| 1 | <html>
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| 2 | <head>
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| 3 | <title>ADG: Geometry</title>
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| 4 | <script language="JavaScript">
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| 5 | function remote_win(urlnum)
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| 6 | {
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| 7 | var url = "geometry.src/pic" + urlnum + ".html";
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| 8 | RemoteWin=window.open(url,"","resizable=no,toolbar=0,location=0,directories=0,status=0,menubar=0,scrollbars=0,copyhistory=0,width=520,height=520")
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| 9 | RemoteWin.creator=self
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| 10 | }
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| 11 | </script>
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| 12 | </head>
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| 13 |
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| 14 | <!-- Changed by: Gabriele Cosmo, 18-Apr-2005 -->
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| 15 | <!-- $Id: geomSolids.html,v 1.8 2006/11/23 16:36:33 gcosmo Exp $ -->
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| 16 | <!-- $Name: $ -->
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| 17 | <body>
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| 18 | <table WIDTH="100%"><TR>
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| 19 | <td>
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| 20 | <a href="../../../../Overview/html/index.html">
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| 21 | <IMG SRC="../../../../resources/html/IconsGIF/Overview.gif" ALT="Overview"></a>
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| 22 | <a href="geometry.html">
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| 23 | <IMG SRC="../../../../resources/html/IconsGIF/Contents.gif" ALT="Contents"></a>
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| 24 | <a href="geomIntro.html">
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| 25 | <IMG SRC="../../../../resources/html/IconsGIF/Previous.gif" ALT="Previous"></a>
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| 26 | <a href="geomLogical.html">
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| 28 | </td>
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| 29 | <td ALIGN="Right">
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| 30 | <font SIZE="-1" COLOR="#238E23">
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| 31 | <b>Geant4 User's Guide</b>
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| 32 | <br>
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| 33 | <b>For Application Developers</b>
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| 34 | <br>
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| 35 | <b>Geometry</b>
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| 36 | </font>
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| 37 | </td>
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| 38 | </tr></table>
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| 39 | <br><br>
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| 40 |
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| 41 | <a name="4.1.2">
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| 42 | <h2>4.1.2 Solids</h2></a>
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| 43 |
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| 44 | <p>
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| 45 | The STEP standard supports multiple solid representations. Constructive
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| 46 | Solid Geometry (CSG) representations and Boundary Represented Solids (BREPs)
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| 47 | are available. Different representations are suitable for different
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| 48 | purposes, applications, required complexity, and levels of detail.
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| 49 | CSG representations are easy to use and normally give superior performance,
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| 50 | but they cannot reproduce complex solids such as those used in CAD systems.
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| 51 | BREP representations can handle more extended topologies and reproduce the
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| 52 | most complex solids, thus allowing the exchange of models with CAD systems.
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| 53 | <br>
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| 54 | All constructed solids can stream out their contents via appropriate methods
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| 55 | and streaming operators.
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| 56 | </p>
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| 57 |
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| 58 | <p>
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| 59 | For all solids it is possible to estimate the geometrical volume and the
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| 60 | surface area by invoking the methods:
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| 61 | <pre>
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| 62 | G4double GetCubicVolume()
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| 63 | G4double GetSurfaceArea()
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| 64 | </pre>
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| 65 | which return an estimate of the solid volume and total area in internal
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| 66 | units respectively. For elementary solids the functions compute the exact
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| 67 | geometrical quantities, while for composite or complex solids an estimate
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| 68 | is made using Monte Carlo techniques.
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| 69 | </p>
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| 70 |
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| 71 | <p>
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| 72 | For all solids it is also possible to generate pseudo-random points lying
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| 73 | on their surfaces, by invoking the method
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| 74 | <pre>
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| 75 | G4ThreeVector GetPointOnSurface() const
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| 76 | </pre>
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| 77 | which returns the generated point in local coordinates relative to the solid.
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| 78 | </p>
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| 79 |
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| 80 | <a name="4.1.2.1">
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| 81 | <H4>4.1.2.1 Constructed Solid Geometry (CSG) Solids</H4></a>
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| 82 |
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| 83 | CSG solids are defined directly as three-dimensional primitives. They are
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| 84 | described by a minimal set of parameters necessary to define the shape and
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| 85 | size of the solid. CSG solids are Boxes, Tubes and their sections, Cones
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| 86 | and their sections, Spheres, Wedges, and Toruses.
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| 87 | <P>
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| 88 | <HR width=40% align=center noshade>
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| 89 | </P>
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| 90 | To create a <b>box</b> one can use the constructor:
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| 91 |
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| 92 | <table border="0" width="100%" id="table1">
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| 93 | <tr>
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| 94 | <td width="480" valign="top">
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| 95 | <font face="Courier">
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| 96 | G4Box(const G4String& pName,<br>
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| 97 |
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| 98 | G4double pX,<br>
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| 99 |
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| 100 | G4double pY,<br>
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| 101 |
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| 102 | G4double pZ)
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| 103 | </font>
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| 104 | <P>
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| 105 | by giving the box a name and its half-lengths along the
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| 106 | X, Y and Z axis:
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| 107 | </P>
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| 108 | <P>
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| 109 | <table border=1 cellpadding=8>
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| 110 | <tr>
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| 111 | <td><tt>pX</tt><td>half length in X
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| 112 | <td><tt>pY</tt><td>half length in Y
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| 113 | <td><tt>pZ</tt><td>half length in Z
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| 114 | </tr>
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| 115 | </table>
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| 116 | </P>
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| 117 | <P>
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| 118 | This will create a box that extends from <tt>-pX</tt> to
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| 119 | <tt>+pX</tt> in X, from <tt>-pY</tt> to <tt>+pY</tt> in Y,
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| 120 | and from <tt>-pZ</tt> to <tt>+pZ</tt> in Z.
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| 121 | </P>
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| 122 | <P> </P><P> </P>
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| 123 | <P>
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| 124 | <div align="right"><font size=-1><I>
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| 125 | <U>In the picture</U>: pX = 30, pY = 40, pZ = 60
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| 126 | </I></font></div>
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| 127 | </P>
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| 128 | <P>
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| 129 | For example to create a box that is 2 by 6 by 10 centimeters
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| 130 | in full length, and called <tt>BoxA</tt> one should use the
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| 131 | following code:
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| 132 | </P>
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| 133 | </td>
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| 134 | <td>
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| 135 | <a href="javascript:remote_win(1)"
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| 136 | onMouseOver="window.status='Get alive picture...'; return true">
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| 137 | <img src="geometry.src/aBox.jpg" border=0></a>
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| 138 | </td>
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| 139 | </tr>
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| 140 | </table>
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| 141 |
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| 142 | <PRE>
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| 143 | G4Box* aBox = new G4Box("BoxA", 1.0*cm, 3.0*cm, 5.0*cm);
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| 144 | </PRE>
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| 145 | </P>
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| 146 | <P>
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| 147 | <HR width=40% align=center noshade>
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| 148 | </P>
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| 149 | <P>
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| 150 | <table border="0" width="100%" id="table2">
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| 151 | <tr>
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| 152 | <td width="480" valign="top">
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| 153 | Similarly to create a <b>cylindrical section</b> or <b>tube</b>,
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| 154 | one would use the constructor:
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| 155 | <P>
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| 156 | <font face="Courier">
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| 157 | G4Tubs(const G4String& pName,<br>
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| 158 |
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| 159 | G4double pRMin,<br>
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| 160 |
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| 161 | G4double pRMax,<br>
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| 162 |
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| 163 | G4double pDz,<br>
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| 164 |
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| 165 | G4double pSPhi,<br>
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| 166 |
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| 167 | G4double pDPhi)
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| 168 | </font>
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| 169 | <P> </P><P> </P><P> </P><P> </P>
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| 170 | <P>
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| 171 | <div align="right"><font size=-1><I>
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| 172 | <U>In the picture</U>: pRMin = 10, pRMax = 15, pDz = 20<br>
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| 173 | pSPhi = 0*Degree, pDPhi = 90*Degree
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| 174 | </I></font></div>
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| 175 | </P>
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| 176 | </td>
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| 177 | <td>
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| 178 | <a href="javascript:remote_win(2)"
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| 179 | onMouseOver="window.status='Get alive picture...'; return true">
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| 180 | <img src="geometry.src/aTubs.jpg" border=0 height=380></a>
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| 181 | </td>
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| 182 | </tr>
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| 183 | </table>
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| 184 |
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| 185 | giving its name <tt>pName</tt> and its parameters which are:</P>
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| 186 | <p>
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| 187 | <table border=1 cellpadding=8>
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| 188 | <tr>
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| 189 | <td><tt>pRMin</tt> <td>Inner radius
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| 190 | <td><tt>pRMax</tt> <td>Outer radius
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| 191 | <tr>
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| 192 | <td><tt>pDz</tt> <td> half length in z
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| 193 | <td><tt>pSPhi</tt> <td>the starting phi angle in radians
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| 194 | <tr>
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| 195 | <td><tt>pDPhi</tt> <td>the angle of the segment in radians
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| 196 | <td> <td>&n
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| 197 | </table>
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| 198 | </P>
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| 199 | <P>
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| 200 | <HR width=40% align=center noshade>
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| 201 | </P>
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| 202 | <P>
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| 203 | <table border="0" width="100%" id="table3">
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| 204 | <tr>
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| 205 | <td width="480" valign="top">
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| 206 | Similarly to create a <b>cone</b>, or <b>conical section</b>,
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| 207 | one would use the constructor:
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| 208 | <P>
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| 209 | <font face="Courier">
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| 210 | G4Cons(const G4String& pName,<br>
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| 211 |
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| 212 | G4double pRmin1,<br>
