Reference:Isosurface - Revision history

Jholsenback: version changes

2017-06-30T08:47:45Z

version changes

Jholsenback: addition notations

2016-12-20T11:30:18Z

addition notations

Jholsenback: updates

2016-12-18T13:38:20Z

updates

Jholsenback: restored previous formatting in one area, minor grammar in others

2016-12-08T15:22:51Z

restored previous formatting in one area, minor grammar in others

Jholsenback: closing note clarification

2016-12-08T00:02:09Z

closing note clarification

Jholsenback: cleanup and corrections

2016-12-07T23:49:02Z

cleanup and corrections

Show changes

Jholsenback: 1 revision: Reference Migration Initial Load

2012-03-15T19:06:26Z

1 revision: Reference Migration Initial Load

Jholsenback: 1 revision: Initial Load (TF)

2012-03-11T22:26:58Z

1 revision: Initial Load (TF)

New page

[[Category:Objects]]
[[Category:Finite Solid Primitives]]
{{#indexentry:isosurface, keyword}}
{{#indexentry:keyword, isosurface}}
{{#indexentry:function, isosurface}}
{{#indexentry:keyword, function}}
Details about many of the things that can be done with the isosurface object are
discussed in the isosurface tutorial section. Below you will only find the syntax basics:

<pre>
isosurface {
function { FUNCTION_ITEMS }
[contained_by { SPHERE | BOX }]
[threshold FLOAT_VALUE]
[accuracy FLOAT_VALUE]
[max_gradient FLOAT_VALUE]
[evaluate P0, P1, P2]
[open]
[max_trace INTEGER] | [all_intersections]
[OBJECT_MODIFIERS...]
}
</pre>

{{#indexentry:default values, isosurface}}
Isosurface default values:
<pre>
contained_by : box{-1,1}
threshold : 0.0
accuracy : 0.001
max_gradient : 1.1
</pre>

<code>function { ... }</code> This must be specified and be the first item of the
<code>isosurface</code> statement. Here you place all the mathematical functions that
will describe the surface.

{{#indexentry:contained_by, isosurface}}
{{#indexentry:keyword, contained_by}}
<code>contained_by { ... }</code> The <code>contained_by</code> 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.
<pre>
contained_by { sphere { CENTER, RADIUS } }
contained_by { box { CORNER1, CORNER2 } }
</pre>

{{#indexentry:threshold, isosurface}}
{{#indexentry:keyword, threshold}}
<code>threshold</code> This specifies how much strength, or substance to give the
<code>isosurface</code>. The surface appears where the <code>function</code> value
equals the <code>threshold</code> value. The default threshold is 0.
<pre>function = threshold</pre>

{{#indexentry:accuracy, isosurface}}
{{#indexentry:keyword, accuracy}}
<code>accuracy</code> The isosurface finding method is a recursive subdivision method.
This subdivision goes on until the length of the interval where POV-Ray finds a surface
point is less than the specified <code>accuracy</code>. The default value is 0.001.
 Smaller values produces more accurate surfaces, but it takes longer to render.

{{#indexentry:max_gradient, isosurface}}
{{#indexentry:keyword, max_gradient}}
<code>max_gradient</code> POV-Ray can find the first intersecting point between a ray and
the <code>isosurface</code> of any continuous function if the maximum gradient of the function
is known. Therefore you can specify a <code>max_gradient</code> for the function.
The default value is 1.1. When the <code>max_gradient</code> used to find the
intersecting point is too high, the render slows down considerably. When it is too
low, artifacts or holes may appear on the isosurface. When it is way too low, the surface
does not show at all. While rendering the isosurface POV-Ray records the found gradient values
and prints a warning if these values are higher or much lower than the specified
<code>max_gradient</code>:

<pre>
Warning: The maximum gradient found was 5.257, but max_gradient of
the isosurface was set to 5.000. The isosurface may contain holes!
Adjust max_gradient to get a proper rendering of the isosurface.
</pre>

<pre>
Warning: The maximum gradient found was 5.257, but max_gradient of
the isosurface was set to 7.000. Adjust max_gradient to
get a faster rendering of the isosurface.
</pre>

