diff --git a/docs/img/halfspace.svg b/docs/img/halfspace.svg
index 9e8c2b90f4..8f5c5d54da 100644
--- a/docs/img/halfspace.svg
+++ b/docs/img/halfspace.svg
@@ -7,48 +7,12 @@
xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#"
xmlns:svg="http://www.w3.org/2000/svg"
xmlns="http://www.w3.org/2000/svg"
- xmlns:sodipodi="http://sodipodi.sourceforge.net/DTD/sodipodi-0.dtd"
- xmlns:inkscape="http://www.inkscape.org/namespaces/inkscape"
- width="302"
- height="198.50891"
- id="svg2"
version="1.1"
- inkscape:version="0.48.3.1 r9886"
- sodipodi:docname="New document 1">
+ width="338.45703"
+ height="172"
+ id="svg2">
-
-
-
@@ -62,40 +26,29 @@
+ transform="translate(-152.54297,-201.36218)"
+ id="layer1">
+ style="fill:none;stroke:#000000;stroke-width:2;stroke-miterlimit:4;stroke-opacity:1;stroke-dasharray:none" />
+1
-1
diff --git a/docs/img/union.svg b/docs/img/union.svg
index 0949ca5b51..066fa2ba14 100644
--- a/docs/img/union.svg
+++ b/docs/img/union.svg
@@ -7,48 +7,12 @@
xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#"
xmlns:svg="http://www.w3.org/2000/svg"
xmlns="http://www.w3.org/2000/svg"
- xmlns:sodipodi="http://sodipodi.sourceforge.net/DTD/sodipodi-0.dtd"
- xmlns:inkscape="http://www.inkscape.org/namespaces/inkscape"
+ version="1.1"
width="452"
height="272"
- id="svg2"
- version="1.1"
- inkscape:version="0.48.3.1 r9886"
- sodipodi:docname="halfspace.svg">
+ id="svg2">
-
-
-
@@ -62,102 +26,80 @@
+ transform="translate(-109,-151.36218)"
+ id="layer1">
+ style="fill:none;stroke:#000000;stroke-width:2;stroke-miterlimit:4;stroke-opacity:1;stroke-dasharray:none" />
+ style="fill:none;stroke:#000000;stroke-width:2;stroke-linecap:butt;stroke-linejoin:miter;stroke-miterlimit:4;stroke-opacity:1;stroke-dasharray:none" />
+ style="fill:none;stroke:#000000;stroke-width:2;stroke-linecap:butt;stroke-linejoin:miter;stroke-miterlimit:4;stroke-opacity:1;stroke-dasharray:none" />
+ style="fill:#aab4ff;fill-opacity:1;stroke:none" />
+1
- +1
+ -1
- -1
+ -2
- -2
+ +2
- +2
+ -3
- -3
+ +3
+ y="297.36218"
+ id="tspan3825-1-8-2-2">+3
diff --git a/docs/source/methods/geometry.rst b/docs/source/methods/geometry.rst
index cb83dcf636..806321f740 100644
--- a/docs/source/methods/geometry.rst
+++ b/docs/source/methods/geometry.rst
@@ -5,9 +5,51 @@ Geometry
========
OpenMC uses a technique known as `constructive solid geometry`_ (CSG) to build
-arbitrarily complex 3D models. In a CSG model, every simply-connected region is
-described as the union, intersection, or difference of half-spaces created by
-bounding surfaces. In OpenMC, any second-order surface of the form
+arbitrarily complex three-dimensional models in Euclidean space. In a CSG model,
+every unique object is described as the union, intersection, or difference of
+half-spaces created by bounding `surfaces`_. Every surface divides all of space
+into exactly two half-spaces. We can mathematically define a surface as a
+collection of points that satisfy an equation of the form :math:`f(x,y,z) = 0`
+where :math:`f(x,y,z)` is a given function. The region for which :math:`f(x,y,z)
+< 0` can be called the negative half-space (or simply the "negative side") and
+the region for which :math:`f(x,y,z) > 0` can be called the positive half-space.
+
+Let us take the example of a sphere centered at the point :math:`(x_0,y_0,z_0)`
+with radius :math:`R`. One would normally write the equation of the sphere as
+
+.. math::
+
+ (x - x_0)^2 + (y - y_0)^2 + (z - z_0)^2 = R^2
+
+By subtracting the right-hand term from both sides of the equation, we can then
+write the surface equation:
+
+.. math::
+
+ f(x,y,z) = (x - x_0)^2 + (y - y_0)^2 + (z - z_0)^2 - R^2 = 0
+
+One can confirm that any point inside this sphere will correspond to
+:math:`f(x,y,z) < 0` and any point outside the sphere will correspond to
+:math:`f(x,y,z) > 0`.
+
+In OpenMC, every surface defined by the user is assigned an integer to uniquely
+identify it. We can then refer to either of the two half-spaces created by a
+surface by a combination of the unique ID of the surface and a positive/negative
+sign. For example, to refer to the negative half-space of a sphere (the volume
+inside the sphere) with unique ID 35, the reference would be -35. These
+references to half-spaces are used in created regions in space of homogeneous
+material, known as "cells".
+
+
+.. figure:: ../../img/halfspace.svg
+ :align: center
+ :figclass: align-center
+
+.. figure:: ../../img/union.svg
+ :align: center
+ :figclass: align-center
+
+In OpenMC, any second-order surface of the form
.. math::
@@ -16,9 +58,6 @@ bounding surfaces. In OpenMC, any second-order surface of the form
can be modeled in OpenMC. For example, the equation for a sphere centered at
:math:`(\bar{x},\bar{y},\bar{z})` and of radius :math:`R` can be written as
-.. math::
-
- f(x,y,z) = (x - \bar{x})^2 + (y - \bar{y})^2 + (z - \bar{z})^2 + R^2 = 0
-------------------
Reflective Surfaces
@@ -40,3 +79,4 @@ gradient to the surface at the point of crossing, i.e. :math:`\mathbf{n} =
\nabla f(x,y,z)`.
.. _constructive solid geometry: http://en.wikipedia.org/wiki/Constructive_solid_geometry
+.. _surfaces: http://en.wikipedia.org/wiki/Surface