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| 213 |
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| 214 | G4double pRmax1,<br>
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| 215 |
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| 216 | G4double pRmin2,<br>
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| 217 |
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| 218 | G4double pRmax2,<br>
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| 219 |
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| 220 | G4double pDz,<br>
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| 221 |
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| 222 | G4double pSPhi,<br>
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| 223 |
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| 224 | G4double pDPhi)
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| 225 | </font>
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| 226 | <P>
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| 227 | <div align="right"><font size=-1><I>
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| 228 | <U>In the picture</U>: pRmin1 = 5, pRmax1 = 10,<br>
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| 229 | pRmin2 = 20, pRmax2 = 25<br>
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| 230 | pDz = 40, pSPhi = 0, pDPhi = 4/3*Pi
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| 231 | </I></font></div>
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| 232 | </P>
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| 233 | </td>
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| 234 | <td><a href="javascript:remote_win(3)"
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| 235 | onMouseOver="window.status='Get alive picture...'; return true">
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| 236 | <img src="geometry.src/aCons.jpg" border="0"></a>
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| 237 | </td>
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| 238 | </tr>
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| 239 | </table>
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| 240 |
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| 241 | giving its name <tt>pName</tt>, and its parameters which are:</P>
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| 242 | <P>
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| 243 | <table border=1 cellpadding=8>
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| 244 | <tr>
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| 245 | <TD><tt>pRmin1 <td>inside radius at <tt>-pDz</tt>
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| 246 | <TD><tt>pRmax1 <td>outside radius at <tt>-pDz</tt>
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| 247 | <tr>
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| 248 | <TD><tt>pRmin2 <td>inside radius at <tt>+pDz</tt>
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| 249 | <TD><tt>pRmax2 <td>outside radius at <tt>+pDz</tt>
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| 250 | <tr>
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| 251 | <TD><tt>pDz </tt> <td> half length in z
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| 252 | <TD><tt>pSPhi</tt> <td> starting angle of the segment in radians
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| 253 | <tr>
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| 254 | <TD><tt>pDPhi</tt> <td> the angle of the segment in radians
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| 255 | <td> <td>
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| 256 | </table>
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| 257 | </P>
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| 258 | <P>
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| 259 | <HR width=40% align=center noshade>
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| 260 | </P>
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| 261 | <P>
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| 262 | <table border="0" width="100%" id="table4">
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| 263 | <tr>
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| 264 | <td width="480" valign="top">
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| 265 | A <b>parallelepiped</b> is constructed using:
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| 266 | <P>
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| 267 | <font face="Courier">
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| 268 | G4Para(const G4String& pName,<br>
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| 269 |
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| 270 | G4double dx,<br>
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| 271 |
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| 272 | G4double dy,<br>
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| 273 |
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| 274 | G4double dz,<br>
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| 275 |
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| 276 | G4double alpha,<br>
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| 277 |
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| 278 | G4double theta,<br>
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| 279 |
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| 280 | G4double phi)
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| 281 | </font>
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| 282 | <P>
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| 283 | <div align="right"><font size=-1><I>
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| 284 | <U>In the picture</U>: dx = 30, dy = 40, dz = 60<br>
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| 285 | alpha = 10*Degree, theta = 20*Degree,<br>
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| 286 | phi = 5*Degree
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| 287 | </I></font></div>
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| 288 | </P>
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| 289 | </td>
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| 290 | <td><a href="javascript:remote_win(4)"
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| 291 | onMouseOver="window.status='Get alive picture...'; return true">
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| 292 | <img src="geometry.src/aPara.jpg" border="0"></a>
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| 293 | </td>
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| 294 | </tr>
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| 295 | </table>
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| 296 |
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| 297 | giving its name <tt>pName</tt> and its parameters which are:</P>
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| 298 | <P>
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| 299 | <table border=1 cellpadding=8>
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| 300 | <tr>
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| 301 | <TD><tt>dx,dy,dz</tt> <td> Half-length in x,y,z
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| 302 | <tr>
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| 303 | <TD valign=top><tt>alpha</tt> <td>Angle formed by the y axis and by the
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| 304 | plane joining the centre of the faces <i>parallel</i> to
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| 305 | the z-x plane at -dy and +dy
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| 306 | <tr>
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| 307 | <TD valign=top><tt>theta</tt> <td>Polar angle of the line joining the
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| 308 | centres of the faces at -dz and +dz in z
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| 309 | <tr>
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| 310 | <TD valign=top><tt>phi</tt> <td>Azimuthal angle of the line joining the
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| 311 | centres of the faces at -dz and +dz in z
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| 312 | </table>
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| 313 | </P>
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| 314 | <P>
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| 315 | <HR width=40% align=center noshade>
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| 316 | </P>
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| 317 | <P>
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| 318 | <table border="0" width="100%" id="table5">
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| 319 | <tr>
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| 320 | <td width="480" valign="top">
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| 321 | To construct a <b>trapezoid</b> use:
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| 322 | <P>
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| 323 | <font face="Courier">
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| 324 | G4Trd(const G4String& pName,<br>
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| 325 |
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| 326 | G4double dx1,<br>
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| 327 |
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| 328 | G4double dx2,<br>
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| 329 |
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| 330 | G4double dy1,<br>
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| 331 |
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| 332 | G4double dy2,<br>
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| 333 |
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| 334 | G4double dz)
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| 335 | </font>
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| 336 | <P> </P><P> </P>
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| 337 | <P>
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| 338 | <div align="right"><font size=-1><I>
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| 339 | <U>In the picture</U>: dx1 = 30, dx2 = 10<br>
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| 340 | dy1 = 40, dy2 = 15<br>
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| 341 | dz = 60
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| 342 | </I></font></div>
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| 343 | </P>
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| 344 | </td>
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| 345 | <td><a href="javascript:remote_win(5)"
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| 346 | onMouseOver="window.status='Get alive picture...'; return true">
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| 347 | <img src="geometry.src/aTrd.jpg" border="0"></a>
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| 348 | </td>
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| 349 | </tr>
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| 350 | </table>
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| 351 |
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| 352 | to obtain a solid with name <tt>pName</tt> and parameters</P>
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| 353 | <P>
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| 354 | <table border=1 cellpadding=8>
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| 355 | <tr>
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| 356 | <TD><tt>dx1</tt> <td>Half-length along x at the surface positioned at <tt>-dz</tt>
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| 357 | <tr>
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| 358 | <TD><tt>dx2</tt> <td>Half-length along x at the surface positioned at <tt>+dz</tt>
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| 359 | <tr>
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| 360 | <TD><tt>dy1</tt> <td>Half-length along y at the surface positioned at <tt>-dz</tt>
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| 361 | <tr>
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| 362 | <TD><tt>dy2</tt> <td>Half-length along y at the surface positioned at <tt>+dz</tt>
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| 363 | <tr>
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| 364 | <TD><tt>dz</tt> <td>Half-length along z axis
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| 365 | </table>
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| 366 | </P>
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| 367 | <P>
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| 368 | <HR width=40% align=center noshade>
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| 369 | </P>
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| 370 | <P>
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| 371 | <table border="0" width="100%" id="table6">
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| 372 | <tr>
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| 373 | <td width="480" valign="top">
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| 374 | To build a <b>generic trapezoid</b>, the <tt>G4Trap</tt> class is provided.
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| 375 | Here are the two costructors for a Right Angular Wedge and for the general
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| 376 | trapezoid for it:
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| 377 | <P>
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| 378 | <font face="Courier">
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| 379 | G4Trap(const G4String& pName,<br>
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| 380 |
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| 381 | G4double pZ,<br>
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| 382 |
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| 383 | G4double pY,<br>
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| 384 |
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| 385 | G4double pX,<br>
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| 386 |
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| 387 | G4double pLTX)
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| 388 | <P></P>
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| 389 | G4Trap(const G4String& pName,<br>
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| 390 |
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| 391 | G4double pDz,
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| 392 | G4double pTheta,<br>
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| 393 |
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| 394 | G4double pPhi,
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| 395 | G4double pDy1,<br>
|
|---|
| 396 |
|
|---|
| 397 | G4double pDx1,
|
|---|
| 398 | G4double pDx2,<br>
|
|---|
| 399 |
|
|---|
| 400 | G4double pAlp1,
|
|---|
| 401 | G4double pDy2,<br>
|
|---|
| 402 |
|
|---|
| 403 | G4double pDx3,
|
|---|
| 404 | G4double pDx4,<br>
|
|---|
| 405 |
|
|---|
| 406 | G4double pAlp2)
|
|---|
| 407 | </font>
|
|---|
| 408 | <P>
|
|---|
| 409 | <div align="right"><font size=-1><I>
|
|---|
| 410 | <U>In the picture</U>: pDx1 = 30, pDx2 = 40, pDy1 = 40<br>
|
|---|
| 411 | pDx3 = 10, pDx4 = 14, pDy2 = 16<br>
|
|---|
| 412 | pDz = 60, pTheta = 20*Degree<br>
|
|---|
| 413 | pDphi = 5*Degree, pAlph1 = pAlph2 = 10*Degree
|
|---|
| 414 | </I></font></div>
|
|---|
| 415 | </P>
|
|---|
| 416 | </td>
|
|---|
| 417 | <td><a href="javascript:remote_win(6)"
|
|---|
| 418 | onMouseOver="window.status='Get alive picture...'; return true">
|
|---|
| 419 | <img src="geometry.src/aTrap.jpg" border="0"></a>
|
|---|
| 420 | </td>
|
|---|
| 421 | </tr>
|
|---|
| 422 | </table>
|
|---|
| 423 |
|
|---|
| 424 | to obtain a Right Angular Wedge with name <tt>pName</tt> and parameters:</P>
|
|---|
| 425 | <p>
|
|---|
| 426 | <table border=1 cellpadding=8>
|
|---|
| 427 | <tr>
|
|---|
| 428 | <TD><tt>pZ</tt> <td>Length along z
|
|---|
| 429 | <tr>
|
|---|
| 430 | <TD><tt>pY</tt> <td>Length along y
|
|---|
| 431 | <tr>
|
|---|
| 432 | <TD><tt>pX</tt> <td>Length along x at the wider side
|
|---|
| 433 | <tr>
|
|---|
| 434 | <TD><tt>pLTX</tt> <td>Length along x at the narrower side (<tt>plTX<=pX</tt>)
|
|---|
| 435 | </table>
|
|---|
| 436 | </P>
|
|---|
| 437 | <p>
|
|---|
| 438 | or to obtain the general trapezoid (see the Software Reference Manual):
|
|---|
| 439 | </p>
|
|---|
| 440 | <table border=1 cellpadding=8 id="table31">
|
|---|
| 441 | <tr>
|
|---|
| 442 | <td><tt>pDx1</tt><td>Half x length at y=-pDy
|
|---|
| 443 | <tr>
|
|---|
| 444 | <td><tt>pDx2</tt><td>Half x length at y=+pDy
|
|---|
| 445 | <tr>
|
|---|
| 446 | <td><tt>pDy</tt><td>Half y length
|
|---|
| 447 | <tr>
|
|---|
| 448 | <td><tt>pDz</tt><td>Half z length
|
|---|
| 449 | <tr>
|
|---|
| 450 | <td><tt>pTheta</tt><td>Polar angle of the line joining the centres of the faces at -/+pDz
|
|---|
| 451 | <tr>
|
|---|
| 452 | <td><tt>pDy1</tt><td>Half y length at -pDz
|
|---|
| 453 | <tr>
|
|---|
| 454 | <td><tt>pDx1</tt><td>Half x length at -pDz, y=-pDy1
|
|---|
| 455 | <tr>
|
|---|
| 456 | <td><tt>pDx2</tt><td>Half x length at -pDz, y=+pDy1
|
|---|
| 457 | <tr>
|
|---|
| 458 | <td><tt>pDy2</tt><td>Half y length at +pDz
|
|---|
| 459 | <tr>
|
|---|
| 460 | <td><tt>pDx3</tt><td>Half x length at +pDz, y=-pDy2
|
|---|
| 461 | <tr>
|
|---|
| 462 | <td><tt>pDx4</tt><td>Half x length at +pDz, y=+pDy2
|
|---|
| 463 | <tr>
|
|---|
| 464 | <td><tt>pAlph1</tt><td>Angle with respect to the y axis from the centre of the side
|
|---|
| 465 | (lower endcap)</tr>
|
|---|
| 466 | <tr>
|
|---|
| 467 | <td><tt>pAlph2</tt><td>Angle with respect to the y axis from the centre of the side
|
|---|
| 468 | (upper endcap)</table>
|
|---|
| 469 | <P>
|
|---|
| 470 | <B>Note on <tt>pAlph1/2</tt></B>:
|
|---|
| 471 | the two angles have to be the same due to the planarity condition.