{{#indexentry:evaluate, isosurface}}
{{#indexentry:keyword, evaluate}}
{{#indexentry:dynamic max_gradient}}
For best performance you should specify a value close to the real maximum gradient.
<code>evaluate</code> POV-Ray can also dynamically adapt the used max_gradient.
To activate this technique you have to specify the <code>evaluate</code> keyword
followed by three parameters:
<ul>
<li>  P0: the minimum max_gradient in the estimation process,</li>
<li>  P1: an over-estimating factor. This means that the max_gradient is
multiplied by the P1 parameter.</li>
<li>  P2: an attenuation parameter (1 or less)</li>
</ul>
In this case POV-Ray starts with the <code>max_gradient</code> value <code>P0</code>
and dynamically changes it during the render using <code>P1</code> and <code>P2</code>.
In the evaluation process, the P1 and P2 parameters are used in
quadratic functions. This means that over-estimation increases more
rapidly with higher values and attenuation more rapidly with lower
values. Also with dynamic <code>max_gradient</code>, there can be artifacts and holes.

If you are unsure what values to use, start a render without <code>evaluate</code> to get
a value for <code>max_gradient</code>. Now you can use it with <code>evaluate</code> like this:
<ul>
<li>P0 : found max_gradient * min_factor 
min_factor being a float between 0 and 1 to reduce the
<code>max_gradient</code> to a minimum max_gradient. The ideal value for P0
would be the average of the found max_gradients, but we do not
have access to that information. 
A good starting point is 0.6 for the min_factor</li>
<li>P1 : sqrt(found max_gradient/(found max_gradient * min_factor)) 
min_factor being the same as used in P0
this will give an over-estimation factor of more than 1, based
on your minimum max_gradient and the found max_gradient.</li>
<li>P2 : 1 or less 
0.7 is a good starting point.</li>
</ul>

When there are artifacts / holes in the isosurface, increase the min_factor and / or P2 a bit.
Example: when the first run gives a found max_gradient of 356, start with
<pre>
#declare Min_factor= 0.6;
isosurface {
...
evaluate 356*Min_factor, sqrt(356/(356*Min_factor)), 0.7
//evaluate 213.6, 1.29, 0.7
...
}
</pre>


This method is only an approximation of what happens internally, but it
gives faster rendering speeds with the majority of isosurfaces.

{{#indexentry:open, isosurface}}
{{#indexentry:keyword, open}}
<code>open</code> When the isosurface is not fully contained within the contained_by object,
there will be a cross section. Where this happens, you will see the surface of the container.
With the <code>open</code> keyword, these cross section surfaces are removed. The inside of the isosurface
becomes visible.
Note: Using <code>open</code> slows down the render speed, and it is not recommended to use it with CSG operations.

{{#indexentry:max_trace, isosurface}}
{{#indexentry:keyword, max_trace}}
{{#indexentry:all_intersections, isosurface}}
{{#indexentry:keyword, all_intersections}}
<code>max_trace</code> Isosurfaces can be used in CSG shapes since they are solid finite objects
- if not finite by themselves, they are through the cross section with the container.
 By default POV-Ray searches only for the first surface which the ray intersects. But when using an
<code>isosurface</code> in CSG operations, the other surfaces must also be found. Therefore,
the keyword <code>max_trace</code> must be added to the <code>isosurface</code> statement.
It must be followed by an integer value. To check for all surfaces, use the keyword <code>all_intersections</code> instead.
 With <code>all_intersections</code> POV-Ray keeps looking until all surfaces are found.
With a <code>max_trace</code> it only checks until that number is reached.

