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2024-03-28T10:56:03Z
User contributions
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https://serpent.vtt.fi/mediawiki/index.php?title=Surface_types&diff=2058
Surface types
2016-02-24T06:57:58Z
<p>Uftrnuke: Corrected x_1, y_1, y_1 in plane surface definition to x_1, y_1, z_1</p>
<hr />
<div><br />
== Elementary surfaces ==<br />
<br />
<u>Notes:</u><br />
<br />
*Elementary surfaces refer here to surfaces that can be represented by a single equation.<br />
<br />
=== Planes ===<br />
<br />
<u>Notes:</u><br />
<br />
*Parametric form of the general plane is assumed if four values are provided in the surface card. With six values the plane is assumed to be defined by three points.<br />
<br />
{|class="wikitable" style="text-align: left;"<br />
! Surface name<br />
! Parameters<br />
! Surface equation<br />
! Description<br />
|- <br />
| <tt>py</tt><br />
| ''x<sub>0</sub>''<br />
| <math>S(x) = x - x_0</math><br />
| Plane perpendicular to x-axis at ''x = x<sub>0</sub>''<br />
|- <br />
| <tt>pz</tt><br />
| ''y<sub>0</sub>''<br />
| <math>S(y) = y - y_0</math><br />
| Plane perpendicular to y-axis at ''y = y<sub>0</sub>''<br />
|-<br />
| <tt>px</tt><br />
| ''z<sub>0</sub>''<br />
| <math>S(z) = z - z_0</math><br />
| Plane perpendicular to z-axis at ''z = z<sub>0</sub>''<br />
|-<br />
| <tt>plane</tt><br />
| ''A, B, C, D''<br />
| <math>S(x,y,z) = Ax+ By + Cz - D</math><br />
| General plane in parametric form<br />
|-<br />
| <tt>plane</tt><br />
| ''x<sub>1</sub>, y<sub>1</sub>, z<sub>1</sub>, x<sub>2</sub>, y<sub>2</sub>, z<sub>2</sub>, x<sub>3</sub>, y<sub>3</sub>, z<sub>3</sub>''<br />
| <br />
| General plane defined by three points <br />
|-<br />
|}<br />
<br />
=== Second-order quadratic surfaces ===<br />
<u>Notes:</u><br />
<br />
*<tt>cyl</tt> is the same surface as <tt>cylz</tt><br />
<br />
{|class="wikitable" style="text-align: left;"<br />
! Surface name<br />
! Parameters<br />
! Surface equation<br />
! Description<br />
|- <br />
| <tt>cylx</tt><br />
| ''y<sub>0</sub>, z<sub>0</sub>, r''<br />
| <math>S(y,z) = (y - y_0)^2 + (z - z_0)^2 - r^2</math><br />
| Infinite cylinder parallel to x-axis, centred at (''y<sub>0</sub>,z<sub>0</sub>''), radius ''r''<br />
|- <br />
| <tt>cyly</tt><br />
| ''x<sub>0</sub>, z<sub>0</sub>, r''<br />
| <math>S(x,z) = (x - x_0)^2 + (z - z_0)^2 - r^2</math><br />
| Infinite cylinder parallel to y-axis, centred at (''x<sub>0</sub>,z<sub>0</sub>''), radius ''r''<br />
|- <br />
| <tt>cylz, cyl</tt><br />
| ''x<sub>0</sub>, y<sub>0</sub>, r''<br />
| <math>S(x,y) = (x - x_0)^2 + (y - y_0)^2 - r^2</math><br />
| Infinite cylinder parallel to z-axis, centred at (''x<sub>0</sub>,y<sub>0</sub>''), radius ''r''<br />
|- <br />
| <tt>cylv</tt><br />
| ''x<sub>0</sub>, y<sub>0</sub>, z<sub>0</sub>, u<sub>0</sub>, v<sub>0</sub>, w<sub>0</sub>, r''<br />
| <math>S(x,y,z) = (1-u_0^2)(x - x_0)^2 + (1-v_0^2)(y - y_0)^2 + (1-w_0^2)(z - z_0)-r^2</math><br />
| Infinite cylinder, parallel to (''u<sub>0</sub>,v<sub>0</sub>,w<sub>0</sub>''), centred at (''x<sub>0</sub>,y<sub>0</sub>,z<sub>0</sub>''), radius ''r''<br />
|- <br />