|
|---|
| 472 | </P>
|
|---|
| 473 | <P>
|
|---|
| 474 | <HR width=40% align=center noshade>
|
|---|
| 475 | </P>
|
|---|
| 476 | <P>
|
|---|
| 477 | <table border="0" width="100%" id="table7">
|
|---|
| 478 | <tr>
|
|---|
| 479 | <td width="480" valign="top">
|
|---|
| 480 | To build a <b>sphere</b>, or a <b>spherical shell section</b>, use:
|
|---|
| 481 | <P>
|
|---|
| 482 | <font face="Courier">
|
|---|
| 483 | G4Sphere(const G4String& pName,<br>
|
|---|
| 484 |
|
|---|
| 485 | G4double pRmin,<br>
|
|---|
| 486 |
|
|---|
| 487 | G4double pRmax,<br>
|
|---|
| 488 |
|
|---|
| 489 | G4double pSPhi,<br>
|
|---|
| 490 |
|
|---|
| 491 | G4double pDPhi,<br>
|
|---|
| 492 |
|
|---|
| 493 | G4double pSTheta,<br>
|
|---|
| 494 |
|
|---|
| 495 | G4double pDTheta )
|
|---|
| 496 | </font>
|
|---|
| 497 | <P>
|
|---|
| 498 | <div align="right"><font size=-1><I>
|
|---|
| 499 | <U>In the picture</U>: pRmin = 100, pRmax = 120<br>
|
|---|
| 500 | pSPhi = 0*Degree, pDPhi = 180*Degree<br>
|
|---|
| 501 | pSTheta = 0 Degree, pDTheta = 180*Degree
|
|---|
| 502 | </I></font>
|
|---|
| 503 | </P>
|
|---|
| 504 | </td>
|
|---|
| 505 | <td><a href="javascript:remote_win(7)"
|
|---|
| 506 | onMouseOver="window.status='Get alive picture...'; return true">
|
|---|
| 507 | <img src="geometry.src/aSphere.jpg" border="0"></a>
|
|---|
| 508 | </td>
|
|---|
| 509 | </tr>
|
|---|
| 510 | </table>
|
|---|
| 511 |
|
|---|
| 512 | to obtain a solid with name <tt>pName</tt> and parameters:</P>
|
|---|
| 513 | <p>
|
|---|
| 514 | <table border=1 cellpadding=8>
|
|---|
| 515 | <tr>
|
|---|
| 516 | <TD><tt>pRmin</tt> <td>Inner radius
|
|---|
| 517 | <tr>
|
|---|
| 518 | <TD><tt>pRmax</tt> <td>Outer radius
|
|---|
| 519 | <tr>
|
|---|
| 520 | <TD><tt>pSPhi</tt> <td>Starting Phi angle of the segment in radians
|
|---|
| 521 | <tr>
|
|---|
| 522 | <TD><tt>pDPhi</tt> <td>Delta Phi angle of the segment in radians
|
|---|
| 523 | <tr>
|
|---|
| 524 | <TD><tt>pSTheta</tt> <td>Starting Theta angle of the segment in radians
|
|---|
| 525 | <tr>
|
|---|
| 526 | <TD><tt>pDTheta</tt> <td>Delta Theta angle of the segment in radians
|
|---|
| 527 | </table>
|
|---|
| 528 | </p>
|
|---|
| 529 | <P>
|
|---|
| 530 | <HR width=40% align=center noshade>
|
|---|
| 531 | </P>
|
|---|
| 532 | <P>
|
|---|
| 533 | <table border="0" width="100%" id="table29">
|
|---|
| 534 | <tr>
|
|---|
| 535 | <td width="480" valign="top">
|
|---|
| 536 | To build a <b>full solid sphere</b> use:
|
|---|
| 537 | <P>
|
|---|
| 538 | <font face="Courier">
|
|---|
| 539 | G4Orb(const G4String& pName, <br>
|
|---|
| 540 |
|
|---|
| 541 | G4double pRmax)
|
|---|
| 542 | </font>
|
|---|
| 543 | <P>
|
|---|
| 544 | <div align="right"><font size=-1><I>
|
|---|
| 545 | <U>In the picture</U>: pRmax = 100
|
|---|
| 546 | </I></font></div>
|
|---|
| 547 | </P>
|
|---|
| 548 | <P>
|
|---|
| 549 | The Orb can be obtained from a Sphere with:<br>
|
|---|
| 550 | <tt>pRmin</tt> = 0, <tt>pSPhi</tt> = 0, <tt>pDPhi</tt> = 2*Pi,
|
|---|
| 551 | <tt>pSTheta</tt> = 0, <tt>pDTheta</tt> = Pi.
|
|---|
| 552 | </p>
|
|---|
| 553 |
|
|---|
| 554 | <table border=1 cellpadding=8 id="table30">
|
|---|
| 555 | <tr>
|
|---|
| 556 | <TD><tt>pRmax</tt> <td>Outer radius
|
|---|
| 557 | </tr>
|
|---|
| 558 | </table>
|
|---|
| 559 | </td>
|
|---|
| 560 | <td><a href="javascript:remote_win(8)"
|
|---|
| 561 | onMouseOver="window.status='Get alive picture...'; return true">
|
|---|
| 562 | <img src="geometry.src/aOrb.jpg" border="0"></a>
|
|---|
| 563 |
|
|---|
| 564 | </td>
|
|---|
| 565 | </tr>
|
|---|
| 566 | </table>
|
|---|
| 567 | </P>
|
|---|
| 568 | <P>
|
|---|
| 569 | <HR width=40% align=center noshade>
|
|---|
| 570 | </P>
|
|---|
| 571 | <P>
|
|---|
| 572 | <table border="0" width="100%" id="table8">
|
|---|
| 573 | <tr>
|
|---|
| 574 | <td width="480" valign="top">
|
|---|
| 575 | To build a <b>torus</b> use:
|
|---|
| 576 | <P>
|
|---|
| 577 | <font face="Courier">
|
|---|
| 578 | G4Torus(const G4String& pName,<br>
|
|---|
| 579 |
|
|---|
| 580 | G4double pRmin,<br>
|
|---|
| 581 |
|
|---|
| 582 | G4double pRmax,<br>
|
|---|
| 583 |
|
|---|
| 584 | G4double pRtor,<br>
|
|---|
| 585 |
|
|---|
| 586 | G4double pSPhi,<br>
|
|---|
| 587 |
|
|---|
| 588 | G4double pDPhi)
|
|---|
| 589 | </font>
|
|---|
| 590 | <P>
|
|---|
| 591 | <div align="right"><font size=-1><I>
|
|---|
| 592 | <U>In the picture</U>: pRmin = 40, pRmax = 60, pRtor = 200<br>
|
|---|
| 593 | pSPhi = 0, pDPhi = 90*Degree
|
|---|
| 594 | </I></font></div>
|
|---|
| 595 | </P>
|
|---|
| 596 | </td>
|
|---|
| 597 | <td><a href="javascript:remote_win(9)"
|
|---|
| 598 | onMouseOver="window.status='Get alive picture...'; return true">
|
|---|
| 599 | <img src="geometry.src/aTorus.jpg" border="0"></a>
|
|---|
| 600 | </td>
|
|---|
| 601 | </tr>
|
|---|
| 602 | </table>
|
|---|
| 603 |
|
|---|
| 604 | to obtain a solid with name <tt>pName</tt> and parameters:</P>
|
|---|
| 605 | <p>
|
|---|
| 606 | <table border=1 cellpadding=8>
|
|---|
| 607 | <tr>
|
|---|
| 608 | <TD><tt>pRmin</tt> <td>Inside radius
|
|---|
| 609 | <tr>
|
|---|
| 610 | <TD><tt>pRmax</tt> <td>Outside radius
|
|---|
| 611 | <tr>
|
|---|
| 612 | <TD><tt>pRtor</tt> <td>Swept radius of torus
|
|---|
| 613 | <tr>
|
|---|
| 614 | <TD><tt>pSPhi</tt> <td>Starting Phi angle in radians
|
|---|
| 615 | (<tt>fSPhi+fDPhi<=2PI</tt>, <tt>fSPhi>-2PI</tt>)
|
|---|
| 616 | <tr>
|
|---|
| 617 | <TD><tt>pDPhi</tt> <td>Delta angle of the segment in radians
|
|---|
| 618 | </table>
|
|---|
| 619 | </P>
|
|---|
| 620 | <P>
|
|---|
| 621 | In addition, the Geant4 Design Documentation shows in the Solids Class Diagram
|
|---|
| 622 | the complete list of CSG classes, and the STEP documentation contains a
|
|---|
| 623 | detailed EXPRESS description of each CSG solid.</P>
|
|---|
| 624 |
|
|---|
| 625 | <P></P>
|
|---|
| 626 |
|
|---|
| 627 | <b>Specific CSG Solids</b>
|
|---|
| 628 | <P>
|
|---|
| 629 | <b>Polycons</b> (PCON) are implemented in Geant4 through the
|
|---|
| 630 | <tt>G4Polycon</tt> class:
|
|---|
| 631 | </P>
|
|---|
| 632 | <table border="0" width="100%" id="table9">
|
|---|
| 633 | <tr>
|
|---|
| 634 | <td width="480" valign="top">
|
|---|
| 635 | <font face="Courier">
|
|---|
| 636 | G4Polycone(const G4String& pName,<br>
|
|---|
| 637 |
|
|---|
| 638 | G4double phiStart,<br>
|
|---|
| 639 |
|
|---|
| 640 | G4double phiTotal,<br>
|
|---|
| 641 |
|
|---|
| 642 | G4int numZPlanes,<br>
|
|---|
| 643 |
|
|---|
| 644 | const G4double zPlane[],<br>
|
|---|
| 645 |
|
|---|
| 646 | const G4double rInner[],<br>
|
|---|
| 647 |
|
|---|
| 648 | const G4double rOuter[])<br>
|
|---|
| 649 | <br>
|
|---|
| 650 | G4Polycone(const G4String& pName, <br>
|
|---|
| 651 |
|
|---|
| 652 | G4double phiStart,<br>
|
|---|
| 653 |
|
|---|
| 654 | G4double phiTotal,<br>
|
|---|
| 655 |
|
|---|
| 656 | G4int numRZ,<br>
|
|---|
| 657 |
|
|---|
| 658 | const G4double r[],<br>
|
|---|
| 659 |
|
|---|
| 660 | const G4double z[])
|
|---|
| 661 | </font>
|
|---|
| 662 | <P>
|
|---|
| 663 | <div align="right"><font size=-1><I>
|
|---|
| 664 | <U>In the picture</U>: phiStart = 0*Degree, phiTotal = 2*Pi<br>
|
|---|
| 665 | numZPlanes = 9<br>
|
|---|
| 666 | rInner = { 0, 0, 0, 0, 0, 0, 0, 0, 0}<br>
|
|---|
| 667 | rOuter = { 0, 10, 10, 5 , 5, 10 , 10 , 2, 2}<br>
|
|---|
| 668 | z = { 5, 7, 9, 11, 25, 27, 29, 31, 35 }
|
|---|
| 669 | </I></font></div>
|
|---|
| 670 | </P>
|
|---|
| 671 | </td>
|
|---|
| 672 | <td><a href="javascript:remote_win(10)"
|
|---|
| 673 | onMouseOver="window.status='Get alive picture...'; return true">
|
|---|
| 674 | <img src="geometry.src/aBREPSolidPCone.jpg" border="0"></a>
|
|---|
| 675 | </td>
|
|---|
| 676 | </tr>
|
|---|
| 677 | </table>
|
|---|
| 678 |
|
|---|
| 679 | where:
|
|---|
| 680 | <p>
|
|---|
| 681 | <table border=1 cellpadding=8>
|
|---|
| 682 | <tr>
|
|---|
| 683 | <TD><tt>phiStart</tt> <td>Initial Phi starting angle
|
|---|
| 684 | <tr>
|
|---|
| 685 | <TD><tt>phiTotal</tt> <td>Total Phi angle
|
|---|
| 686 | <tr>
|
|---|
| 687 | <TD><tt>numZPlanes</tt> <td>Number of z planes
|
|---|
| 688 | <tr>
|
|---|
| 689 | <TD><tt>numRZ</tt> <td>Number of corners in r,z space
|
|---|
| 690 | <tr>
|
|---|
| 691 | <TD><tt>zPlane</tt> <td>Position of z planes
|
|---|
| 692 | <tr>
|
|---|
| 693 | <TD><tt>rInner</tt> <td>Tangent distance to inner surface
|
|---|
| 694 | <tr>
|
|---|
| 695 | <TD><tt>rOuter</tt> <td>Tangent distance to outer surface
|
|---|
| 696 | <tr>
|
|---|
| 697 | <TD><tt>r</tt> <td>r coordinate of corners
|
|---|
| 698 | <tr>
|
|---|
| 699 | <TD><tt>z</tt> <td>z coordinate of corners
|
|---|
| 700 | </table>
|
|---|
| 701 | </P>
|
|---|
| 702 | <P>
|
|---|
| 703 | <HR width=40% align=center noshade>
|
|---|
| 704 | </P>
|
|---|
| 705 | <P>
|
|---|
| 706 | <b>Polyhedra</b> (PGON) are implemented through <tt>G4Polyhedra</tt>:
|
|---|
| 707 | </P>
|
|---|