@@ Line 8: / Line 8: @@
 <p>See the <code>isosurface</code> [[Documentation:Tutorial Section 3.2#Isosurface Object|tutorial]] for more about working with <em>isosurfaces</em>.</p>
-<p>{{New}} in version 3.7.1 a <code>potential</code> pattern has been added to define a pattern based on the <em>potential</em> field of a <code>blob</code> or <code>isosurface</code> object. See also: [[Reference:Potential Pattern|Potential Pattern]].</p>
+<p>{{New}} in version 3.8 a <code>potential</code> pattern has been added to define a pattern based on the <em>potential</em> field of a <code>blob</code> or <code>isosurface</code> object. See also: [[Reference:Potential Pattern|Potential Pattern]].</p>
 <p>The syntax basics are as follows:</p>
@@ Line 123: / Line 123: @@
 <p><em>Isosurfaces</em> can be used in CSG shapes since they are solid finite objects - if not finite by themselves, they are through the cross section with the container. By default POV-Ray searches only for the first surface which the ray intersects. However, when using an <code>isosurface</code> in CSG operations, the other surfaces must also be found. Consequently, the keyword <code>max_trace</code> followed by an integer value, must be added to the <code>isosurface</code> statement. To check for all surfaces, use the keyword <code>all_intersections</code> instead. With <code>max_trace</code> it only checks until that number is reached.</p>
 <p class="Note"><strong>Note:</strong> The current implementation has a <em>limit</em> of 10 <em>intersections</em> in all cases.</p>
-<p>By default, the inside of an <code>isosurface</code> is defined as the set of all points inside the <code>contained_by</code> shape where the function values are below the threshold. {{New}} in version 3.7.1 this can be changed via the <code>polarity</code> keyword. Specifying a <em>positive</em> setting or <code>on</code> will instead cause function values <em>above</em> the threshold to be considered inside. Specifying a <em>negative</em> setting or <code>off</code> will give the default behavior.
+<p>By default, the inside of an <code>isosurface</code> is defined as the set of all points inside the <code>contained_by</code> shape where the function values are below the threshold. {{New}} in version 3.8 this can be changed via the <code>polarity</code> keyword. Specifying a <em>positive</em> setting or <code>on</code> will instead cause function values <em>above</em> the threshold to be considered inside. Specifying a <em>negative</em> setting or <code>off</code> will give the default behavior.

@@ Line 6: / Line 6: @@
 {{#indexentry:keyword, function}}
 {{#indexentry:keyword, polarity}}
-<p>See the <code>isosurface</code> [[Documentation:Tutorial Section 3.2#Isosurface Object|tutorial]] for more about working with <em>isosurfaces</em>. The syntax basics are as follows:</p>
+<p>See the <code>isosurface</code> [[Documentation:Tutorial Section 3.2#Isosurface Object|tutorial]] for more about working with <em>isosurfaces</em>.</p>
 <pre>

@@ Line 113: / Line 113: @@
 {{#indexentry:keyword, all_intersections}}
 <p><em>Isosurfaces</em> can be used in CSG shapes since they are solid finite objects - if not finite by themselves, they are through the cross section with the container. By default POV-Ray searches only for the first surface which the ray intersects. However, when using an <code>isosurface</code> in CSG operations, the other surfaces must also be found. Consequently, the keyword <code>max_trace</code> followed by an integer value, must be added to the <code>isosurface</code> statement. To check for all surfaces, use the keyword <code>all_intersections</code> instead. With <code>max_trace</code> it only checks until that number is reached.</p>
-<p class="Note"><strong>Note:</strong> The <code>max_trace</code> value is set to the maximum supported value of 10 when <code>all_intersections</code> is used.</p>
+<p class="Note"><strong>Note:</strong> The current implementation has a <em>limit</em> of 10 <em>intersections</em> in all cases.</p>

