mirror of
https://github.com/openmc-dev/openmc.git
synced 2026-07-29 06:35:48 -04:00
Enhanced description of CSG in docs.
This commit is contained in:
Paul Romano
parent
3ff8762f75
commit
fe5b61b941
3 changed files with 106 additions and 171 deletions
|
|
@ -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">
|
||||
<defs
|
||||
id="defs4" />
|
||||
<sodipodi:namedview
|
||||
id="base"
|
||||
pagecolor="#ffffff"
|
||||
bordercolor="#666666"
|
||||
borderopacity="1.0"
|
||||
inkscape:pageopacity="0.0"
|
||||
inkscape:pageshadow="2"
|
||||
inkscape:zoom="0.98994949"
|
||||
inkscape:cx="186"
|
||||
inkscape:cy="5.0242485"
|
||||
inkscape:document-units="px"
|
||||
inkscape:current-layer="layer1"
|
||||
showgrid="true"
|
||||
fit-margin-top="0"
|
||||
fit-margin-left="0"
|
||||
fit-margin-right="0"
|
||||
fit-margin-bottom="0"
|
||||
inkscape:window-width="1366"
|
||||
inkscape:window-height="712"
|
||||
inkscape:window-x="0"
|
||||
inkscape:window-y="27"
|
||||
inkscape:window-maximized="1">
|
||||
<inkscape:grid
|
||||
type="xygrid"
|
||||
id="grid2985"
|
||||
empspacing="5"
|
||||
visible="true"
|
||||
enabled="true"
|
||||
snapvisiblegridlinesonly="true"
|
||||
originx="-189px"
|
||||
originy="-678.98718px" />
|
||||
</sodipodi:namedview>
|
||||
<metadata
|
||||
id="metadata7">
|
||||
<rdf:RDF>
|
||||
|
|
@ -62,40 +26,29 @@
|
|||
</rdf:RDF>
|
||||
</metadata>
|
||||
<g
|
||||
inkscape:label="Layer 1"
|
||||
inkscape:groupmode="layer"
|
||||
id="layer1"
|
||||
transform="translate(-189,-174.86609)">
|
||||
transform="translate(-152.54297,-201.36218)"
|
||||
id="layer1">
|
||||
<path
|
||||
sodipodi:type="arc"
|
||||
style="fill:none;stroke:#000000;stroke-width:2;stroke-miterlimit:4;stroke-opacity:1;stroke-dasharray:none"
|
||||
d="m 490,287.36218 a 150,85 0 1 1 -300,0 150,85 0 1 1 300,0 z"
|
||||
id="path2987"
|
||||
sodipodi:cx="340"
|
||||
sodipodi:cy="287.36218"
|
||||
sodipodi:rx="150"
|
||||
sodipodi:ry="85"
|
||||
d="m 490,287.36218 c 0,46.94421 -67.15729,85 -150,85 -82.84271,0 -150,-38.05579 -150,-85 0,-46.9442 67.15729,-85 150,-85 82.84271,0 150,38.0558 150,85 z" />
|
||||
style="fill:none;stroke:#000000;stroke-width:2;stroke-miterlimit:4;stroke-opacity:1;stroke-dasharray:none" />
|
||||
<text
|
||||
xml:space="preserve"
|
||||
style="font-size:24px;font-style:normal;font-variant:normal;font-weight:normal;font-stretch:normal;text-align:start;line-height:125%;letter-spacing:0px;word-spacing:0px;writing-mode:lr-tb;text-anchor:start;fill:#000000;fill-opacity:1;stroke:none;font-family:Sans;-inkscape-font-specification:Sans"
|
||||
x="210"
|
||||
y="192.36218"
|
||||
x="150"
|
||||
y="272.36218"
|
||||
id="text3765"
|
||||
sodipodi:linespacing="125%"><tspan
|
||||
sodipodi:role="line"
|
||||
x="210"
|
||||
y="192.36218"
|
||||
xml:space="preserve"
|
||||
style="font-size:24px;font-style:normal;font-variant:normal;font-weight:normal;font-stretch:normal;text-align:start;line-height:125%;letter-spacing:0px;word-spacing:0px;writing-mode:lr-tb;text-anchor:start;fill:#000000;fill-opacity:1;stroke:none;font-family:Sans;-inkscape-font-specification:Sans"><tspan
|
||||
x="150"
|
||||
y="272.36218"
|
||||
id="tspan3769">+1</tspan></text>
|
||||
<text
|
||||
xml:space="preserve"
|
||||
style="font-size:24px;font-style:normal;font-variant:normal;font-weight:normal;font-stretch:normal;text-align:start;line-height:125%;letter-spacing:0px;word-spacing:0px;writing-mode:lr-tb;text-anchor:start;fill:#000000;fill-opacity:1;stroke:none;font-family:Sans;-inkscape-font-specification:Sans"