| 708 | <table border="0" width="100%" id="table10">
|
|---|
| 709 | <tr>
|
|---|
| 710 | <td width="480" valign="top">
|
|---|
| 711 | <font face="Courier">
|
|---|
| 712 | G4Polyhedra(const G4String& pName,<br>
|
|---|
| 713 |
|
|---|
| 714 | G4double phiStart,<br>
|
|---|
| 715 |
|
|---|
| 716 | G4double phiTotal,<br>
|
|---|
| 717 |
|
|---|
| 718 | G4int numSide,<br>
|
|---|
| 719 |
|
|---|
| 720 | G4int numZPlanes,<br>
|
|---|
| 721 |
|
|---|
| 722 | const G4double zPlane[],<br>
|
|---|
| 723 |
|
|---|
| 724 | const G4double rInner[],<br>
|
|---|
| 725 |
|
|---|
| 726 | const G4double rOuter[] )<br>
|
|---|
| 727 | <br>
|
|---|
| 728 | G4Polyhedra(const G4String& pName,<br>
|
|---|
| 729 |
|
|---|
| 730 | G4double phiStart,<br>
|
|---|
| 731 |
|
|---|
| 732 | G4double phiTotal,<br>
|
|---|
| 733 |
|
|---|
| 734 | G4int numSide,<br>
|
|---|
| 735 |
|
|---|
| 736 | G4int numRZ,<br>
|
|---|
| 737 |
|
|---|
| 738 | const G4double r[],<br>
|
|---|
| 739 |
|
|---|
| 740 | const G4double z[])
|
|---|
| 741 | </font>
|
|---|
| 742 | <P>
|
|---|
| 743 | <div align="right"><font size=-1><I>
|
|---|
| 744 | <U>In the picture</U>: phiStart = 0, phiTotal= 2 Pi<br>
|
|---|
| 745 | numSide = 5, nunZPlanes = 7<br>
|
|---|
| 746 | rInner = { 0, 0, 0, 0, 0, 0, 0 }<br>
|
|---|
| 747 | rOuter = { 0, 15, 15, 4, 4, 10, 10 }<br>
|
|---|
| 748 | z = { 0, 5, 8, 13 , 30, 32, 35 }
|
|---|
| 749 | </I></font></div>
|
|---|
| 750 | </P>
|
|---|
| 751 | </td>
|
|---|
| 752 | <td><a href="javascript:remote_win(11)"
|
|---|
| 753 | onMouseOver="window.status='Get alive picture...'; return true">
|
|---|
| 754 | <img src="geometry.src/aBREPSolidPolyhedra.jpg" border="0"></a>
|
|---|
| 755 | </td>
|
|---|
| 756 | </tr>
|
|---|
| 757 | </table>
|
|---|
| 758 |
|
|---|
| 759 | where:
|
|---|
| 760 | <p>
|
|---|
| 761 | <table border=1 cellpadding=8>
|
|---|
| 762 | <tr>
|
|---|
| 763 | <TD><tt>phiStart</tt> <td>Initial Phi starting angle
|
|---|
| 764 | <tr>
|
|---|
| 765 | <TD><tt>phiTotal</tt> <td>Total Phi angle
|
|---|
| 766 | <tr>
|
|---|
| 767 | <TD><tt>numSide</tt> <td>Number of sides
|
|---|
| 768 | <tr>
|
|---|
| 769 | <TD><tt>numZPlanes</tt> <td>Number of z planes
|
|---|
| 770 | <tr>
|
|---|
| 771 | <TD><tt>numRZ</tt> <td>Number of corners in r,z space
|
|---|
| 772 | <tr>
|
|---|
| 773 | <TD><tt>zPlane</tt> <td>Position of z planes
|
|---|
| 774 | <tr>
|
|---|
| 775 | <TD><tt>rInner</tt> <td>Tangent distance to inner surface
|
|---|
| 776 | <tr>
|
|---|
| 777 | <TD><tt>rOuter</tt> <td>Tangent distance to outer surface
|
|---|
| 778 | <tr>
|
|---|
| 779 | <TD><tt>r</tt> <td>r coordinate of corners
|
|---|
| 780 | <tr>
|
|---|
| 781 | <TD><tt>z</tt> <td>z coordinate of corners
|
|---|
| 782 | </table>
|
|---|
| 783 | </P>
|
|---|
| 784 | <P>
|
|---|
| 785 | <HR width=40% align=center noshade>
|
|---|
| 786 | </P>
|
|---|
| 787 | <P>
|
|---|
| 788 |
|
|---|
| 789 | <table border="0" width="100%" id="table11">
|
|---|
| 790 | <tr>
|
|---|
| 791 | <td width="480" valign="top">
|
|---|
| 792 | A <b>tube with an elliptical cross section</b> (ELTU) can be defined
|
|---|
| 793 | as follows:
|
|---|
| 794 | <P>
|
|---|
| 795 | <font face="Courier">
|
|---|
| 796 | G4EllipticalTube(const G4String& pName,<br>
|
|---|
| 797 |
|
|---|
| 798 | G4double Dx,<br>
|
|---|
| 799 |
|
|---|
| 800 | G4double Dy,<br>
|
|---|
| 801 |
|
|---|
| 802 | G4double Dz)
|
|---|
| 803 | </font>
|
|---|
| 804 | <P>
|
|---|
| 805 | The equation of the surface in x/y is
|
|---|
| 806 | <tt>1.0 = (x/dx)**2 + (y/dy)**2</tt>
|
|---|
| 807 | </P>
|
|---|
| 808 | <P>
|
|---|
| 809 | <table border=1 cellpadding=8 width="455" id="table23">
|
|---|
| 810 | <tr>
|
|---|
| 811 | <td><tt>Dx</tt><td>Half length X
|
|---|
| 812 | <td><tt>Dy</tt><td>Half length Y
|
|---|
| 813 | <td><tt>Dz</tt><td>Half length Z
|
|---|
| 814 | </table></P>
|
|---|
| 815 | <P> </P><P> </P><P> </P><P> </P>
|
|---|
| 816 | <div align="right"><font size=-1><I>
|
|---|
| 817 | <U>In the picture</U>: Dx = 5, Dy = 10, Dz = 20
|
|---|
| 818 | </I></font></div>
|
|---|
| 819 | </td>
|
|---|
| 820 | <td><a href="javascript:remote_win(12)"
|
|---|
| 821 | onMouseOver="window.status='Get alive picture...'; return true">
|
|---|
| 822 | <img src="geometry.src/aEllipticalTube.jpg" border="0"></a>
|
|---|
| 823 | </td>
|
|---|
| 824 | </tr>
|
|---|
| 825 | </table>
|
|---|
| 826 | </P>
|
|---|
| 827 | <P>
|
|---|
| 828 | <HR width=40% align=center noshade>
|
|---|
| 829 | </P>
|
|---|
| 830 | <table border="0" width="100%" id="table17">
|
|---|
| 831 | <tr>
|
|---|
| 832 | <td width="480" valign="top">
|
|---|
| 833 | The general <b>ellipsoid</b> with possible cut in <tt>Z</tt> can be
|
|---|
| 834 | defined as follows:
|
|---|
| 835 | <P>
|
|---|
| 836 | <font face="Courier">
|
|---|
| 837 | G4Ellipsoid(const G4String& pName,<br>
|
|---|
| 838 |
|
|---|
| 839 | G4double pxSemiAxis,<br>
|
|---|
| 840 |
|
|---|
| 841 | G4double pySemiAxis,<br>
|
|---|
| 842 |
|
|---|
| 843 | G4double pzSemiAxis,<br>
|
|---|
| 844 |
|
|---|
| 845 | G4double pzBottomCut=0,<br>
|
|---|
| 846 |
|
|---|
| 847 | G4double pzTopCut=0)
|
|---|
| 848 | </font>
|
|---|
| 849 | <P> </P><P> </P><P> </P>
|
|---|
| 850 | <div align="right"><font size=-1><I>
|
|---|
| 851 | <U>In the picture</U>: pxSemiAxis = 10, pySemiAxis = 20, pzSemiAxis = 50<br>
|
|---|
| 852 | pzBottomCut = -10, pzTopCut = 40
|
|---|
| 853 | </I></font></div>
|
|---|
| 854 | </td>
|
|---|
| 855 | <td><a href="javascript:remote_win(13)"
|
|---|
| 856 | onMouseOver="window.status='Get alive picture...'; return true">
|
|---|
| 857 | <img src="geometry.src/aEllipsoid.jpg" border="0"></a>
|
|---|
| 858 | </td>
|
|---|
| 859 | </tr>
|
|---|
| 860 | </table>
|
|---|
| 861 |
|
|---|
| 862 | A general (or triaxial) ellipsoid is a quadratic surface which is given in
|
|---|
| 863 | Cartesian coordinates by:
|
|---|
| 864 | <p>
|
|---|
| 865 |
|
|---|
| 866 | <tt>1.0 = (x/pxSemiAxis)**2 + (y/pySemiAxis)**2 + (z/pzSemiAxis)**2</tt>
|
|---|
| 867 | </p>
|
|---|
| 868 | where:
|
|---|
| 869 | <P>
|
|---|
| 870 | <table border=1 cellpadding=8 id="table26">
|
|---|
| 871 | <tr>
|
|---|
| 872 | <TD><tt>pxSemiAxis</tt><td>Semiaxis in X
|
|---|
| 873 | <tr>
|
|---|
| 874 | <TD><tt>pySemiAxis</tt> <td>Semiaxis in Y
|
|---|
| 875 | <tr>
|
|---|
| 876 | <TD><tt>pzSemiAxis</tt><td>Semiaxis in Z
|
|---|
| 877 | <tr>
|
|---|
| 878 | <TD><tt>pzBottomCut</tt> <td>lower cut plane level, z<tr>
|
|---|
| 879 | <TD><tt>pzTopCut</tt><td>upper cut plane level, z
|
|---|
| 880 | </table>
|
|---|
| 881 | </P>
|
|---|
| 882 | <P>
|
|---|
| 883 | <HR width=40% align=center noshade>
|
|---|
| 884 | </P>
|
|---|
| 885 | <P>
|
|---|
| 886 | A <b>cone with an elliptical cross section</b> can be defined as follows:
|
|---|
| 887 | <P>
|
|---|
| 888 | <table border="0" width="100%" id="table24">
|
|---|
| 889 | <tr>
|
|---|
| 890 | <td width="480" valign="top">
|
|---|
| 891 | <font face="Courier">
|
|---|
| 892 | G4EllipticalCone(const G4String& pName,<br>
|
|---|
| 893 |
|
|---|
| 894 | G4double pxSemiAxis,<br>
|
|---|
| 895 |
|
|---|
| 896 | G4double pySemiAxis,<br>
|
|---|
| 897 |
|
|---|
| 898 | G4double zMax,<br>
|
|---|
| 899 |
|
|---|
| 900 | G4double pzTopCut)
|
|---|
| 901 | </font>
|
|---|
| 902 | <P> </P>
|
|---|
| 903 | <div align="right"><font size=-1><I>
|
|---|
| 904 | <U>In the picture</U>: pxSemiAxis = 30, pySemiAxis = 60<br>
|
|---|
| 905 | zMax = 50, pzTopCut = 25
|
|---|
| 906 | </I></font></div>
|
|---|
| 907 | </td>
|
|---|
| 908 | <td><a href="javascript:remote_win(14)"
|
|---|
| 909 | onMouseOver="window.status='Get alive picture...'; return true">
|
|---|
| 910 | <img src="geometry.src/aEllipticalCone.jpg" border="0"></a>
|
|---|
| 911 | </td>
|
|---|
| 912 | </tr>
|
|---|
| 913 | </table>
|
|---|
| 914 | </P>
|
|---|
| 915 |
|
|---|
| 916 | where:
|
|---|
| 917 | <P>
|
|---|
| 918 | <table border=1 cellpadding=8 id="table25">
|
|---|
| 919 | <tr>
|
|---|
| 920 | <TD><tt>pxSemiAxis</tt><td>Semiaxis in X
|
|---|
| 921 | <tr>
|
|---|
| 922 | <TD><tt>pySemiAxis</tt> <td>Semiaxis in Y
|
|---|
| 923 | <tr>
|
|---|
| 924 | <TD><tt>zMax</tt> <td>Height of elliptical cone<tr>
|
|---|
| 925 | <TD><tt>pzTopCut</tt> <td>upper cut plane level
|
|---|
| 926 | </table>
|
|---|
| 927 | </P>
|
|---|
| 928 | <P>
|
|---|
| 929 | An elliptical cone of height <tt>zMax</tt>, semiaxis <tt>pxSemiAxis</tt>,
|
|---|
| 930 | and semiaxis <tt>pySemiAxis</tt> is given by the parametric equations:
|
|---|
| 931 | <P>
|
|---|
| 932 |
|
|---|
| 933 | <tt>x = pxSemiAxis * ( zMax - u ) / u * Cos(v)</tt><br>
|
|---|
| 934 |
|
|---|
| 935 | <tt>y = pySemiAxis * ( zMax - u ) / u * Sin(v)</tt><br>
|
|---|
| 936 |
|
|---|
| 937 | <tt>z = u</tt>
|
|---|
| 938 | </P>
|
|---|
| 939 | <P>
|
|---|
| 940 | Where <tt>v</tt> is between <tt>0</tt> and <tt>2*Pi</tt>,
|
|---|
| 941 | and <tt>u</tt> between <tt>0</tt> and <tt>h</tt> respectively.
