Reference:Parametric - Revision history

Jr: changed category.

2025-05-23T09:56:19Z

changed category.

Jholsenback: one more point

2016-11-22T00:12:01Z

one more point

Jholsenback: more markup changes

2016-11-21T23:57:47Z

more markup changes

Jholsenback: markup and grammar cleanup

2016-11-21T21:56:05Z

markup and grammar cleanup

Jholsenback: 1 revision: Reference Migration Initial Load

2012-03-15T19:07:39Z

1 revision: Reference Migration Initial Load

Jholsenback: 1 revision: Initial Load (TF)

2012-03-11T22:27:00Z

1 revision: Initial Load (TF)

New page

[[Category:Objects]]
[[Category:Finite Solid Primitives]]
{{#indexentry:parametric, keyword}}
{{#indexentry:keyword, parametric}}
{{#indexentry:function, parametric}}
{{#indexentry:keyword, function}}
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.

The parametric object is not a solid object it is hollow, like a thin shell.

Syntax:
<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>

{{#indexentry:default values, parametric}}
Parametric default values:

<pre>
accuracy : 0.001
</pre>

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.

<code><u1,v1>,<u2,v2></code> boundaries of the <code>(u,v)</code> space, in which
the surface has to be calculated

{{#indexentry:contained_by, parametric}}
{{#indexentry:keyword, contained_by}}
<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.

{{#indexentry:max_gradient, parametric}}
{{#indexentry:keyword, max_gradient}}
<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.


{{#indexentry:accuracy, parametric}}
{{#indexentry:keyword, accuracy}}
<code>accuracy</code> The default value is 0.001. Smaller values produces more accurate surfaces,
but take longer to render.

{{#indexentry:precompute, parametric}}
{{#indexentry:keyword, precompute}}
<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.

Example, a unit sphere:
<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>

@@ Line 43: / Line 43: @@
    <ol type="a">
      <li>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</li>
-     <li>The <code>max_gradient</code> is the maximum (absolute value) of all of those values.</li>
+     <li>The <code>max_gradient</code> should be at least the maximum (absolute value) of all of those values.</li>
    </ol>
    <li>For <code>accuracy</code> smaller values produces more accurate surfaces, but take longer to render.</li>

@@ Line 40: / Line 40: @@
    <li>The <code>&lt;u1,v1&gt;</code> and the <code>&lt;u2,v2&gt;</code> boundaries of the <code>(u,v)</code> space, in which the surface <em>has</em> to be calculated.</li>
    <li>The <code>contained_by</code> <em>object</em> limits the area where POV-Ray samples for the surface of the function. The container can either be a <code>sphere</code> or a <code>box</code>.</li>
-   <li>The <code>max_gradient</code> is the maximum magnitude of all six partial derivatives over the specified ranges of u and v. That is, if you take <em>dx/du</em>, <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.</li>
+   <li>The <code>max_gradient</code> is the maximum magnitude of all six partial derivatives over the specified ranges of u and v.</li>
    <li>For <code>accuracy</code> smaller values produces more accurate surfaces, but take longer to render.</li>
-   <li>Using <code>precompute</code> can speedup rendering of parametric surfaces. It simply divides parametric surfaces into small ones (2^depth) and precomputes the 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 <code>precompute</code> keyword and then use it twice, all arrays are in memory only once.</li>
+   <li>Using <code>precompute</code> can speedup the rendering of parametric surfaces by simply dividing the parametric surfaces into smaller ones</li>
 </ol>
 <p>Example, a unit sphere:</p>

@@ Line 1: / Line 1: @@
 [[Category:Objects]]
-[[Category:Finite Solid Primitives]]
+[[Category:Finite Patch Primitives]]
 {{#indexentry:parametric, keyword}}
 {{#indexentry:keyword, parametric}}

@@ Line 5: / Line 5: @@
 {{#indexentry:function, parametric}}
 {{#indexentry:keyword, function}}
-<p>Where the isosurface object uses implicit surface functions, F(x,y,z)=0, the parametric object
+<p>While the <code>isosurface</code> object uses implicit surface functions like <strong><em>F(x,y,z) = 0</em></strong> the <code>parametric</code> object uses is a set of equations for a surface expressed in the form of the parameters that locate points on the surface. For example: <code>x(u,v)</code>, <code>y(u,v)</code>, <code>z(u,v)</code>. Each of the pairs of values for <code>u</code> and <code>v</code> gives a single point <code>&lt;x,y,z&gt;</code> in 3d space.</p>
-<p>The parametric object is not a solid object it is <em>hollow</em>, like a thin shell.</p>
+<p>The <code>parametric</code> object is not a solid it is <em>hollow</em>, like a thin shell. The syntax is as follows:</p>
 <pre>
 parametric {
@@ Line 28: / Line 23: @@
 {{#indexentry:default values, parametric}}
-<p>Parametric default values:</p>
+<p>The default values are:</p>
 <pre>
 accuracy     : 0.001
 </pre>
 {{#indexentry:contained_by, parametric}}
 {{#indexentry:keyword, contained_by}}
 {{#indexentry:max_gradient, parametric}}
 {{#indexentry:keyword, max_gradient}}
 {{#indexentry:accuracy, parametric}}
 {{#indexentry:keyword, accuracy}}
 {{#indexentry:precompute, parametric}}
 {{#indexentry:keyword, precompute}}
-<p><code>precompute</code> can speedup rendering of parametric surfaces. It simply divides parametric
+<ol>
-surfaces into small ones (2^depth) and precomputes ranges of the variables(x,y,z) which you specify
+  <li>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. Any function that results in a float is allowed.</li>
-after depth. The maximum depth is 20. High values of depth can produce arrays that use a lot of memory,
+  <li>The <code>&lt;u1,v1&gt;</code> and the <code>&lt;u2,v2&gt;</code> boundaries of the <code>(u,v)</code> space, in which the surface <em>has</em> to be calculated.</li>
-take longer to parse and render faster. If you declare a parametric surface with the precompute keyword
+  <li>The <code>contained_by</code> <em>object</em> limits the area where POV-Ray samples for the surface of the function. The container can either be a <code>sphere</code> or a <code>box</code>.</li>
-and then use it twice, all arrays are in memory only once.</p>
+  <li>The <code>max_gradient</code> is the maximum magnitude of all six partial derivatives over the specified ranges of u and v. That is, if you take <em>dx/du</em>, <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.</li>
+  <li>For <code>accuracy</code> smaller values produces more accurate surfaces, but take longer to render.</li>
 <p>Example, a unit sphere:</p>
 <pre>

← Older revision	Revision as of 19:07, 15 March 2012
(No difference)