.. _8-1B:
Keno Appendix B: KENO VI Shape Descriptions
===========================================
The geometry **shape**\ s allowed in KENO-VI geometry description are:
**CONE**, **CUBOID**, **CYLINDER**, **DODECAHEDRON**, **ECYLINDER**,
**ELLIPSOID**, **HEXPRISM**, **HOPPER**, **PARALLELEPIPED**,
**PPIPED**, **PENTAGON**, **PLANE**, **QUADRATIC**, **RHEXPRISM**,
**RHOMBOID**, **SPHERE**, **WEDGE**, **XCYLINDER**, **XPPLANE**,
**YCYLINDER**, **YPPLANE**, **ZCYLINDER**, **ZPPLANE**
**CONE**
specifies a body consisting of one nappe of a right circular
cone. It is defined by specifying the top radius of the cone,
R\ :sub:`t`, the Z coordinate of the top face, Z\ :sub:`t`, the bottom
radius of the cone, R\ :sub:`b`, and the Z coordinate of the bottom
face, Z\ :sub:`b`. :numref:`fig8-1b-1` shows the correct input sequence for a
cone.
.. _fig8-1b-1:
.. figure:: figs/KenoB/fig1.png
:align: center
:width: 500
Example of cone construction.
**CUBOID**
specifies a rectangular parallelepiped. It is defined by
specifying the +X dimension, −X dimension, +Y dimension, −Y dimension,
+Z dimension, −Z dimension. It is perpendicular to the X, Y, and Z axes
unless otherwise specified by the option geometry modification data.
:numref:`fig8-1b-2` shows the correct input sequence for a cuboid.
.. _fig8-1b-2:
.. figure:: figs/KenoB/fig2.png
:align: center
:width: 500
Example of cuboid construction.
**CYLINDER**
specifies a right circular cylinder. It is defined by
specifying the radius of the cylinder, R, the Z coordinate of the top
face, Z\ :sub:`t`, and the Z coordinate of the bottom face, Z\ :sub:`b`.
Its centerline must lie on the Z axis, unless otherwise specified by the
optional geometry modification data. :numref:`fig8-1b-3` shows the correct
input sequence for a cylinder.
.. _fig8-1b-3:
.. figure:: figs/KenoB/fig3.png
:align: center
:width: 600
Example of cylinder construction.
**DODECAHEDRON**
specifies a body whose surface consists of 12 rhombuses
of the same size and shape. It is defined by specifying the radius of
the inscribed sphere, R. It is centered on the origin in a fixed
orientation unless otherwise specified by the optional geometry
modification data. :numref:`fig8-1b-4` shows the correct input sequence for a
dodecahedron.
.. _fig8-1b-4:
.. figure:: figs/KenoB/fig4.png
:align: center
:width: 600
Example of dodecahedron construction.
**ECYLINDER**
specifies a right cylinder with an elliptical cross
section. It is defined by specifying the semiradius along the X-axis,
R\ :sub:`x`, the semiradius along the Y-axis, R\ :sub:`y`, the
Z coordinate of the top face, Z\ :sub:`t`, and the Z coordinate of the
bottom face, Z\ :sub:`b`. Its centerline must lie on the Z axis, unless
otherwise specified by the optional geometry modification data.
:numref:`fig8-1b-5` shows the correct input sequence for an elliptical
cylinder.
.. _fig8-1b-5:
.. figure:: figs/KenoB/fig5.png
:align: center
:width: 600
Example of elliptical cylinder construction.
**ELLIPSOID**
specifies a body whose cross-section slices parallel to
each of the coordinate axes are ellipses. It is defined by specifying
the semiradius along the X-axis, R\ :sub:`x`, the semiradius along the
Y-axis, R\ :sub:`y`, and the semiradius along the Z-axis, R\ :sub:`z`.
It is centered about the origin, unless otherwise specified by the
optional geometry modification data.
:numref:`fig8-1b-6` shows the correct input sequence for an ellipsoid.
.. _fig8-1b-6:
.. figure:: figs/KenoB/fig6.png
:align: center
:width: 600
Example of ellipsoid construction.
**HEXPRISM**
specifies a body whose top and bottom faces are hexagons
that have the same orientation and are perpendicular to the Z axis. It
is defined by specifying the inscribed radius, R, the Z coordinate of
the top face, Z\ :sub:`t`, and the Z coordinate of the bottom face,
Z\ :sub:`b`. :numref:`fig8-1b-7` is an example input for a hexprism.
.. _fig8-1b-7:
.. figure:: figs/KenoB/fig7.png
:align: center
:width: 600
Example of hexprism construction.
**HOPPER**
specifies a body whose top and bottom faces are rectangular
parallelepipeds centered about the Z-axis and parallel to the X and
Y axes. It is defined by specifying the half-length of the top face
along the X-axis, X\ :sub:`t`, the half-length of the top face along the
Y-axis, Y\ :sub:`t`, the Z coordinate of the top face, Z\ :sub:`t`, the
half-length of the bottom face along the X-axis, X\ :sub:`b`, the
half-length of the bottom face along the Y-axis, Y\ :sub:`b`, and the
Z coordinate of the bottom face, Z\ :sub:`b`. Its centerline must lie on
the Z axis unless otherwise specified by the optional geometry
modification data. :numref:`fig8-1b-8` shows the correct input sequence for a
hopper.