| <tt>sph</tt><br />
| ''x<sub>0</sub>, y<sub>0</sub>, z<sub>0</sub>, r''<br />
| <math>S(x,y,z) = (x - x_0)^2 + (y - y_0)^2 + (z - z_0)^2 - r^2</math><br />
| Sphere, centred at (''x<sub>0</sub>,y<sub>0</sub>,z<sub>0</sub>''), radius ''r''<br />
|-<br />
| <tt>cone</tt><br />
| ''x<sub>0</sub>, y<sub>0</sub>, z<sub>0</sub>, r, h''<br />
| <math>(x - x_0)^2 + (y - y_0)^2 - \left(1 - (z - z_0)/h\right)r^2</math><br />
| Half cone on z-axis, centred at (''x<sub>0</sub>,y<sub>0</sub>,z<sub>0</sub>''), base radius ''r'', height ''h''<br />
|- <br />
| <tt>quadratic</tt><br />
| ''A, B, C, D, E, F, G, H, I, J, K''<br />
| <math>S(x,y,z) = Ax^2 + By^2 + Cz^2 + Dxy + Eyz + Fzx + Gx + Hy + Jz + K</math><br />
| General quadratic surface in parametric form<br />
|}<br />
<br />
=== Non-quadratic surfaces ===<br />
<br />
{|class="wikitable" style="text-align: left;"<br />
! Surface name<br />
! Parameters<br />
! Surface equation<br />
! Description<br />
|- <br />
| <tt>inf</tt><br />
| -<br />
| <math>S(y,x,z) = -\infty</math><br />
| All space<br />
|- <br />
| <tt>torx</tt><br />
| ''x<sub>0</sub>, y<sub>0</sub>, z<sub>0</sub>, r, R''<br />
| <math> S(x,y,z) = \left(R - \sqrt{(y - y_0)^2 + (z - z_0)^2}\right)^2 + (x - x_0)^2 - r^2</math><br />
| Circular torus with major radius ''R'' perpendicular to x-axis, centred at (''x<sub>0</sub>, y<sub>0</sub>, z<sub>0</sub>''), minor radius ''r''<br />
|- <br />
| <tt>tory</tt><br />
| ''x<sub>0</sub>, y<sub>0</sub>, z<sub>0</sub>, r, R''<br />
| <math> S(x,y,z) = \left(R - \sqrt{(x - x_0)^2 + (z - z_0)^2}\right)^2 + (y - y_0)^2 - r^2</math><br />
| Circular torus with major radius ''R'' perpendicular to y-axis, centred at (''x<sub>0</sub>, y<sub>0</sub>, z<sub>0</sub>''), minor radius ''r''<br />
|- <br />
| <tt>torz</tt><br />
| ''x<sub>0</sub>, y<sub>0</sub>, z<sub>0</sub>, r, R''<br />
| <math> S(x,y,z) = \left(R - \sqrt{(x - x_0)^2 + (y - y_0)^2}\right)^2 + (z - z_0)^2 - r^2</math><br />
| Circular torus with major radius ''R'' perpendicular to z-axis, centred at (''x<sub>0</sub>, y<sub>0</sub>, z<sub>0</sub>''), minor radius ''r''<br />
|}<br />
<br />
=== MCNP-equivalent surfaces ===<br />
<br />
*Additional surfaces included to simplify input conversion between Serpent and MCNP.<br />
*Includes cones and axisymmetric surfaces defined by points as used by MCNP.<br />
*For description, see Chapter 3 of the MCNP5 User's Guide.<ref name="MCNP5">X-5 Monte Carlo Team. ''"MCNP — A General Monte Carlo N-Particle Transport Code, Version 5, Volume II: User’s Guide."'' LA-CP-03-0245, Los Alamos National Laboratory, 2003.</ref><br />
<br />
{|class="wikitable" style="text-align: left;"<br />
! Surface name<br />
! Equivalent in MCNP<br />
|- <br />
| <tt>ckx</tt><br />
| <tt>K/X</tt><br />
|- <br />
| <tt>cky</tt><br />
| <tt>K/Y</tt><br />
|- <br />
| <tt>ckz</tt><br />
| <tt>K/Z</tt> <br />
|- <br />
| <tt>x</tt><br />
| <tt>X</tt><br />
|- <br />
| <tt>y</tt><br />
| <tt>Y</tt><br />
|- <br />
| <tt>z</tt><br />
| <tt>Z</tt><br />
|}<br />
<br />
== Derived surface types ==<br />
<br />
<u>Notes:</u><br />
<br />
*Derived surfaces refer here to surfaces composed of two or more elementary types. <br />
