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{{#indexentry:CSG}}
In addition to all of the primitive shapes POV-Ray supports, you can also combine multiple simple shapes into complex shapes using Constructive Solid Geometry (CSG). There are four basic types of CSG operations: [[Reference:Union|union]], [[Reference:Intersection|intersection]], [[Reference:Difference|difference]], and [[Reference:Merge|merge]]. CSG objects can be composed of primitives or other CSG objects to create more, and more complex shapes.

===Inside and Outside===
Most shape primitives, like spheres, boxes and blobs divide the world into
two regions. One region is inside the object and one is outside. Given any
point in space you can say it is either inside or outside any particular
primitive object. Well, it could be exactly on the surface but this case is
rather hard to determine due to numerical problems.

Even planes have an inside and an outside. By definition, the surface normal
of the plane points towards the outside of the plane. You should note that
triangles cannot be used as solid objects in CSG since they have no well defined inside and outside. Triangle-based shapes (<code>mesh</code> and <code>mesh2</code>) can only be used in CSG when they are closed objects and have an inside vector specified. 
Note: Although the <code>triangle</code>, the <code>bicubic_patch</code> and some other shapes have no well defined inside and outside, they have a front- and backside which makes it possible to use a texture on the front side and an <code>interior_texture</code> on the back side.

CSG uses the concepts of inside and outside to combine shapes together as
explained in the following sections.

Imagine you have two objects that partially overlap like shown in the figure
below. Four different areas of points can be distinguished: points that are
neither in object <code>A</code> nor in object <code>B</code>, points that
are in object <code>A</code> but not in object <code>B</code>, points that
are not in object <code>A</code> but in object <code>B</code> and last not
least points that are in object <code>A</code> and object <code>B</code>.


<table class="centered" width="660x" cellpadding="0" cellspacing="10">
<tr>
<td>
[[Image:RefImgObjoverl.gif|center|640px]]
</td>
</tr>
<tr>
<td>
Two overlapping objects.
</td>
</tr>
</table>

Keeping this in mind it will be quite easy to understand how the CSG
operations work.

When using CSG it is often useful to invert an object so that it will be
inside-out. The appearance of the object is not changed, just the way that
POV-Ray perceives it. When the <code>inverse</code> keyword is used the 
inside of the shape is flipped to become the outside and vice
versa.

The inside/outside distinction is not important for a <code>union</code>, but is important for <code>intersection</code>, <code>difference</code>, and <code>merge</code>. Therefore any objects may be combined using <code>union</code> but only solid objects, i.e. objects that have a well-defined interior can be used in the other kinds of CSG. The objects described in
[[Reference:Finite Patch Primitives|Finite Patch Primitives]] have no well defined inside/outside. All objects described in the sections [[Reference:Finite Solid Primitives|Finite Solid Primitives]] and [[Reference:Infinite Solid Primitives|Infinite Solid Primitives]].

@@ Line 1: / Line 1: @@
 {{#indexentry:CSG}}
-<p>In addition to all of the primitive shapes POV-Ray supports, you can also combine multiple simple shapes into complex shapes using <em> Constructive Solid Geometry</em> (CSG). There are four basic types of CSG operations: [[Reference:Union|union]], [[Reference:Intersection|intersection]], [[Reference:Difference|difference]], and [[Reference:Merge|merge]]. CSG objects can be composed of primitives or other CSG objects to create more, and more complex shapes.</p>
+<p>In addition to all of the primitive shapes POV-Ray supports, you can also combine multiple simple shapes into complex shapes using <em> Constructive Solid Geometry</em> (CSG). There are four basic types of CSG operations: [[Reference:Union|union]], [[Reference:Intersection|intersection]], [[Reference:Difference|difference]], and [[Reference:Merge|merge]]. CSG objects can be composed of primitives or other CSG objects to create more, and more complex shapes. See also: [[Reference:Object Modifiers|Object Modifiers]].</p>
 ===Inside and Outside===
@@ Line 12: / Line 12: @@
 of the plane points towards the outside of the plane. You should note that
 triangles cannot be used as solid objects in CSG since they have no well defined inside and outside. Triangle-based shapes (<code>mesh</code> and <code>mesh2</code>) can only be used in CSG when they are closed objects and have an inside vector specified. </p>
-<p class="Note"><strong>Note:</strong> Although the <code>triangle</code>, the <code>bicubic_patch</code> and some other shapes have no well defined inside and outside, they have a front- and backside which makes it possible to use a texture on the front side and an <code>interior_texture</code> on the back side.</p>
+<p class="Note"><strong>Note:</strong> Although the <code>triangle</code>, the <code>bicubic_patch</code> and some other shapes have no well defined inside and outside, they have a front and backside which makes it possible to use a texture on the front side and an <code>interior_texture</code> on the back side.</p>
 <p>
 CSG uses the concepts of inside and outside to combine shapes together as
@@ Line 47: / Line 47: @@
 versa.</p>
 <p>
-The inside/outside distinction is not important for a <code>union</code>, but is important for <code>intersection</code>, <code>difference</code>, and <code>merge</code>. Therefore any objects may be combined using <code>union</code> but only solid objects, i.e. objects that have a well-defined interior can be used in the other kinds of CSG. The objects described in
+The inside / outside distinction is not important for a <code>union</code>, but is important for <code>intersection</code>, <code>difference</code>, and <code>merge</code>. Therefore any objects may be combined using <code>union</code> but only solid objects, i.e. objects that have a well-defined interior can be used in the other kinds of CSG. The objects described in
-[[Reference:Finite Patch Primitives|Finite Patch Primitives]] have no well defined inside/outside. All objects described in the sections [[Reference:Finite Solid Primitives|Finite Solid Primitives]] and [[Reference:Infinite Solid Primitives|Infinite Solid Primitives]].</p>
+[[Reference:Finite Patch Primitives|Finite Patch Primitives]] have no well defined inside / outside, while the objects described in the sections [[Reference:Finite Solid Primitives|Finite Solid Primitives]] and [[Reference:Infinite Solid Primitives|Infinite Solid Primitives]] do.</p>

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