Reference:Torus - Revision history

Jholsenback: version changes

2017-06-26T10:35:57Z

version changes

Jholsenback: corrected another link issue

2016-07-17T14:14:36Z

corrected another link issue

Jholsenback: corrected link issue

2016-07-17T14:04:47Z

corrected link issue

Jholsenback: update to support "New" temple

2016-07-16T13:29:09Z

update to support "New" temple

Jholsenback: clean up and consistency

2016-05-31T17:20:13Z

clean up and consistency

Clipka: /* Spindle Torus */ "node", huh?

2016-05-05T00:22:15Z

Spindle Torus: "node", huh?

Clipka: added spindle torus section

2016-05-04T23:47:33Z

added spindle torus section

Jholsenback: 1 revision: Reference Migration Initial Load

2012-03-15T19:09:03Z

1 revision: Reference Migration Initial Load

Jholsenback: 1 revision: Initial Load (TF)

2012-03-11T22:27:03Z

1 revision: Initial Load (TF)

New page

[[Category:Objects]]
[[Category:Finite Solid Primitives]]
{{#indexentry:torus, keyword}}
{{#indexentry:keyword, torus}}
A <code>torus</code> is a 4th order quartic polynomial shape that looks
like a donut or inner tube. Because this shape is so useful and quartics are
difficult to define, POV-Ray lets you take a short-cut and define a torus
by:
<pre>
TORUS:
torus {
Major, Minor
[TORUS_MODIFIER...]
}
TORUS_MODIFIER:
sturm | OBJECT_MODIFIER
</pre>

{{#indexentry:default values, torus}}
Torus default values:
<pre>
sturm : off
</pre>

where <code>Major</code> is a float value giving the major radius
and <code>Minor</code> is a float specifying the minor radius. The
major radius extends from the center of the hole to the mid-line of the rim
while the minor radius is the radius of the cross-section of the rim. The
torus is centered at the origin and lies in the x-z-plane with the y-axis
sticking through the hole.

<table class="centered" width="660x" cellpadding="0" cellspacing="10">
<tr>
<td>
[[Image:RefImgMimxrtor.gif|center|640px]]
</td>
</tr>
<tr>
<td>
Major and minor radius of a torus.
</td>
</tr>
</table>

The torus is internally bounded by two cylinders and two rings forming a
thick cylinder. With this bounding cylinder the performance of the torus
intersection test is vastly increased. The test for a valid torus
intersection, i.e. solving a 4th order polynomial, is only performed if the
bounding cylinder is hit. Thus a lot of slow root solving calculations are
avoided.

{{#indexentry:sturm, torus}}
{{#indexentry:keyword, sturm}}
Calculations for all higher order polynomials must be very accurate. If the
torus renders improperly you may add the keyword <code>sturm</code> to use
POV-Ray's slower-yet-more-accurate Sturmian root solver.

@@ Line 45: / Line 45: @@
 {{#indexentry:keyword, merge, torus}}
 {{#indexentry:keyword, union, torus}}
-<p>{{New}} in version 3.7.1 is a torus with a minor radius greater than the major radius (aka <em>spindle torus</em>) will self-intersect in a spindle-shaped region. The behavior with respect to the spindle can be controlled by specifying either of the <code>difference</code>,<code>intersection</code>, <code>merge</code> or <code>union</code> keywords, which act similar to the corresponding CSG operations:</p>
+<p>{{New}} in version 3.8 is a torus with a minor radius greater than the major radius (aka <em>spindle torus</em>) will self-intersect in a spindle-shaped region. The behavior with respect to the spindle can be controlled by specifying either of the <code>difference</code>,<code>intersection</code>, <code>merge</code> or <code>union</code> keywords, which act similar to the corresponding CSG operations:</p>
 <ul>
 <li>Using the <code>difference</code> keyword, the self-intersecting portion is cut away from the torus, so that the spindle volume is considered <em>outside</em> the primitive; the spindle surface is visible (provided you cut open the torus, or make it semi-transparent).</li>