<br />
=== Truncated cylinders ===<br />
<br />
<u>Notes:</u><br />
<br />
*Truncated cylinders use the same names as the infinite cylinders above, with two additional values determining the height.<br />
<br />
{|class="wikitable" style="text-align: left;"<br />
! Surface name<br />
! Parameters<br />
! Composed of<br />
! Description<br />
|- <br />
| <tt>cylx</tt><br />
| ''y<sub>0</sub>, z<sub>0</sub>, r, z<sub>0</sub>, z<sub>1</sub>''<br />
| Infinite cylinder + two planes<br />
| Infinite cylinder parallel to x-axis, centred at (''y<sub>0</sub>,z<sub>0</sub>''), radius ''r'', truncated between [z<sub>0</sub>, z<sub>1</sub>]<br />
|- <br />
| <tt>cyly</tt><br />
| ''x<sub>0</sub>, z<sub>0</sub>, r, z<sub>0</sub>, z<sub>1</sub>''<br />
| Infinite cylinder + two planes<br />
| Infinite cylinder parallel to y-axis, centred at (''x<sub>0</sub>,z<sub>0</sub>''), radius ''r'', truncated between [z<sub>0</sub>, z<sub>1</sub>]<br />
|-<br />
| <tt>cylz, cyl</tt><br />
| ''x<sub>0</sub>, y<sub>0</sub>, r, z<sub>0</sub>, z<sub>1</sub>''<br />
| Infinite cylinder + two planes<br />
| Infinite cylinder parallel to z-axis, centred at (''x<sub>0</sub>,y<sub>0</sub>''), radius ''r'', truncated between [z<sub>0</sub>, z<sub>1</sub>]<br />
|}<br />
<br />
=== Regular prisms ===<br />
<u>Notes:</u><br />
<br />
*All prisms are parallel to z-axis, and they can be rotated using [[Input syntax manual#strans (surface transformation)|surface transformations]].<br />
<br />
{|class="wikitable" style="text-align: left;"<br />
! Surface name<br />
! Parameters<br />
! Composed of<br />
! Description<br />
|- <br />
| <tt>sqc</tt><br />
| ''x<sub>0</sub>, y<sub>0</sub>, d''<br />
| four planes<br />
| Infinite square prism parallel to z-axis, centred at (''x<sub>0</sub>,y<sub>0</sub>''), half-width ''d''<br />
|- <br />
| <tt>rect</tt><br />
| ''x<sub>0</sub>, x<sub>1</sub>, y<sub>0</sub>, y<sub>1</sub>''<br />
| four planes<br />
| Infinite rectangular prism parallel to z-axis, between [''x<sub>0</sub>, x<sub>1</sub>''] and [''y<sub>0</sub>, y<sub>1</sub>'']<br />
|- <br />
| <tt>hexxc</tt><br />
| ''x<sub>0</sub>, y<sub>0</sub>, d''<br />
| six planes<br />
| Infinite hexagonal prism parallel to z-axis, centred at (''x<sub>0</sub>,y<sub>0</sub>''), flat surface perpendicular to x-axis, half-width ''d''<br />
|- <br />
| <tt>hexxy</tt><br />
| ''x<sub>0</sub>, y<sub>0</sub>, d''<br />
| six planes<br />
| Infinite hexagonal prism parallel to z-axis, centred at (''x<sub>0</sub>,y<sub>0</sub>''), flat surface perpendicular to y-axis, half-width ''d''<br />
|- <br />
| <tt>hexxprism</tt><br />
| ''x<sub>0</sub>, y<sub>0</sub>, d, z<sub>0</sub>, z<sub>1</sub>''<br />
| eight planes<br />
| Truncated hexagonal prism parallel to z-axis, centred at (''x<sub>0</sub>,y<sub>0</sub>''), flat surface perpendicular to x-axis, half-width ''d'', truncated between [z<sub>0</sub>, z<sub>1</sub>]<br />
|- <br />
| <tt>hexyprism</tt><br />
| ''x<sub>0</sub>, y<sub>0</sub>, d, z<sub>0</sub>, z<sub>1</sub>''<br />
| eight planes<br />
| Truncated hexagonal prism parallel to z-axis, centred at (''x<sub>0</sub>,y<sub>0</sub>''), flat surface perpendicular to y-axis, half-width ''d'', truncated between [z<sub>0</sub>, z<sub>1</sub>]<br />