|
|---|
| 942 | </P>
|
|---|
| 943 | <P>
|
|---|
| 944 | <HR width=40% align=center noshade>
|
|---|
| 945 | </P>
|
|---|
| 946 | <table border="0" width="100%" id="table12">
|
|---|
| 947 | <tr>
|
|---|
| 948 | <td width="480" valign="top">
|
|---|
| 949 | A <b>tube with a hyperbolic profile</b> (HYPE) can be defined as follows:
|
|---|
| 950 | <P>
|
|---|
| 951 | <font face="Courier">
|
|---|
| 952 | G4Hype(const G4String& pName,<br>
|
|---|
| 953 |
|
|---|
| 954 | G4double innerRadius,<br>
|
|---|
| 955 |
|
|---|
| 956 | G4double outerRadius,<br>
|
|---|
| 957 |
|
|---|
| 958 | G4double innerStereo,<br>
|
|---|
| 959 |
|
|---|
| 960 | G4double outerStereo,<br>
|
|---|
| 961 |
|
|---|
| 962 | G4double halfLenZ)
|
|---|
| 963 | </font>
|
|---|
| 964 | <div align="right"><font size=-1><I>
|
|---|
| 965 | <U>In the picture</U>: innerStereo = 0.7, outerStereo = 0.7<br>
|
|---|
| 966 | halfLenZ = 50<br>
|
|---|
| 967 | innerRadius = 20, outerRadius = 30
|
|---|
| 968 | </I></font></div>
|
|---|
| 969 | </td>
|
|---|
| 970 | <td><a href="javascript:remote_win(15)"
|
|---|
| 971 | onMouseOver="window.status='Get alive picture...'; return true">
|
|---|
| 972 | <img src="geometry.src/aHyperboloid.jpg" border="0"></a>
|
|---|
| 973 | </td>
|
|---|
| 974 | </tr>
|
|---|
| 975 | </table>
|
|---|
| 976 | <P>
|
|---|
| 977 | <tt>G4Hype</tt> is shaped with curved sides parallel to the <tt>z</tt>-axis,
|
|---|
| 978 | has a specified half-length along the <tt>z</tt> axis about which it is
|
|---|
| 979 | centred, and a given minimum and maximum radius.<BR>
|
|---|
| 980 | A minimum radius of <tt>0</tt> defines a filled Hype (with hyperbolic
|
|---|
| 981 | inner surface), i.e. inner radius = 0 AND inner stereo angle = 0.<BR>
|
|---|
| 982 | The inner and outer hyperbolic surfaces can have different
|
|---|
| 983 | stereo angles. A stereo angle of <tt>0</tt> gives a cylindrical surface:</P>
|
|---|
| 984 | <P>
|
|---|
| 985 | <table border=1 cellpadding=8>
|
|---|
| 986 | <tr>
|
|---|
| 987 | <td><tt>innerRadius</tt><td>Inner radius
|
|---|
| 988 | <tr>
|
|---|
| 989 | <td><tt>outerRadius</tt><td>Outer radius
|
|---|
| 990 | <tr>
|
|---|
| 991 | <td><tt>innerStereo</tt><td>Inner stereo angle in radians
|
|---|
| 992 | <tr>
|
|---|
| 993 | <td><tt>outerStereo</tt><td>Outer stereo angle in radians
|
|---|
| 994 | <tr>
|
|---|
| 995 | <td><tt>halfLenZ</tt><td>Half length in Z
|
|---|
| 996 | </table>
|
|---|
| 997 | </P>
|
|---|
| 998 | <P>
|
|---|
| 999 | <HR width=40% align=center noshade>
|
|---|
| 1000 | </P>
|
|---|
| 1001 | <P>
|
|---|
| 1002 | <table border="0" width="100%" id="table27">
|
|---|
| 1003 | <tr>
|
|---|
| 1004 | <td width="480" valign="top">
|
|---|
| 1005 | A <b>tetrahedra</b> solid can be defined as follows:
|
|---|
| 1006 | <P>
|
|---|
| 1007 | <font face="Courier">
|
|---|
| 1008 | G4Tet(const G4String& pName,<br>
|
|---|
| 1009 |
|
|---|
| 1010 | G4ThreeVector anchor,<br>
|
|---|
| 1011 |
|
|---|
| 1012 | G4ThreeVector p2,<br>
|
|---|
| 1013 |
|
|---|
| 1014 | G4ThreeVector p3,<br>
|
|---|
| 1015 |
|
|---|
| 1016 | G4ThreeVector p4,<br>
|
|---|
| 1017 |
|
|---|
| 1018 | G4bool *degeneracyFlag=0)
|
|---|
| 1019 | </font>
|
|---|
| 1020 | <div align="right"><font size=-1><I>
|
|---|
| 1021 | <U>In the picture</U>: anchor = {0, 0, sqrt(3)}<br>
|
|---|
| 1022 | p2 = { 0, 2*sqrt(2/3), -1/sqrt(3) }<br>
|
|---|
| 1023 | p3 = { -sqrt(2), -sqrt(2/3),-1/sqrt(3) }<br>
|
|---|
| 1024 | p4 = { sqrt(2), -sqrt(2/3) , -1/sqrt(3) }
|
|---|
| 1025 | </I></font></div>
|
|---|
| 1026 | </td>
|
|---|
| 1027 | <td><a href="javascript:remote_win(16)"
|
|---|
| 1028 | onMouseOver="window.status='Get alive picture...'; return true">
|
|---|
| 1029 | <img src="geometry.src/aTet.jpg" border="0"></a>
|
|---|
| 1030 | </td>
|
|---|
| 1031 | </tr>
|
|---|
| 1032 | </table>
|
|---|
| 1033 |
|
|---|
| 1034 | The solid is defined by 4 points in space:
|
|---|
| 1035 | <P>
|
|---|
| 1036 | <table border=1 cellpadding=8 id="table28" width="292">
|
|---|
| 1037 | <tr>
|
|---|
| 1038 | <td><tt>anchor</tt><td>Anchor point
|
|---|
| 1039 | <tr>
|
|---|
| 1040 | <td><tt>p2</tt><td>Point 2
|
|---|
| 1041 | <tr>
|
|---|
| 1042 | <td><tt>p3</tt><td>Point 3<tr>
|
|---|
| 1043 | <td><tt>p4</tt><td>Point 4<tr>
|
|---|
| 1044 | <td><tt>degeneracyFlag</tt><td>Flag indicating degeneracy of points
|
|---|
| 1045 | </table>
|
|---|
| 1046 | </P>
|
|---|
| 1047 | <P>
|
|---|
| 1048 | <HR width=40% align=center noshade>
|
|---|
| 1049 | </P>
|
|---|
| 1050 | <P>
|
|---|
| 1051 | <table border="0" width="100%" id="table13">
|
|---|
| 1052 | <tr>
|
|---|
| 1053 | <td width="480" valign="top">
|
|---|
| 1054 | A <b>box twisted</b> along one axis can be defined as follows:
|
|---|
| 1055 | <P>
|
|---|
| 1056 | <font face="Courier">
|
|---|
| 1057 | G4TwistedBox(const G4String& pName,<br>
|
|---|
| 1058 |
|
|---|
| 1059 | G4double twistedangle,<br>
|
|---|
| 1060 |
|
|---|
| 1061 | G4double pDx,<br>
|
|---|
| 1062 |
|
|---|
| 1063 | G4double pDy,<br>
|
|---|
| 1064 |
|
|---|
| 1065 | G4double pDz)
|
|---|
| 1066 | </font>
|
|---|
| 1067 | <P> </P><P> </P>
|
|---|
| 1068 | <div align="right"><font size=-1><I>
|
|---|
| 1069 | <U>In the picture</U>: twistedangle = 30*Degree<br>
|
|---|
| 1070 | pDx = 30, pDy =40, pDz = 60
|
|---|
| 1071 | </I></font></div>
|
|---|
| 1072 | </td>
|
|---|
| 1073 | <td><a href="javascript:remote_win(17)"
|
|---|
| 1074 | onMouseOver="window.status='Get alive picture...'; return true">
|
|---|
| 1075 | <img src="geometry.src/aTwistedBox.jpg" border="0"></a>
|
|---|
| 1076 | </td>
|
|---|
| 1077 | </tr>
|
|---|
| 1078 | </table>
|
|---|
| 1079 | <P>
|
|---|
| 1080 | <tt>G4TwistedBox</tt> is a box twisted along the z-axis.
