precompute 10 x,y,z
pigment {rgb 1}
}
</pre>
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