@@ Line 54: / Line 54: @@
 <p>In a non-spindle torus, the <code>intersection</code> keyword will cause a "possible parse error" warning and make the torus invisible, while the other spindle mode keywords will have no effect whatsoever.</p>
 <p class="Note"><strong>Note:</strong> The <code>difference</code> spindle mode does <em>not</em> affect the behavior with respect to the
-<code>[[Reference:Interior_Texture|interior_texture]]</code> keyword. An <code>interior_texture</code> will always be applied to the side of the spindle surface facing the spindle volume.</p>
+<code>[[Reference:Interior Texture|interior_texture]]</code> keyword. An <code>interior_texture</code> will always be applied to the side of the spindle surface facing the spindle volume.</p>
 <table class="centered" width="420px" cellpadding="0" cellspacing="10">

← Older revision		Revision as of 14:04, 17 July 2016
Line 71:		Line 71:
	{{#indexentry:keyword, sturm}}		{{#indexentry:keyword, sturm}}

−	<p>If additional accuracy is required you can add the <code>[[Reference:~~Sturm_Object_Modifier~~\|sturm]]</code> object modifier.</p>	+	<p>If additional accuracy is required you can add the <code>[[Reference:Sturm Object Modifier\|sturm]]</code> object modifier.</p>

@@ Line 45: / Line 45: @@
 {{#indexentry:keyword, merge, torus}}
 {{#indexentry:keyword, union, torus}}
-<p>{{New.3.7.1}} A torus with a minor radius greater than the major radius (aka <em>spindle torus</em>) will self-intersect in a spindle-shaped region. The behavior with respect to the spindle can be controlled by specifying either of the <code>difference</code>,<code>intersection</code>, <code>merge</code> or <code>union</code> keywords, which act similar to the corresponding CSG operations:</p>
+<p>{{New}} in version 3.7.1 is a torus with a minor radius greater than the major radius (aka <em>spindle torus</em>) will self-intersect in a spindle-shaped region. The behavior with respect to the spindle can be controlled by specifying either of the <code>difference</code>,<code>intersection</code>, <code>merge</code> or <code>union</code> keywords, which act similar to the corresponding CSG operations:</p>
 <ul>
 <li>Using the <code>difference</code> keyword, the self-intersecting portion is cut away from the torus, so that the spindle volume is considered <em>outside</em> the primitive; the spindle surface is visible (provided you cut open the torus, or make it semi-transparent).</li>