|
||||
x="300"
|
||||
y="262.36218"
|
||||
x="205"
|
||||
y="272.36218"
|
||||
id="text3765-4"
|
||||
sodipodi:linespacing="125%"><tspan
|
||||
sodipodi:role="line"
|
||||
x="300"
|
||||
y="262.36218"
|
||||
xml:space="preserve"
|
||||
style="font-size:24px;font-style:normal;font-variant:normal;font-weight:normal;font-stretch:normal;text-align:start;line-height:125%;letter-spacing:0px;word-spacing:0px;writing-mode:lr-tb;text-anchor:start;fill:#000000;fill-opacity:1;stroke:none;font-family:Sans;-inkscape-font-specification:Sans"><tspan
|
||||
x="205"
|
||||
y="272.36218"
|
||||
id="tspan3794">-1</tspan></text>
|
||||
</g>
|
||||
</svg>
|
||||
|
|
|
|||
|
Before Width: | Height: | Size: 3.4 KiB After Width: | Height: | Size: 2 KiB |
|
|
@ -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">
|
||||
<defs
|
||||
id="defs4" />
|
||||
<sodipodi:namedview
|
||||
id="base"
|
||||
pagecolor="#ffffff"
|
||||
bordercolor="#666666"
|
||||
borderopacity="1.0"
|
||||
inkscape:pageopacity="0.0"
|
||||
inkscape:pageshadow="2"
|
||||
inkscape:zoom="1.4"
|
||||
inkscape:cx="266"
|
||||
inkscape:cy="103.43381"
|
||||
inkscape:document-units="px"
|
||||
inkscape:current-layer="layer1"
|
||||
showgrid="true"
|
||||
fit-margin-top="0"
|
||||
fit-margin-left="0"
|
||||
fit-margin-right="0"
|
||||
fit-margin-bottom="0"
|
||||
inkscape:window-width="1366"
|
||||
inkscape:window-height="712"
|
||||
inkscape:window-x="0"
|
||||
inkscape:window-y="27"
|
||||
inkscape:window-maximized="1">
|
||||
<inkscape:grid
|
||||
type="xygrid"
|
||||
id="grid2985"
|
||||
empspacing="5"
|
||||
visible="true"
|
||||
enabled="true"
|
||||
snapvisiblegridlinesonly="true"
|
||||
originx="-109px"
|
||||
originy="-629px" />
|
||||
</sodipodi:namedview>
|
||||
<metadata
|
||||
id="metadata7">
|
||||
<rdf:RDF>
|
||||
|
|
@ -62,102 +26,80 @@
|
|||
</rdf:RDF>
|
||||
</metadata>
|
||||
<g
|
||||
inkscape:label="Layer 1"
|
||||
inkscape:groupmode="layer"
|
||||
id="layer1"
|
||||
transform="translate(-109,-151.36218)">
|
||||
transform="translate(-109,-151.36218)"
|
||||
id="layer1">
|
||||
<path
|
||||
sodipodi:type="arc"
|
||||
style="fill:none;stroke:#000000;stroke-width:2;stroke-miterlimit:4;stroke-opacity:1;stroke-dasharray:none"
|
||||
d="m 490,287.36218 a 150,85 0 1 1 -300,0 150,85 0 1 1 300,0 z"
|
||||
id="path2987"
|
||||
sodipodi:cx="340"
|
||||
sodipodi:cy="287.36218"
|
||||
sodipodi:rx="150"
|
||||
sodipodi:ry="85"
|
||||
d="m 490,287.36218 c 0,46.94421 -67.15729,85 -150,85 -82.84271,0 -150,-38.05579 -150,-85 0,-46.9442 67.15729,-85 150,-85 82.84271,0 150,38.0558 150,85 z" />
|
||||
style="fill:none;stroke:#000000;stroke-width:2;stroke-miterlimit:4;stroke-opacity:1;stroke-dasharray:none" />
|
||||
<path
|
||||
style="fill:none;stroke:#000000;stroke-width:2;stroke-linecap:butt;stroke-linejoin:miter;stroke-miterlimit:4;stroke-opacity:1;stroke-dasharray:none"
|
||||
d="m 151,-22.503909 0,269.999999"
|
||||
transform="translate(189,174.86609)"
|
||||
id="path3817"
|
||||
inkscape:connector-curvature="0"
|
||||
transform="translate(189,174.86609)" />
|
||||
style="fill:none;stroke:#000000;stroke-width:2;stroke-linecap:butt;stroke-linejoin:miter;stroke-miterlimit:4;stroke-opacity:1;stroke-dasharray:none" />
|
||||
<path
|
||||
style="fill:none;stroke:#000000;stroke-width:2;stroke-linecap:butt;stroke-linejoin:miter;stroke-miterlimit:4;stroke-opacity:1;stroke-dasharray:none"
|
||||
d="m -79,127.49609 450,0"