.. _fig8-1b-8:
.. figure:: figs/KenoB/fig8.png
:align: center
:width: 600
Example of hopper construction.
**PARALLELEPIPED** or **PPIPED**
is a body with six faces composed
of parallelograms, whose opposing
faces are parallel. It is defined
by specifying the length of the
faces in the X direction, XDIST,
the length of the faces in the
Y direction, YDIST, the length of
the faces in the Z direction,
ZDIST, the angle between the
X-face and the Y-axis, PSI, the
angle between the Y-face and the
Z-axis, THETA, and the angle
between the projection of the top
corner nearest the Z-axis onto
the X-Y plane and the X-axis,
PHI. The bottom face must lie on
the X-Y plane at Z = 0 with a
corner at the origin unless
otherwise specified by the
optional geometry modification
data. :numref:`fig8-1b-9` shows the
correct input sequence for a
parallelepiped. The angles psi,
theta, and phi must be in the
range 0 to 90°.
.. _fig8-1b-9:
.. figure:: figs/KenoB/fig9.png
:align: center
:width: 600
Example of parallelepiped construction.
**PENTAGON**
specifies a body whose top and bottom faces are pentagons
that have the same orientation and are perpendicular to the Z axis. It
is defined by specifying the inscribed radius, R, the Z coordinate of
the top face, Z\ :sub:`t`, and the Z coordinate of the bottom face,
Z\ :sub:`b`. :numref:`fig8-1b-10` is an example input for a pentagon.
.. _fig8-1b-10:
.. figure:: figs/KenoB/fig10.png
:align: center
:width: 600
Example of pentagon construction.
**PLANE**
is a surface where any two points can be connected by a
straight line entirely contained within a plane that divides all space
into two regions. The positive side of the plane is the side the normal
points to or where the equation aX + bY + cZ + d > 0. It is defined by
specifying the coefficients of the equation aX + bY + cZ + d = 0 using
the keywords XPL=a, YPL=b, ZPL=c, and CON=d. Only the nonzero
coefficients of the equation need to be specified. :numref:`fig8-1b-11` shows
the correct input sequence for a plane.
.. _fig8-1b-11:
.. figure:: figs/KenoB/fig11.png
:align: center
:width: 600
Example of plane construction.
**QUADRATIC**
specifies a surface using a quadratic equation of the
form:
aX\ :sup:`2` + bY\ :sup:`2` + cZ\ :sup:`2` + dXY + eXZ + fYZ + gX +
hY + iZ + j = 0.
It is defined by specifying the coefficients of the above equation
using the keywords AQU=a, BQU=b, CQU=c, DQU=d, EQU=e, FQU=f, GQU=g,
HQU=h, IQU=i, and JQU=j. Only the nonzero coefficients of the
equation need to be specified.
**RHEXPRISM**
specifies a body whose top and bottom faces are rotated
hexagons that have the same orientation and are perpendicular to the
Z axis. It is defined by specifying the inscribed radius, R, the
Z coordinate of the top face, Z\ :sub:`t`, and the Z coordinate of the
bottom face, Z\ :sub:`b`. :numref:`fig8-1b-12` is an example input for a
rotated hexprism.
.. _fig8-1b-12:
.. figure:: figs/KenoB/fig12.png
:align: center
:width: 600
Example of rotated hexprism construction.
**RING**
is a body composed of the space between 2 concentric cylinders.
It is defined by specifying the radius Rin of the inner cylinder and
Rout of the outer cylinder, and the coordinate Zt of the top and Zb of
the bottom of the annulus. Its center line lies on the Z axis unless
specified by the optional geometry modification data. :numref:`fig8-1b-13`
shows the correct input sequence for a ring.
.. _fig8-1b-13:
.. figure:: figs/KenoB/fig13.png
:align: center
:width: 600
Example of ring construction.
**RHOMBOID**
is a body composed of six identical faces, each one a
rhombus. It is defined by specifying the length of the edge of the base
along the X-axis, DX and the angle between Y edge of the base and the
Y-axis, Ψ. Its base is in the XY plane at Z = 0, with a corner at the
origin unless otherwise specified by the optional geometry modification
data. :numref:`fig8-1b-14` shows the correct input sequence for a rhomboid.
.. _fig8-1b-14:
.. figure:: figs/KenoB/fig14.png
:align: center
:width: 500
Example of rhomboid construction.
**SPHERE**
specifies a sphere. It is defined by specifying the radius,
R. It is centered about the origin, unless otherwise specified by the
optional geometry modification data.
:numref:`fig8-1b-15` shows the correct input sequence for a sphere.
.. _fig8-1b-15:
.. figure:: figs/KenoB/fig15.png
:align: center
:width: 600
Example of sphere construction.