@@ Line 3: / Line 3: @@
 {{#indexentry:torus, keyword}}
 {{#indexentry:keyword, torus}}
-<p>A <code>torus</code> is a 4th order quartic polynomial shape that looks
+<p>A <code>torus</code> is a 4th order quartic polynomial shape that looks like a donut or inner tube. Because this shape is so useful and quartics are difficult to define, POV-Ray lets you take a short-cut and define a torus by:</p>
 <pre>
 TORUS:
@@ Line 26: / Line 23: @@
 </pre>
-<p>where <em><code>Major</code></em> is a float value giving the major radius
+<p>where <em><code>Major</code></em> is a float value giving the major radius and <em><code>Minor</code></em> is a float specifying the minor radius. The major radius extends from the center of the hole to the mid-line of the rim while the minor radius is the radius of the cross-section of the rim. The torus is centered at the origin and lies in the x-z-plane with the y-axis
 sticking through the hole.</p>
@@ Line 46: / Line 39: @@
 </table>
-<p>The torus is internally bounded by two cylinders and two rings forming a
+<p>The torus is internally bounded by two cylinders and two rings forming a thick cylinder. With this bounding cylinder the performance of the torus intersection test is vastly increased. The test for a valid torus intersection, i.e. solving a 4th order polynomial, is only performed if the bounding cylinder is hit. Thus a lot of slow root solving calculations are avoided.</p>
 {{#indexentry:keyword, difference, torus}}
@@ Line 57: / Line 45: @@
 {{#indexentry:keyword, merge, torus}}
 {{#indexentry:keyword, union, torus}}
-===Spindle Torus===
+<p>{{New.3.7.1}} A torus with a minor radius greater than the major radius (aka <em>spindle torus</em>) will self-intersect in a spindle-shaped region. The behavior with respect to the spindle can be controlled by specifying either of the <code>difference</code>,<code>intersection</code>, <code>merge</code> or <code>union</code> keywords, which act similar to the corresponding CSG operations:</p>
 <ul>
-<li>Using the <code>difference</code> keyword, the self-intersecting portion
+<li>Using the <code>difference</code> keyword, the self-intersecting portion is cut away from the torus, so that the spindle volume is considered <em>outside</em> the primitive; the spindle surface is visible (provided you cut open the torus, or make it semi-transparent).</li>
-is cut away from the torus, so that the spindle volume is considered
+<li>Using the <code>intersection</code> keyword, the resulting shape consists of <em>only</em> the self-intersecting portion, so that only the spindle volume is considered inside the primitive, and only the spindle surface is visible.</li>
-<em>outside</em> the primitive; the spindle surface is visible (provided you
+<li>Using the <code>merge</code> keyword, the surface within the self-intersecting portion is hidden, so that the spindle surface is <em>not</em> visible; the spindle volume is considered inside the primitive.</li>
-cut open the torus, or make it semi-transparent).</li>
+<li>Using the <code>union</code> keyword, the entire torus surface remains visible and the spindle volume is considered inside the primitive (this is the default).</li>
 </ul>
-<p>In a non-spindle torus, the <code>intersection</code> keyword will cause a
+<p>In a non-spindle torus, the <code>intersection</code> keyword will cause a "possible parse error" warning and make the torus invisible, while the other spindle mode keywords will have no effect whatsoever.</p>
-"possible parse error" warning and make the torus invisible, while the other
+<p class="Note"><strong>Note:</strong> The <code>difference</code> spindle mode does <em>not</em> affect the behavior with respect to the
-spindle mode keywords will have no effect whatsoever.</p>
+<code>[[Reference:Interior_Texture|interior_texture]]</code> keyword. An <code>interior_texture</code> will always be applied to the side of the spindle surface facing the spindle volume.</p>
 <table class="centered" width="420px" cellpadding="0" cellspacing="10">
@@ Line 103: / Line 71: @@
 {{#indexentry:keyword, sturm}}
-===Sturm===
+<p>If additional accuracy is required you can add the <code>[[Reference:Sturm_Object_Modifier|sturm]]</code> object modifier.</p>

@@ Line 82: / Line 82: @@
 "possible parse error" warning and make the torus invisible, while the other
 spindle mode keywords will have no effect whatsoever.</p>
-<p class="Note"><strong>Node:</strong> The <code>difference</code> spindle mode
+<p class="Note"><strong>Note:</strong> The <code>difference</code> spindle mode
 does <em>not</em> affect the behaviour with respect to the
 <code>[[Reference:Interior_Texture|interior_texture]]</code> keyword. An
@@ Line 102: / Line 102: @@
 {{#indexentry:sturm, torus}}
 {{#indexentry:keyword, sturm}}
 ===Sturm===
 <p>Calculations for all higher order polynomials must be very accurate. If the
 torus renders improperly you may add the keyword <code>sturm</code> to use
 POV-Ray's slower-yet-more-accurate Sturmian root solver.</p>

@@ Line 10: / Line 10: @@
 TORUS:
    torus {
-     Major, Minor
+     Major, Minor [SPINDLE_MODE]
      [TORUS_MODIFIER...]
+     }
 TORUS_MODIFIER:
    sturm | OBJECT_MODIFIER
 </pre>
@@ Line 20: / Line 22: @@
 <p>Torus default values:</p>
 <pre>
 sturm : off
 </pre>
@@ Line 49: / Line 52: @@
 bounding cylinder is hit. Thus a lot of slow root solving calculations are
 avoided.</p>
 {{#indexentry:sturm, torus}}
 {{#indexentry:keyword, sturm}}
 <p>Calculations for all higher order polynomials must be very accurate. If the
 torus renders improperly you may add the keyword <code>sturm</code> to use
 POV-Ray's slower-yet-more-accurate Sturmian root solver.</p>

← Older revision	Revision as of 19:09, 15 March 2012
(No difference)