|
|---|
| 1081 | The twist angle cannot be greater than 90 degrees:</P>
|
|---|
| 1082 | <P>
|
|---|
| 1083 | <table border=1 cellpadding=8>
|
|---|
| 1084 | <tr>
|
|---|
| 1085 | <td><tt>twistedangle</tt><td>Twist angle
|
|---|
| 1086 | <tr>
|
|---|
| 1087 | <td><tt>pDx</tt><td>Half x length
|
|---|
| 1088 | <tr>
|
|---|
| 1089 | <td><tt>pDy</tt><td>Half y length
|
|---|
| 1090 | <tr>
|
|---|
| 1091 | <td><tt>pDz</tt><td>Half z length
|
|---|
| 1092 | </table>
|
|---|
| 1093 | </P>
|
|---|
| 1094 | <P>
|
|---|
| 1095 | <HR width=40% align=center noshade>
|
|---|
| 1096 | </P>
|
|---|
| 1097 | <p>
|
|---|
| 1098 | A <b>trapezoid twisted</b> along one axis can be defined as follows:
|
|---|
| 1099 | <p>
|
|---|
| 1100 | <table border="0" width="100%" id="table14">
|
|---|
| 1101 | <tr>
|
|---|
| 1102 | <td width="480" valign="top">
|
|---|
| 1103 | <font face="Courier">
|
|---|
| 1104 | G4TwistedTrap(const G4String& pName,<br>
|
|---|
| 1105 |
|
|---|
| 1106 | G4double twistedangle,<br>
|
|---|
| 1107 |
|
|---|
| 1108 | G4double pDxx1, G4double pDxx2,<br>
|
|---|
| 1109 |
|
|---|
| 1110 | G4double pDy, G4double pDz)<br>
|
|---|
| 1111 | <br>
|
|---|
| 1112 | G4TwistedTrap(const G4String& pName,<br>
|
|---|
| 1113 |
|
|---|
| 1114 | G4double twistedangle,<br>
|
|---|
| 1115 |
|
|---|
| 1116 | G4double pDz,<br>
|
|---|
| 1117 |
|
|---|
| 1118 | G4double pTheta, G4double pPhi,<br>
|
|---|
| 1119 |
|
|---|
| 1120 | G4double pDy1, G4double pDx1,<br>
|
|---|
| 1121 |
|
|---|
| 1122 | G4double pDx2, G4double pDy2,<br>
|
|---|
| 1123 |
|
|---|
| 1124 | G4double pDx3, G4double pDx4,<br>
|
|---|
| 1125 |
|
|---|
| 1126 | G4double pAlph)
|
|---|
| 1127 | </font>
|
|---|
| 1128 | <div align="right"><font size=-1><I>
|
|---|
| 1129 | <U>In the picture</U>: pDx1 = 30, pDx2 = 40, pDy1 = 40<br>
|
|---|
| 1130 | pDx3 = 10, pDx4 = 14, pDy2 = 16<br>
|
|---|
| 1131 | pDz = 60<br>
|
|---|
| 1132 | pTheta = 20*Degree, pDphi = 5*Degree<br>
|
|---|
| 1133 | pAlph = 10*Degree, twistedangle = 30*Degree
|
|---|
| 1134 | </I></font></div>
|
|---|
| 1135 | </td>
|
|---|
| 1136 | <td><a href="javascript:remote_win(18)"
|
|---|
| 1137 | onMouseOver="window.status='Get alive picture...'; return true">
|
|---|
| 1138 | <img src="geometry.src/aTwistedTrap.jpg" border="0"></a>
|
|---|
| 1139 | </td>
|
|---|
| 1140 | </tr>
|
|---|
| 1141 | </table>
|
|---|
| 1142 | <P>
|
|---|
| 1143 | The first constructor of <tt>G4TwistedTrap</tt> produces a regular trapezoid
|
|---|
| 1144 | twisted along the <tt>z</tt>-axis, where the caps of the trapezoid are of the
|
|---|
| 1145 | same shape and size.<br>
|
|---|
| 1146 | The second constructor produces a generic trapezoid with
|
|---|
| 1147 | polar, azimuthal and tilt angles.<br>
|
|---|
| 1148 | The twist angle cannot be greater than 90 degrees:
|
|---|
| 1149 | </P>
|
|---|
| 1150 | <P>
|
|---|
| 1151 | <table border=1 cellpadding=8>
|
|---|
| 1152 | <tr>
|
|---|
| 1153 | <td><tt>twistedangle</tt><td>Twisted angle
|
|---|
| 1154 | <tr>
|
|---|
| 1155 | <td><tt>pDx1</tt><td>Half x length at y=-pDy
|
|---|
| 1156 | <tr>
|
|---|
| 1157 | <td><tt>pDx2</tt><td>Half x length at y=+pDy
|
|---|
| 1158 | <tr>
|
|---|
| 1159 | <td><tt>pDy</tt><td>Half y length
|
|---|
| 1160 | <tr>
|
|---|
| 1161 | <td><tt>pDz</tt><td>Half z length
|
|---|
| 1162 | <tr>
|
|---|
| 1163 | <td><tt>pTheta</tt><td>Polar angle of the line joining the centres of the faces at -/+pDz
|
|---|
| 1164 | <tr>
|
|---|
| 1165 | <td><tt>pDy1</tt><td>Half y length at -pDz
|
|---|
| 1166 | <tr>
|
|---|
| 1167 | <td><tt>pDx1</tt><td>Half x length at -pDz, y=-pDy1
|
|---|
| 1168 | <tr>
|
|---|
| 1169 | <td><tt>pDx2</tt><td>Half x length at -pDz, y=+pDy1
|
|---|
| 1170 | <tr>
|
|---|
| 1171 | <td><tt>pDy2</tt><td>Half y length at +pDz
|
|---|
| 1172 | <tr>
|
|---|
| 1173 | <td><tt>pDx3</tt><td>Half x length at +pDz, y=-pDy2
|
|---|
| 1174 | <tr>
|
|---|
| 1175 | <td><tt>pDx4</tt><td>Half x length at +pDz, y=+pDy2
|
|---|
| 1176 | <tr>
|
|---|
| 1177 | <td><tt>pAlph</tt><td>Angle with respect to the y axis from the centre of the side
|
|---|
| 1178 | </table>
|
|---|
| 1179 | </P>
|
|---|
| 1180 | <P>
|
|---|
| 1181 | <HR width=40% align=center noshade>
|
|---|
| 1182 | </P>
|
|---|
| 1183 | <p>
|
|---|
| 1184 | <table border="0" width="100%" id="table15">
|
|---|
| 1185 | <tr>
|
|---|
| 1186 | <td width="480" valign="top">
|
|---|
| 1187 | A <b>twisted trapezoid</b> with the <tt>x</tt> and </tt>y</tt> dimensions
|
|---|
| 1188 | <b>varying along <tt>z</tt></b> can be defined as follows:
|
|---|
| 1189 | <P>
|
|---|
| 1190 | <font face="Courier">
|
|---|
| 1191 | G4TwistedTrd(const G4String& pName,<br>
|
|---|
| 1192 |
|
|---|
| 1193 | G4double pDx1,<br>
|
|---|
| 1194 |
|
|---|
| 1195 | G4double pDx2,<br>
|
|---|
| 1196 |
|
|---|
| 1197 | G4double pDy1,<br>
|
|---|
| 1198 |
|
|---|
| 1199 | G4double pDy2,<br>
|
|---|
| 1200 |
|
|---|
| 1201 | G4double pDz,<br>
|
|---|
| 1202 |
|
|---|
| 1203 | G4double twistedangle)
|
|---|
| 1204 | </font>
|
|---|
| 1205 | <div align="right"><font size=-1><I>
|
|---|
| 1206 | <U>In the picture</U>: dx1 = 30, dx2 = 10<br>
|
|---|
| 1207 | dy1 = 40, dy2 = 15<br>
|
|---|
| 1208 | dz = 60<br>
|
|---|
| 1209 | twistedangle = 30*Degree
|
|---|
| 1210 | </I></font></div>
|
|---|
| 1211 | </td>
|
|---|
| 1212 | <td><a href="javascript:remote_win(19)"
|
|---|
| 1213 | onMouseOver="window.status='Get alive picture...'; return true">
|
|---|
| 1214 | <img src="geometry.src/aTwistedTrd.jpg" border="0"></a>
|
|---|
| 1215 | </td>
|
|---|
| 1216 | </tr>
|
|---|
| 1217 | </table>
|
|---|
| 1218 | </p>
|
|---|
| 1219 | where:
|
|---|
| 1220 | <p>
|
|---|
| 1221 | <table border=1 cellpadding=8>
|
|---|
| 1222 | <tr>
|
|---|
| 1223 | <td><tt>pDx1</tt><td>Half x length at the surface positioned at -dz
|
|---|
| 1224 | <tr>
|
|---|
| 1225 | <td><tt>pDx2</tt><td>Half x length at the surface positioned at +dz
|
|---|
| 1226 | <tr>
|
|---|
| 1227 | <td><tt>pDy1</tt><td>Half y length at the surface positioned at -dz
|
|---|
| 1228 | <tr>
|
|---|
| 1229 | <td><tt>pDy2</tt><td>Half y length at the surface positioned at +dz
|
|---|
| 1230 | <tr>
|
|---|
| 1231 | <td><tt>pDz</tt><td>Half z length
|
|---|
| 1232 | <tr>
|
|---|
| 1233 | <td><tt>twistedangle</tt><td>Twisted angle
|
|---|
| 1234 | </table>
|
|---|
| 1235 | </P>
|
|---|
| 1236 | <P>
|
|---|
| 1237 | <HR width=40% align=center noshade>
|
|---|
| 1238 | </P>
|
|---|
| 1239 | <P>
|
|---|
| 1240 | <table border="0" width="100%" id="table16">
|
|---|
| 1241 | <tr>
|
|---|
| 1242 | <td width="480" valign="top">
|
|---|
| 1243 | A <b>tube section twisted</b> along its axis can be defined as follows:
|
|---|
| 1244 | <P>
|
|---|
| 1245 | <font face="Courier">
|
|---|
| 1246 | G4TwistedTubs(const G4String& pName,<br>
|
|---|
| 1247 |
|
|---|
| 1248 | G4double twistedangle,<br>
|
|---|
| 1249 |
|
|---|
| 1250 | G4double endinnerrad,<br>
|
|---|
| 1251 |
|
|---|
| 1252 | G4double endouterrad,<br>
|
|---|
| 1253 |
|
|---|
| 1254 | G4double halfzlen,<br>
|
|---|
| 1255 |
|
|---|
| 1256 | G4double dphi)
|
|---|
| 1257 | </font>
|
|---|
| 1258 | <P> </P><P> </P><P> </P>
|
|---|
| 1259 | <div align="right"><font size=-1><I>
|
|---|
| 1260 | <U>In the picture</U>: endinnerrad = 10, endouterrad = 15<br>
|
|---|
| 1261 | halfzlen = 20, dphi = 90*Degree<br>
|
|---|
| 1262 | twistedangle = 60*Degree
|
|---|
| 1263 | </I></font></div>
|
|---|
| 1264 | </td>
|
|---|
| 1265 | <td><a href="javascript:remote_win(20)"
|
|---|
| 1266 | onMouseOver="window.status='Get alive picture...'; return true">
|
|---|
| 1267 | <img src="geometry.src/aTwistedTubs.jpg" border="0"></a>
|
|---|
| 1268 | </td>
|
|---|
| 1269 | </tr>
|
|---|
| 1270 | </table>
|
|---|
| 1271 | </P>
|
|---|
| 1272 | <P>
|
|---|
| 1273 | <tt>G4TwistedTubs</tt> is a sort of twisted cylinder which, placed along
|
|---|
| 1274 | the <tt>z</tt>-axis and divided into <tt>phi</tt>-segments is shaped like an
|
|---|
| 1275 | hyperboloid, where each of its segmented pieces can be tilted with a stereo
|
|---|
| 1276 | angle.<br>
|
|---|
| 1277 | It can have inner and outer surfaces with the same stereo angle:
|
|---|
| 1278 | </P>
|
|---|
| 1279 | <P>
|
|---|
| 1280 | <table border=1 cellpadding=8>
|
|---|
| 1281 | <tr>
|
|---|
| 1282 | <td><tt>twistedangle</tt><td>Twisted angle
|
|---|
| 1283 | <tr>
|
|---|
| 1284 | <td><tt>endinnerrad</tt><td>Inner radius at endcap
|
|---|
| 1285 | <tr>
|
|---|
| 1286 | <td><tt>endouterrad</tt><td>Outer radius at endcap
|
|---|
| 1287 | <tr>
|
|---|
| 1288 | <td><tt>halfzlen</tt><td>Half z length
|
|---|
| 1289 | <tr>
|
|---|
| 1290 | <td><tt>dphi</tt><td>Phi angle of a segment
|
|---|
| 1291 | </table>
|
|---|
| 1292 | </P>
|
|---|
| 1293 | <P>
|
|---|
| 1294 | Additional constructors are provided, allowing the shape to be specified
|
|---|
| 1295 | either as:
|
|---|
| 1296 | <UL>
|
|---|
| 1297 | <LI>the number of segments in <tt>phi</tt> and the total angle for all
|
|---|
| 1298 | segments, or</LI>
|
|---|
| 1299 | <LI>a combination of the above constructors providing instead the inner and
|
|---|
| 1300 | outer radii at <TT>z=0</TT> with different <tt>z</tt>-lengths along
|
|---|
| 1301 | negative and positive <tt>z</tt>-axis.</LI>
|
|---|
| 1302 | </UL>
|
|---|
| 1303 | </P>
|
|---|
| 1304 |
|
|---|
| 1305 | <P> </P>
|
|---|
| 1306 |
|
|---|
| 1307 | <a name="4.1.2.2">
|
|---|
| 1308 | <H4>4.1.2.2 Solids made by Boolean operations</H4></a>
|
|---|
| 1309 |
|
|---|
| 1310 | Simple solids can be combined using Boolean operations.
|
|---|
| 1311 | For example, a cylinder and a half-sphere can be combined with the
|
|---|
| 1312 | union Boolean operation.
|
|---|
| 1313 | <P>
|
|---|
| 1314 | Creating such a new <i>Boolean</i> solid, requires:
|
|---|
| 1315 | <UL>
|
|---|
| 1316 | <LI>Two solids
|
|---|
| 1317 | <LI>A Boolean operation: union, intersection or subtraction.
|
|---|
| 1318 | <LI>Optionally a transformation for the second solid.
|
|---|
| 1319 | </UL></P>
|
|---|
| 1320 | <P>
|
|---|
| 1321 | The solids used should be either CSG solids (for examples a box, a
|
|---|
| 1322 | spherical shell, or a tube) or another Boolean solid: the product of a
|
|---|
| 1323 | previous Boolean operation.