**WEDGE**
is a right-triangular prism having five faces. The two ends
are triangles, and the three sides are rectangles. It is defined by
specifying the length of the base along the X-axis, XBASE, the X and
Y coordinate where the other two sides meet, Xpt and Ypt, and the length
along the Z-axis, ZLNG. One side is in the XZ plane at Y = 0, and the
bottom face is in the XY plane at Z = 0, with a corner at the origin
unless otherwise specified by the optional geometry modification data.
:numref:`fig8-1b-16` shows the correct input sequence for a wedge.
.. _fig8-1b-16:
.. figure:: figs/KenoB/fig16.png
:align: center
:width: 600
Example of wedge construction.
**XCYLINDER**
specifies a right circular cylinder oriented about the
X-axis. It is defined by specifying the radius of the cylinder, R, the
X coordinate of the top face, X :sub:`t`, and the X coordinate of the
bottom face, X :sub:`b`. Its centerline must lie on the X axis, unless
otherwise specified by the optional geometry modification data.
:numref:`fig8-1b-17` shows the correct input sequence for a cylinder.
.. _fig8-1b-17:
.. figure:: figs/KenoB/fig17.png
:align: center
:width: 600
Example of xcylinder construction.
**XPPLANE**
is a set of flat parallel surfaces where any two points in
one of the surfaces can be connected by a straight line entirely
contained within that surface. These surface planes divide space into
three sections; one section between the two planes which is considered
inside the surfaces, one section on the negative side of the negative
plane which is considered outside the surfaces, and one section on the
positive side of the positive plane which is considered outside the
surfaces. The set of parallel planes are defined by the keyword XPPLANE,
which places the planes perpendicular to the X-axis, the X-intercept
between the more positive plane and the X-axis (X\ :sub:`+`) and the
X‑intercept between the more negative plane and the X-axis (X\ :sub:`−`).
:numref:`fig8-1b-18` shows the correct input sequence for the set of paired
planes.
.. _fig8-1b-18:
.. figure:: figs/KenoB/fig18.png
:align: center
:width: 600
Example of x-paired plane construction.
**YCYLINDER**
specifies a right circular cylinder oriented about the
Y-axis. It is defined by specifying the radius of the cylinder, R, the
Y coordinate of the top face, Y\ :sub:`t`, and the Y coordinate of the
bottom face, Y\ :sub:`b`. Its centerline must lie on the Y axis, unless
otherwise specified by the optional geometry modification data.
:numref:`fig8-1b-19` shows the correct input sequence for a cylinder.
.. _fig8-1b-19:
.. figure:: figs/KenoB/fig19.png
:align: center
:width: 600
Example of ycylinder construction.
**YPPLANE**
is a set of flat parallel surfaces where any two points in
one of the surfaces can be connected by a straight line entirely
contained within that surface. These surface planes divide space into
three sections; one section between the two planes which is considered
inside the surfaces, one section on the negative side of the negative
plane which is considered outside the surfaces, and one section on the
positive side of the positive plane which is considered outside the
surfaces. The set of parallel planes are defined by the keyword YPPLANE,
which places the planes perpendicular to the Y-axis, the Y‑intercept
between the more positive plane and the Y-axis (Y\ :sub:`+`) and the
Y-intercept between the more negative plane and the Y-axis (Y\ :sub:`−`).
:numref:`fig8-1b-20` shows the correct input sequence for the set of paired
planes.
.. _fig8-1b-20:
.. figure:: figs/KenoB/fig20.png
:align: center
:width: 600
Example of y-paired plane construction.
**ZCYLINDER**
specifies a right circular cylinder oriented about the
Z-axis. It is defined by specifying the radius of the cylinder, R, the
Z coordinate of the top face, Z :sub:`t`, and the Z coordinate of the
bottom face, Z :sub:`b`. Its centerline must lie on the Z-axis, unless
otherwise specified by the optional geometry modification data. The
keyword ZCYLINDER is the same as CYLINDER. It is included to be
consistent with the XCYLINDER and YCYLINDER keywords. :numref:`fig8-1b-21`
shows the correct input sequence for a zcylinder.
.. _fig8-1b-21:
.. figure:: figs/KenoB/fig21.png
:align: center
:width: 600
Example of zcylinder construction.
**ZPPLANE**
is a set of flat parallel surfaces where any two points in
one of the surfaces can be connected by a straight line entirely
contained within that surface. These surface planes divide space into
three sections; one section between the two planes which is considered
inside the surfaces, one section on the negative side of the negative
plane which is considered outside the surfaces, and one section on the
positive side of the positive plane which is considered outside the
surfaces. The set of parallel planes are defined by the keyword ZPPLANE,
which places the planes perpendicular to the Z-axis, the Z-intercept
between the more positive plane and the Z-axis (Z\ :sub:`+`) and the
Z-intercept between the more negative plane and the Z-axis (Z\ :sub:`−`).
:numref:`fig8-1b-22` shows the correct input sequence for the set of paired
planes.
.. _fig8-1b-22:
.. figure:: figs/KenoB/fig22.png
:align: center
:width: 600
Example of z-paired plane construction.