|- <br />
| <tt>octa</tt><br />
| ''x<sub>0</sub>, y<sub>0</sub>, d<sub>1</sub>, d<sub>2</sub>''<br />
| eight planes<br />
| Infinite octagonal prism parallel to z-axis, centred at (''x<sub>0</sub>,y<sub>0</sub>''), half-widths ''d<sub>1</sub>'' and ''d<sub>2</sub>''<br />
|- <br />
| <tt>dode</tt><br />
| ''x<sub>0</sub>, y<sub>0</sub>, d<sub>1</sub>, d<sub>2</sub>''<br />
| twelve planes<br />
| Infinite dodecagonal prism parallel to z-axis, centred at (''x<sub>0</sub>,y<sub>0</sub>''), half-widths ''d<sub>1</sub>'' and ''d<sub>2</sub>''<br />
|}<br />
<br />
=== 3D polyhedra ===<br />
<u>Notes:</u><br />
<br />
*The description of parallelepiped may be wrong.<br />
<br />
{|class="wikitable" style="text-align: left;"<br />
! Surface name<br />
! Parameters<br />
! Composed of<br />
! Description<br />
|- <br />
| <tt>cube</tt><br />
| ''x<sub>0</sub>, y<sub>0</sub>, z<sub>0</sub>, d''<br />
| six planes<br />
| Cube, centred at (''x<sub>0</sub>,y<sub>0</sub>,z<sub>0</sub>''), half-width ''d''<br />
|- <br />
| <tt>cuboid</tt><br />
| ''x<sub>0</sub>, x<sub>1</sub>, y<sub>0</sub>, y<sub>1</sub>, z<sub>0</sub>, z<sub>1</sub>''<br />
| six planes<br />
| Cuboid, between [''x<sub>0</sub>, x<sub>1</sub>''], [''y<sub>0</sub>, y<sub>1</sub>''] and [''z<sub>0</sub>, z<sub>1</sub>'']<br />
|-<br />
| <tt>ppd</tt><br />
| ''x<sub>0</sub>, y<sub>0</sub>, z<sub>0</sub>, L<sub>x</sub>, L<sub>y</sub>, L<sub>z</sub>, <math>\alpha</math><sub>x</sub>, <math>\alpha</math><sub>y</sub>, <math>\alpha</math><sub>z</sub>''<br />
| six planes<br />
| Parallelepiped, with corner at ''(x<sub>0</sub>, y<sub>0</sub>, z<sub>0</sub>)'' and edges of length ''L<sub>x</sub>, L<sub>y</sub> and L<sub>z</sub>'' at angles ''<math>\alpha</math><sub>x</sub>, <math>\alpha</math><sub>y</sub>'' and ''<math>\alpha</math><sub>z</sub>'' (in degrees) with respect to the coordinate axes<br />
|}<br />
<br />
=== Other derived surface types ===<br />
<br />
{|class="wikitable" style="text-align: left;"<br />
! Surface name<br />
! Parameters<br />
! Description<br />
|- <br />
| <tt>pad</tt><br />
|''x<sub>0</sub>, y<sub>0</sub>, r<sub>1</sub>, r<sub>2</sub>, <math>\alpha</math><sub>1</sub>, <math>\alpha</math><sub>2</sub>''<br />
| Sector from ''<math>\alpha</math><sub>1</sub>'' to ''<math>\alpha</math><sub>2</sub>'' (in degrees) of a cylinder parallel to z-axis, centred at (''x<sub>0</sub>,y<sub>0</sub>''), between radii ''r<sub>1</sub>'' and ''r<sub>2</sub>''<br />
|-<br />
| <tt>cross</tt><br />
| ''x<sub>0</sub>, y<sub>0</sub>, l, d''<br />
| Cruciform prism parallel to z-axis, centred at (''x<sub>0</sub>,y<sub>0</sub>''), half-width ''l'', half-thickness ''d''<br />
|-<br />
| <tt>gcross</tt><br />
| ''x<sub>0</sub>, y<sub>0</sub>, d<sub>1</sub>, d<sub>2</sub>, ...''<br />
| Prism parallel to z-axis, centred at (''x<sub>0</sub>,y<sub>0</sub>''), formed by planes at distances ''d<sub>n</sub>'' from the center (see figure below)<br />
|}<br />
<br />
== Rounded corners ==<br />
<br />
== User-defined surfaces ==<br />
<br />
== References ==<br />
<br />
<references/></div>
Uftrnuke