|
||||
transform="translate(189,174.86609)"
|
||||
id="path3819"
|
||||
inkscape:connector-curvature="0"
|
||||
transform="translate(189,174.86609)" />
|
||||
style="fill:none;stroke:#000000;stroke-width:2;stroke-linecap:butt;stroke-linejoin:miter;stroke-miterlimit:4;stroke-opacity:1;stroke-dasharray:none" />
|
||||
<path
|
||||
style="fill:#aab4ff;fill-opacity:1;stroke:none"
|
||||
d="m 152.14286,162.63371 0,-33.57143 72.14285,0 c 39.67858,0 72.14286,0.1556 72.14286,0.34577 0,0.83636 -4.22498,8.93075 -6.5305,12.51137 -1.39125,2.16072 -4.89349,6.45329 -7.78275,9.53904 -19.70935,21.04977 -54.95495,36.54118 -96.04389,42.21394 -7.56736,1.04476 -25.70992,2.51107 -31.25,2.52568 l -2.67857,0.007 0,-33.57143 z"
|
||||
transform="translate(189,174.86609)"
|
||||
id="path3821"
|
||||
inkscape:connector-curvature="0"
|
||||
transform="translate(189,174.86609)" />
|
||||
style="fill:#aab4ff;fill-opacity:1;stroke:none" />
|
||||
<text
|
||||
xml:space="preserve"
|
||||
style="font-size:20px;font-style:normal;font-variant:normal;font-weight:normal;font-stretch:normal;text-align:start;line-height:125%;letter-spacing:0px;word-spacing:0px;writing-mode:lr-tb;text-anchor:start;fill:#000000;fill-opacity:1;stroke:none;font-family:Sans;-inkscape-font-specification:Sans"
|
||||
x="210"
|
||||
y="222.36218"
|
||||
id="text3823"
|
||||
sodipodi:linespacing="125%"><tspan
|
||||
sodipodi:role="line"
|
||||
id="tspan3825"
|
||||
x="210"
|
||||
y="222.36218">+1</tspan></text>
|
||||
<text
|
||||
xml:space="preserve"
|
||||
style="font-size:20px;font-style:normal;font-variant:normal;font-weight:normal;font-stretch:normal;text-align:start;line-height:125%;letter-spacing:0px;word-spacing:0px;writing-mode:lr-tb;text-anchor:start;fill:#000000;fill-opacity:1;stroke:none;font-family:Sans;-inkscape-font-specification:Sans"
|
||||
style="font-size:20px;font-style:normal;font-variant:normal;font-weight:normal;font-stretch:normal;text-align:start;line-height:125%;letter-spacing:0px;word-spacing:0px;writing-mode:lr-tb;text-anchor:start;fill:#000000;fill-opacity:1;stroke:none;font-family:Sans;-inkscape-font-specification:Sans"><tspan
|
||||
x="210"
|
||||
y="222.36218"
|
||||
id="tspan3825">+1</tspan></text>
|
||||
<text
|
||||
x="240"
|
||||
y="242.36218"
|
||||
id="text3823-0"
|
||||
sodipodi:linespacing="125%"><tspan
|
||||
sodipodi:role="line"
|
||||
id="tspan3825-1"
|
||||
x="240"
|
||||
y="242.36218">-1</tspan></text>
|
||||
<text
|
||||
xml:space="preserve"
|
||||
style="font-size:20px;font-style:normal;font-variant:normal;font-weight:normal;font-stretch:normal;text-align:start;line-height:125%;letter-spacing:0px;word-spacing:0px;writing-mode:lr-tb;text-anchor:start;fill:#000000;fill-opacity:1;stroke:none;font-family:Sans;-inkscape-font-specification:Sans"
|
||||
style="font-size:20px;font-style:normal;font-variant:normal;font-weight:normal;font-stretch:normal;text-align:start;line-height:125%;letter-spacing:0px;word-spacing:0px;writing-mode:lr-tb;text-anchor:start;fill:#000000;fill-opacity:1;stroke:none;font-family:Sans;-inkscape-font-specification:Sans"><tspan
|
||||
x="240"
|
||||
y="242.36218"
|
||||
id="tspan3825-1">-1</tspan></text>
|
||||
<text
|
||||
x="315"
|
||||
y="262.36218"
|
||||
id="text3823-0-5"
|
||||
sodipodi:linespacing="125%"><tspan
|
||||
sodipodi:role="line"
|
||||
id="tspan3825-1-8"
|
||||
x="315"
|
||||
y="262.36218">-2</tspan></text>
|
||||
<text
|
||||
xml:space="preserve"
|
||||