@@ Line 4: / Line 4: @@
 {{#indexentry:keyword, isosurface}}
 {{#indexentry:function, isosurface}}
 {{#indexentry:keyword, function}}
 <p>See the <code>isosurface</code> [[Documentation:Tutorial Section 3.2#Isosurface Object|tutorial]] for more about working with <em>isosurfaces</em>. The syntax basics are as follows:</p>
@@ Line 17: / Line 18: @@
    [open]
    [max_trace INTEGER] | [all_intersections]
    [OBJECT_MODIFIERS...]
+   }
@@ Line 28: / Line 30: @@
 accuracy     : 0.001
 max_gradient : 1.1
 </pre>
@@ Line 116: / Line 119: @@
 <p><em>Isosurfaces</em> can be used in CSG shapes since they are solid finite objects - if not finite by themselves, they are through the cross section with the container. By default POV-Ray searches only for the first surface which the ray intersects. However, when using an <code>isosurface</code> in CSG operations, the other surfaces must also be found. Consequently, the keyword <code>max_trace</code> followed by an integer value, must be added to the <code>isosurface</code> statement. To check for all surfaces, use the keyword <code>all_intersections</code> instead. With <code>max_trace</code> it only checks until that number is reached.</p>
 <p class="Note"><strong>Note:</strong> The current implementation has a <em>limit</em> of 10 <em>intersections</em> in all cases.</p>

@@ Line 43: / Line 43: @@
 {{#indexentry:threshold, isosurface}}
 {{#indexentry:keyword, threshold}}
-<p>Using <code>threshold</code> specifies how much strength, or substance to give the <code>isosurface</code>. The surface appears where the <code>function</code> value equals the <code>threshold</code> value. See above for default value.</p>
+<p>Using <code>threshold</code> specifies how much strength, or substance to give the <code>isosurface</code>. The surface appears where the <code>function</code> value equals the <code>threshold</code> value. See above for the listed default value.</p>
 {{#indexentry:accuracy, isosurface}}
 {{#indexentry:keyword, accuracy}}
-<p>The <code>isosurface</code> resolver uses a recursive subdivision method. This subdivision goes on until the length of the interval where POV-Ray finds a surface point is less than the specified <code>accuracy</code>. See above for default value. Be aware that smaller values produce more accurate surfaces, but takes longer to render.</p>
+<p>The <code>isosurface</code> resolver uses a recursive subdivision method. This subdivision goes on until the length of the interval where POV-Ray finds a surface point is less than the specified <code>accuracy</code>. See above for the listed default value. Be aware that smaller values produce more accurate surfaces, but takes longer to render.</p>
 {{#indexentry:max_gradient, isosurface}}
 {{#indexentry:keyword, max_gradient}}
-<p>POV-Ray can find the first intersecting point between a ray and the <code>isosurface</code> of any continuous function if the maximum gradient of the function is known. To that end you can specify a <code>max_gradient</code> for the function. See above for default value. When the <code>max_gradient</code> used to find the intersecting point is too high, the render slows down considerably. Conversely, when it is too low, artifacts or holes may appear on the isosurface, and in some cases when it is way too low, the surface does not show at all. While rendering the <code>isosurface</code> POV-Ray records the found gradient values and prints a warning (seen below) if these values are either higher or much lower than the specified <code>max_gradient</code> value.</p>
+<p>POV-Ray can find the first intersecting point between a ray and the <code>isosurface</code> of any continuous function if the maximum gradient of the function is known. To that end you can specify a <code>max_gradient</code> for the function. See above for the listed default value. When the <code>max_gradient</code> used to find the intersecting point is too high, the render slows down considerably. Conversely, when it is too low, artifacts or holes may appear on the isosurface, and in some cases when it is way too low, the surface does not show at all. While rendering the <code>isosurface</code> POV-Ray stores the found gradient values and issues a warning, if these values are either higher or much lower than the specified <code>max_gradient</code> value:</p>
 <pre>
-Warning: The maximum gradient found was 5.257, but max_gradient of the isosurface was set to 5.000.
+Warning: The maximum gradient found was 5.257, but max_gradient of
-The isosurface may contain holes! Adjust max_gradient to get a proper rendering of the isosurface.
+the isosurface was set to 5.000. The isosurface may contain holes!
 </pre>
 <pre>
-Warning: The maximum gradient found was 5.257, but max_gradient of the isosurface was set to 7.000.
+Warning: The maximum gradient found was 5.257, but max_gradient of
-Adjust max_gradient to get a faster rendering of the isosurface.
+the isosurface was set to 7.000. Adjust max_gradient to
 </pre>

← Older revision	Revision as of 19:06, 15 March 2012
(No difference)