|
|---|
| 1324 | An important purpose of Boolean solids is to allow the description of
|
|---|
| 1325 | solids with peculiar shapes in a simple and intuitive way, still allowing
|
|---|
| 1326 | an efficient geometrical navigation inside them.</P>
|
|---|
| 1327 | <P>
|
|---|
| 1328 | Note: The solids used can actually be of any type. However, in order to
|
|---|
| 1329 | fully support the export of a Geant4 solid model via STEP to CAD
|
|---|
| 1330 | systems, we restrict the use of Boolean operations to this subset of
|
|---|
| 1331 | solids. But this subset contains all the most interesting use cases.</P>
|
|---|
| 1332 | <P>
|
|---|
| 1333 | Note: The tracking cost for navigating in a Boolean solid in the
|
|---|
| 1334 | current implementation, is proportional to the number of constituent
|
|---|
| 1335 | solids. So care must be taken to avoid extensive, unecessary use of
|
|---|
| 1336 | Boolean solids in performance-critical areas of a geometry description,
|
|---|
| 1337 | where each solid is created from Boolean combinations of many other
|
|---|
| 1338 | solids.</P>
|
|---|
| 1339 | <P>
|
|---|
| 1340 | Examples of the creation of the simplest Boolean solids are given below:
|
|---|
| 1341 |
|
|---|
| 1342 | <PRE>
|
|---|
| 1343 | G4Box* box =
|
|---|
| 1344 | new G4Box("Box",20*mm,30*mm,40*mm);
|
|---|
| 1345 | G4Tubs* cyl =
|
|---|
| 1346 | new G4Tubs("Cylinder",0,50*mm,50*mm,0,twopi); // r: 0 mm -> 50 mm
|
|---|
| 1347 | // z: -50 mm -> 50 mm
|
|---|
| 1348 | // phi: 0 -> 2 pi
|
|---|
| 1349 | G4UnionSolid* union =
|
|---|
| 1350 | new G4UnionSolid("Box+Cylinder", box, cyl);
|
|---|
| 1351 | G4IntersectionSolid* intersection =
|
|---|
| 1352 | new G4IntersectionSolid("Box*Cylinder", box, cyl);
|
|---|
| 1353 | G4SubtractionSolid* subtraction =
|
|---|
| 1354 | new G4SubtractionSolid("Box-Cylinder", box, cyl);
|
|---|
| 1355 | </PRE>
|
|---|
| 1356 |
|
|---|
| 1357 | where the union, intersection and subtraction of a box and cylinder are
|
|---|
| 1358 | constructed.</P>
|
|---|
| 1359 | <P>
|
|---|
| 1360 | The more useful case where one of the solids is displaced from the
|
|---|
| 1361 | origin of coordinates also exists. In this case the second solid is
|
|---|
| 1362 | positioned relative to the coordinate system (and thus relative to the
|
|---|
| 1363 | first). This can be done in two ways:
|
|---|
| 1364 | <UL>
|
|---|
| 1365 | <LI>Either by giving a rotation matrix and translation vector that
|
|---|
| 1366 | are used to transform the coordinate system of the second solid to the
|
|---|
| 1367 | coordinate system of the first solid. This is called the <I>passive</I>
|
|---|
| 1368 | method.
|
|---|
| 1369 | <LI>Or by creating a transformation that moves the second solid from
|
|---|
| 1370 | its desired position to its standard position, e.g., a box's standard
|
|---|
| 1371 | position is with its centre at the origin and sides parallel to the
|
|---|
| 1372 | three axes. This is called the <I>active</I> method.
|
|---|
| 1373 | </UL></P>
|
|---|
| 1374 | <P>
|
|---|
| 1375 | In the first case, the translation is applied first to move the origin
|
|---|
| 1376 | of coordinates. Then the rotation is used to rotate the
|
|---|
| 1377 | coordinate system of the second solid to the coordinate system of the
|
|---|
| 1378 | first.</P>
|
|---|
| 1379 | <P>
|
|---|
| 1380 | <PRE>
|
|---|
| 1381 | G4RotationMatrix* yRot = new G4RotationMatrix; // Rotates X and Z axes only
|
|---|
| 1382 | yRot->rotateY(M_PI/4.*rad); // Rotates 45 degrees
|
|---|
| 1383 | G4ThreeVector zTrans(0, 0, 50);
|
|---|
| 1384 |
|
|---|
| 1385 | G4UnionSolid* unionMoved =
|
|---|
| 1386 | new G4UnionSolid("Box+CylinderMoved", box, cyl, yRot, zTrans);
|
|---|
| 1387 | //
|
|---|
| 1388 | // The new coordinate system of the cylinder is translated so that
|
|---|
| 1389 | // its centre is at +50 on the original Z axis, and it is rotated
|
|---|
| 1390 | // with its X axis halfway between the original X and Z axes.
|
|---|
| 1391 |
|
|---|
| 1392 | // Now we build the same solid using the alternative method
|
|---|
| 1393 | //
|
|---|
| 1394 | G4RotationMatrix invRot = *(yRot->invert());
|
|---|
| 1395 | G4Transform3D transform(invRot, zTrans);
|
|---|
| 1396 | G4UnionSolid* unionMoved =
|
|---|
| 1397 | new G4UnionSolid("Box+CylinderMoved", box, cyl, transform);
|
|---|
| 1398 | </PRE>
|
|---|
| 1399 |
|
|---|
| 1400 | Note that the first constructor that takes a pointer to the rotation-matrix
|
|---|
| 1401 | (<tt>G4RotationMatrix*</tt>), does NOT copy it.
|
|---|
| 1402 | Therefore once used a rotation-matrix to construct a Boolean solid, it must
|
|---|
| 1403 | NOT be modified.<BR>
|
|---|
| 1404 | In contrast, with the alternative method shown, a <tt>G4Transform3D</tt> is
|
|---|
| 1405 | provided to the constructor by value, and its transformation is stored by the
|
|---|
| 1406 | Boolean solid. The user may modify the <tt>G4Transform3D</tt> and eventually
|
|---|
| 1407 | use it again.</P>
|
|---|
| 1408 | <P>
|
|---|
| 1409 | When positioning a volume associated to a Boolean solid, the relative center
|
|---|
| 1410 | of coordinates considered for the positioning is the one related to the
|
|---|
| 1411 | <i>first</i> of the two constituent solids.</P>
|
|---|
| 1412 |
|
|---|
| 1413 | <P> </P>
|
|---|
| 1414 |
|
|---|
| 1415 | <a name="4.1.2.3">
|
|---|
| 1416 | <H4>4.1.2.3 Boundary Represented (BREPS) Solids</H4></a>
|
|---|
| 1417 |
|
|---|
| 1418 | BREP solids are defined via the description of their boundaries. The
|
|---|
| 1419 | boundaries can be made of planar and second order surfaces.
|
|---|
| 1420 | Eventually these can be trimmed and have holes.
|
|---|
| 1421 | The resulting solids, such as polygonal, polyconical solids
|
|---|
| 1422 | are known as Elementary BREPS.
|
|---|
| 1423 | <P>
|
|---|
| 1424 | In addition, the boundary surfaces can be made of Bezier surfaces and B-Splines,
|
|---|
| 1425 | or of NURBS (Non-Uniform-Rational-B-Splines) surfaces.
|
|---|
| 1426 | The resulting solids are Advanced BREPS.<BR>
|
|---|
| 1427 | <b>Note</b> - <i>Currently, the implementation for surfaces generated by Beziers, B-Splines
|
|---|
| 1428 | or NURBS is only at the level of prototype and not fully functional</i>.<BR>
|
|---|
| 1429 | Extensions are foreseen in the near future, also to allow exchange of geometrical
|
|---|
| 1430 | models with CAD systems.</P>
|
|---|
| 1431 | <P>
|
|---|
| 1432 | We have defined a few simple Elementary BREPS, that can be instantiated
|
|---|
| 1433 | simply by a user in a manner similar to the construction of Constructed Solids
|
|---|
| 1434 | (CSGs). We summarize their capabilities in the following section.</P>
|
|---|
| 1435 | <P>
|
|---|
| 1436 | However most BREPS Solids are defined by creating each surface separately
|
|---|
| 1437 | and tying them together. Though it is possible to do this using code, it is
|
|---|
| 1438 | potentially error prone. So it is generally much more productive to utilize a tool
|
|---|
| 1439 | to create these volumes, and the tools of choice are CAD systems. In future, it will
|
|---|
| 1440 | be possible to import/export models created in CAD systems, utilizing the STEP standard.</P>
|
|---|
| 1441 |
|
|---|
| 1442 | <P> </P>
|
|---|
| 1443 |
|
|---|
| 1444 | <b>Specific BREP Solids</b>
|
|---|
| 1445 | <P>
|
|---|
| 1446 | We have defined one polygonal and one polyconical shape using BREPS.
|
|---|
| 1447 | The polycone provides a shape defined by a series of conical sections with the
|
|---|
| 1448 | same axis, contiguous along it.</P>
|
|---|
| 1449 | <P>
|
|---|
| 1450 | The polyconical solid <tt>G4BREPSolidPCone</tt> is a shape defined by a set
|
|---|
| 1451 | of inner and outer conical or cylindrical surface sections and
|
|---|
| 1452 | two planes perpendicular to the Z axis. Each conical surface is
|
|---|
| 1453 | defined by its radius at two different
|
|---|
| 1454 | planes perpendicular to the Z-axis. Inner and outer conical surfaces are
|
|---|
| 1455 | defined using common Z planes.</P>
|
|---|
| 1456 | <P>
|
|---|
| 1457 | <PRE>
|
|---|
| 1458 | G4BREPSolidPCone( const G4String& pName,
|
|---|
| 1459 | G4double start_angle,
|
|---|
| 1460 | G4double opening_angle,
|
|---|
| 1461 | G4int num_z_planes, // sections,
|
|---|
| 1462 | G4double z_start,
|
|---|
| 1463 | const G4double z_values[],
|
|---|
| 1464 | const G4double RMIN[],
|
|---|
| 1465 | const G4double RMAX[] )
|
|---|
| 1466 | </PRE>
|
|---|
| 1467 | The conical sections do not need to fill 360 degrees, but can have a common
|
|---|
| 1468 | start and opening angle.</P>
|
|---|
| 1469 | <P>
|
|---|
| 1470 | <table border=1 cellpadding=8>
|
|---|
| 1471 | <tr>
|
|---|
| 1472 | <td><tt>start_angle</tt> <td>starting angle
|
|---|
| 1473 | <tr>
|
|---|
| 1474 | <td><tt>opening_angle</tt> <td>opening angle
|
|---|
| 1475 | <tr>
|
|---|
| 1476 | <td><tt>num_z_planes</tt> <td>number of planes perpendicular to the z-axis used.
|
|---|
| 1477 | <tr>
|
|---|
| 1478 | <td><tt>z_start</tt> <td>starting value of z
|
|---|
| 1479 | <tr>
|
|---|
| 1480 | <td><tt>z_values</tt> <td>z coordinates of each plane
|
|---|
| 1481 | <tr>
|
|---|
| 1482 | <td><tt>RMIN</tt> <td>radius of inner cone at each plane
|
|---|
| 1483 | <tr>
|
|---|
| 1484 | <td><tt>RMAX</tt> <td>radius of outer cone at each plane
|
|---|
| 1485 | </table></P>
|
|---|
| 1486 | <P>
|
|---|
| 1487 | The polygonal solid <tt>G4BREPSolidPolyhedra</tt> is a shape defined by an
|
|---|
| 1488 | inner and outer polygonal surface and two planes perpendicular to the Z axis.
