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Several fixes in documentation thanks to Bryan Herman.

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Paul Romano 2012-07-29 22:01:54 -04:00
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33
docs/source/methods/geometry.rst
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@ -22,13 +22,15 @@ 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::
:label: sphere-equation
(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:
By subtracting the right-hand term from both sides of equation
:eq:`sphere-equation`, we can then write the surface equation for the sphere:
.. math::
:label: surface-equation-sphere
f(x,y,z) = (x - x_0)^2 + (y - y_0)^2 + (z - z_0)^2 - R^2 = 0
@ -97,20 +99,21 @@ direction :math:`u,v,w`. To find the distance :math:`d` to a surface
f(x + du, y + dv, z + dw) = 0
If no solutions to equation :eq:`dist-to-boundary-1` exists or the only
solutions are complex, then the particle's direction of travel will not
intersect the surface. If the solution to equation :eq:`dist-to-boundary-1` is
negative, this means that the surface is "behind" the particle, i.e. if the
particle continues traveling in its current direction, it will not hit the
surface. The complete derivation for different types of surfaces used in OpenMC
will be presented in the following sections.
If no solutions to equation :eq:`dist-to-boundary-1` exist or the only solutions
are complex, then the particle's direction of travel will not intersect the
surface. If the solution to equation :eq:`dist-to-boundary-1` is negative, this
means that the surface is "behind" the particle, i.e. if the particle continues
traveling in its current direction, it will not hit the surface. The complete
derivation for different types of surfaces used in OpenMC will be presented in
the following sections.
Once a distance has been computed to a boundary, we need to check if it is
closer than previously-computed distances to surfaces. Unfortunately, we cannot
just use the minimum function because some distances may be almost identical but
still different due to the use of floating-point arithmetic. Consequently, we
should first check for floating-point equality of the current distance
calculated and the minimum found thus far. This is done by checking if
Once a distance has been computed to a surface, we need to check if it is closer
than previously-computed distances to surfaces. Unfortunately, we cannot just
use the minimum function because some of the calculated distances, which should
be the same in theory (e.g. coincident surfaces), may be slightly different due
to the use of floating-point arithmetic. Consequently, we should first check for
floating-point equality of the current distance calculated and the minimum found
thus far. This is done by checking if
.. math::
:label: fp-distance