style="font-size:20px;font-style:normal;font-variant:normal;font-weight:normal;font-stretch:normal;text-align:start;line-height:125%;letter-spacing:0px;word-spacing:0px;writing-mode:lr-tb;text-anchor:start;fill:#000000;fill-opacity:1;stroke:none;font-family:Sans;-inkscape-font-specification:Sans"
|
||||
style="font-size:20px;font-style:normal;font-variant:normal;font-weight:normal;font-stretch:normal;text-align:start;line-height:125%;letter-spacing:0px;word-spacing:0px;writing-mode:lr-tb;text-anchor:start;fill:#000000;fill-opacity:1;stroke:none;font-family:Sans;-inkscape-font-specification:Sans"><tspan
|
||||
x="315"
|
||||
y="262.36218"
|
||||
id="tspan3825-1-8">-2</tspan></text>
|
||||
<text
|
||||
x="345"
|
||||
y="262.36218"
|
||||
id="text3823-0-5-2"
|
||||
sodipodi:linespacing="125%"><tspan
|
||||
sodipodi:role="line"
|
||||
id="tspan3825-1-8-2"
|
||||
x="345"
|
||||
y="262.36218">+2</tspan></text>
|
||||
<text
|
||||
xml:space="preserve"
|
||||
style="font-size:20px;font-style:normal;font-variant:normal;font-weight:normal;font-stretch:normal;text-align:start;line-height:125%;letter-spacing:0px;word-spacing:0px;writing-mode:lr-tb;text-anchor:start;fill:#000000;fill-opacity:1;stroke:none;font-family:Sans;-inkscape-font-specification:Sans"
|
||||
style="font-size:20px;font-style:normal;font-variant:normal;font-weight:normal;font-stretch:normal;text-align:start;line-height:125%;letter-spacing:0px;word-spacing:0px;writing-mode:lr-tb;text-anchor:start;fill:#000000;fill-opacity:1;stroke:none;font-family:Sans;-inkscape-font-specification:Sans"><tspan
|
||||
x="345"
|
||||
y="262.36218"
|
||||
id="tspan3825-1-8-2">+2</tspan></text>
|
||||
<text
|
||||
x="260"
|
||||
y="322.36218"
|
||||
id="text3823-0-5-0"
|
||||
sodipodi:linespacing="125%"><tspan
|
||||
sodipodi:role="line"
|
||||
id="tspan3825-1-8-0"
|
||||
x="260"
|
||||
y="322.36218">-3</tspan></text>
|
||||
<text
|
||||
xml:space="preserve"
|
||||
style="font-size:20px;font-style:normal;font-variant:normal;font-weight:normal;font-stretch:normal;text-align:start;line-height:125%;letter-spacing:0px;word-spacing:0px;writing-mode:lr-tb;text-anchor:start;fill:#000000;fill-opacity:1;stroke:none;font-family:Sans;-inkscape-font-specification:Sans"
|
||||
style="font-size:20px;font-style:normal;font-variant:normal;font-weight:normal;font-stretch:normal;text-align:start;line-height:125%;letter-spacing:0px;word-spacing:0px;writing-mode:lr-tb;text-anchor:start;fill:#000000;fill-opacity:1;stroke:none;font-family:Sans;-inkscape-font-specification:Sans"><tspan
|
||||
x="260"
|
||||
y="322.36218"
|
||||
id="tspan3825-1-8-0">-3</tspan></text>
|
||||
<text
|
||||
x="255"
|
||||
y="297.36218"
|
||||
id="text3823-0-5-2-4"
|
||||
sodipodi:linespacing="125%"><tspan
|
||||
sodipodi:role="line"
|
||||
id="tspan3825-1-8-2-2"
|
||||
xml:space="preserve"
|
||||
style="font-size:20px;font-style:normal;font-variant:normal;font-weight:normal;font-stretch:normal;text-align:start;line-height:125%;letter-spacing:0px;word-spacing:0px;writing-mode:lr-tb;text-anchor:start;fill:#000000;fill-opacity:1;stroke:none;font-family:Sans;-inkscape-font-specification:Sans"><tspan
|
||||
x="255"
|
||||
y="297.36218">+3</tspan></text>
|
||||
y="297.36218"
|
||||
id="tspan3825-1-8-2-2">+3</tspan></text>
|
||||
</g>
|
||||
</svg>
|
||||
|
|
|
|||
|
Before Width: | Height: | Size: 6.7 KiB After Width: | Height: | Size: 4.9 KiB |
|
|
@ -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
|
||||
|
|
|
|||
Loading…
Add table
Add a link
Reference in a new issue