|
|---|
| 1489 | Each polygonal surface is created by linking a series of polygons created at
|
|---|
| 1490 | different planes perpendicular to the Z-axis. All these polygons all have the
|
|---|
| 1491 | same number of sides (<tt>sides</tt>) and are defined at the same Z planes for
|
|---|
| 1492 | both inner and outer polygonal surfaces.</P>
|
|---|
| 1493 | <P>
|
|---|
| 1494 | The polygons do not need to fill 360 degrees, but have a start and
|
|---|
| 1495 | opening angle.</P>
|
|---|
| 1496 | <P>
|
|---|
| 1497 | The constructor takes the following parameters:
|
|---|
| 1498 | <PRE>
|
|---|
| 1499 | G4BREPSolidPolyhedra( const G4String& pName,
|
|---|
| 1500 | G4double start_angle,
|
|---|
| 1501 | G4double opening_angle,
|
|---|
| 1502 | G4int sides,
|
|---|
| 1503 | G4int num_z_planes,
|
|---|
| 1504 | G4double z_start,
|
|---|
| 1505 | const G4double z_values[],
|
|---|
| 1506 | const G4double RMIN[],
|
|---|
| 1507 | const G4double RMAX[] )
|
|---|
| 1508 | </PRE>
|
|---|
| 1509 | which in addition to its name have the following meaning:</P>
|
|---|
| 1510 | <p>
|
|---|
| 1511 | <table border=1 cellpadding=8>
|
|---|
| 1512 | <tr>
|
|---|
| 1513 | <td><tt>start_angle</tt> <td>starting angle
|
|---|
| 1514 | <tr>
|
|---|
| 1515 | <TD><tt>opening_angle</tt> <td>opening angle
|
|---|
| 1516 | <tr>
|
|---|
| 1517 | <TD><tt>sides</tt> <td>number of sides of each polygon in the x-y plane
|
|---|
| 1518 | <tr>
|
|---|
| 1519 | <TD><tt>num_z_planes</tt> <td>number of planes perpendicular to the z-axis used.
|
|---|
| 1520 | <tr>
|
|---|
| 1521 | <TD><tt>z_start</tt> <td>starting value of z
|
|---|
| 1522 | <tr>
|
|---|
| 1523 | <TD><tt>z_values</tt> <td>z coordinates of each plane
|
|---|
| 1524 | <tr>
|
|---|
| 1525 | <TD><tt>RMIN</tt> <td>radius of inner polygon at each corner
|
|---|
| 1526 | <tr>
|
|---|
| 1527 | <TD><tt>RMAX</tt> <td>radius of outer polygon at each corner
|
|---|
| 1528 | </table></P>
|
|---|
| 1529 | <P>
|
|---|
| 1530 | the shape is defined by the number of sides <tt>sides</tt> of the polygon
|
|---|
| 1531 | in the plane perpendicular to the z-axis. </P>
|
|---|
| 1532 |
|
|---|
| 1533 | <a name="4.1.2.4">
|
|---|
| 1534 | <H4>4.1.2.4 Tessellated Solids</H4></a>
|
|---|
| 1535 |
|
|---|
| 1536 | In Geant4 it is also implemented a class <tt>G4TessellatedSolid</tt> which
|
|---|
| 1537 | can be used to generate a generic solid defined by a number of facets
|
|---|
| 1538 | (<tt>G4VFacet</tt>). Such constructs are especially important for conversion
|
|---|
| 1539 | of complex geometrical shapes imported from CAD systems bounded with generic
|
|---|
| 1540 | surfaces into an approximate description with facets of defined dimension
|
|---|
| 1541 | (see figure 4.1.1).
|
|---|
| 1542 | <P>
|
|---|
| 1543 | <center>
|
|---|
| 1544 | <table BORDER=1 CELLPADDING=8>
|
|---|
| 1545 | <tr>
|
|---|
| 1546 | <td><IMG SRC="geometry.src/cad-tess1.jpg"
|
|---|
| 1547 | ALT="Tessellated imported geometry - 1" height=350 width=420>
|
|---|
| 1548 | <IMG SRC="geometry.src/cad-tess2.jpg"
|
|---|
| 1549 | ALT="Tessellated imported geometry - 2" height=350 width=420></td>
|
|---|
| 1550 | <tr>
|
|---|
| 1551 | <td ALIGN=center>
|
|---|
| 1552 | Figure 4.1.1<br>
|
|---|
| 1553 | Example of geometries imported from CAD system and converted
|
|---|
| 1554 | to tessellated solids.</td>
|
|---|
| 1555 | </tr>
|
|---|
| 1556 | </table>
|
|---|
| 1557 | </center>
|
|---|
| 1558 | </P>
|
|---|
| 1559 | <P>
|
|---|
| 1560 | They can also be used to generate a solid bounded with a generic surface made
|
|---|
| 1561 | of planar facets. It is important that the supplied facets shall form a fully
|
|---|
| 1562 | enclose space to represent the solid.<BR>
|
|---|
| 1563 | Two types of facet can be used for the construction of a
|
|---|
| 1564 | <tt>G4TessellatedSolid</tt>: a triangular facet (<tt>G4TriangularFacet</tt>)
|
|---|
| 1565 | and a quadrangular facet (<tt>G4QuadrangularFacet</tt>).</P>
|
|---|
| 1566 | <P>
|
|---|
| 1567 | An example on how to generate a simple tessellated shape is given below.</P>
|
|---|
| 1568 | <P>
|
|---|
| 1569 | Example:
|
|---|
| 1570 | <center><table border=1 cellpadding=8>
|
|---|
| 1571 | <tr><td>
|
|---|
| 1572 | <PRE>
|
|---|
| 1573 | // First declare a tessellated solid
|
|---|
| 1574 | //
|
|---|
| 1575 | G4TessellatedSolid solidTarget = new G4TessellatedSolid("Solid_name");
|
|---|
| 1576 |
|
|---|
| 1577 | // Define the facets which form the solid
|
|---|
| 1578 | //
|
|---|
| 1579 | G4double targetSize = 10*cm ;
|
|---|
| 1580 | G4TriangularFacet *facet1 = new
|
|---|
| 1581 | G4TriangularFacet (G4ThreeVector(-targetSize,-targetSize, 0.0),
|
|---|
| 1582 | G4ThreeVector(+targetSize,-targetSize, 0.0),
|
|---|
| 1583 | G4ThreeVector( 0.0, 0.0,+targetSize),
|
|---|
| 1584 | ABSOLUTE);
|
|---|
| 1585 | G4TriangularFacet *facet2 = new
|
|---|
| 1586 | G4TriangularFacet (G4ThreeVector(+targetSize,-targetSize, 0.0),
|
|---|
| 1587 | G4ThreeVector(+targetSize,+targetSize, 0.0),
|
|---|
| 1588 | G4ThreeVector( 0.0, 0.0,+targetSize),
|
|---|
| 1589 | ABSOLUTE);
|
|---|
| 1590 | G4TriangularFacet *facet3 = new
|
|---|
| 1591 | G4TriangularFacet (G4ThreeVector(+targetSize,+targetSize, 0.0),
|
|---|
| 1592 | G4ThreeVector(-targetSize,+targetSize, 0.0),
|
|---|
| 1593 | G4ThreeVector( 0.0, 0.0,+targetSize),
|
|---|
| 1594 | ABSOLUTE);
|
|---|
| 1595 | G4TriangularFacet *facet4 = new
|
|---|
| 1596 | G4TriangularFacet (G4ThreeVector(-targetSize,+targetSize, 0.0),
|
|---|
| 1597 | G4ThreeVector(-targetSize,-targetSize, 0.0),
|
|---|
| 1598 | G4ThreeVector( 0.0, 0.0,+targetSize),
|
|---|
| 1599 | ABSOLUTE);
|
|---|
| 1600 | G4QuadrangularFacet *facet5 = new
|
|---|
| 1601 | G4QuadrangularFacet (G4ThreeVector(-targetSize,-targetSize, 0.0),
|
|---|
| 1602 | G4ThreeVector(-targetSize,+targetSize, 0.0),
|
|---|
| 1603 | G4ThreeVector(+targetSize,+targetSize, 0.0),
|
|---|
| 1604 | G4ThreeVector(+targetSize,-targetSize, 0.0),
|
|---|
| 1605 | ABSOLUTE);
|
|---|
| 1606 |
|
|---|
| 1607 | // Now add the facets to the solid
|
|---|
| 1608 | //
|
|---|
| 1609 | solidTarget->AddFacet((G4VFacet*) facet1);
|
|---|
| 1610 | solidTarget->AddFacet((G4VFacet*) facet2);
|
|---|
| 1611 | solidTarget->AddFacet((G4VFacet*) facet3);
|
|---|
| 1612 | solidTarget->AddFacet((G4VFacet*) facet4);
|
|---|
| 1613 | solidTarget->AddFacet((G4VFacet*) facet5);
|
|---|
| 1614 |
|
|---|
| 1615 | Finally declare the solid is complete
|
|---|
| 1616 | //
|
|---|
| 1617 | solidTarget->SetSolidClosed(true);
|
|---|
| 1618 | </PRE>
|
|---|
| 1619 | <tr>
|
|---|
| 1620 | <td align=center>
|
|---|
| 1621 | Source listing 4.1.1<BR>
|
|---|
| 1622 | An example of a simple tessellated solid with <tt>G4TessellatedSolid</tt>.
|
|---|
| 1623 | </table></center></P>
|
|---|
| 1624 | <P>
|
|---|
| 1625 | The <tt>G4TriangularFacet</tt> class is used for the contruction of
|
|---|
| 1626 | <tt>G4TessellatedSolid</tt>. It is defined by three vertices, which shall be
|
|---|
| 1627 | supplied in <I>anti-clockwise order</I> looking from the outside of the solid
|
|---|
| 1628 | where it belongs. Its constructor looks like:</P>
|
|---|
| 1629 | <P>
|
|---|
| 1630 | <PRE>
|
|---|
| 1631 | G4TriangularFacet ( const G4ThreeVector Pt0,
|
|---|
| 1632 | const G4ThreeVector vt1,
|
|---|
| 1633 | const G4ThreeVector vt2,
|
|---|
| 1634 | G4FacetVertexType fType )
|
|---|
| 1635 | </PRE>
|
|---|
| 1636 | i.e., it takes 4 parameters to define the three vertices:</P>
|
|---|
| 1637 | <P>
|
|---|
| 1638 | <table border=1 cellpadding=8>
|
|---|
| 1639 | <tr>
|
|---|
| 1640 | <TD><tt>G4FacetVertexType</tt> <td><tt>ABSOLUTE</tt> in which case <tt>Pt0</tt>,
|
|---|
| 1641 | <tt>vt1</tt> and <tt>vt2</tt> are the three vertices in anti-clockwise
|
|---|
| 1642 | order looking from the outside.
|
|---|
| 1643 | <tr>
|
|---|
| 1644 | <TD><tt>G4FacetVertexType</tt> <td><tt>RELATIVE</tt> in which case the first
|
|---|
| 1645 | vertex is <tt>Pt0</tt>, the second vertex is <tt>Pt0+vt1</tt> and the
|
|---|
| 1646 | third vertex is <tt>Pt0+vt2</tt>, all in anti-clockwise order when
|
|---|
| 1647 | looking from the outside.
|
|---|
| 1648 | </table></P>
|
|---|
| 1649 | <P>
|
|---|
| 1650 | The <tt>G4QuadrangularFacet</tt> class can be used for the contruction of
|
|---|
| 1651 | <tt>G4TessellatedSolid</tt> as well. It is defined by four vertices, which
|
|---|
| 1652 | shall be in the same plane and be supplied in <I>anti-clockwise order</I>
|
|---|
| 1653 | looking from the outside of the solid where it belongs. Its constructor
|
|---|
| 1654 | looks like:</P>
|
|---|
| 1655 | <P>
|
|---|
| 1656 | <PRE>
|
|---|
| 1657 | G4QuadrangularFacet ( const G4ThreeVector Pt0,
|
|---|
| 1658 | const G4ThreeVector vt1,
|
|---|
| 1659 | const G4ThreeVector vt2,
|
|---|
| 1660 | const G4ThreeVector vt3,
|
|---|
| 1661 | G4FacetVertexType fType )
|
|---|
| 1662 | </PRE>
|
|---|
| 1663 | i.e., it takes 5 parameters to define the four vertices:</P>
|
|---|
| 1664 | <P>
|
|---|
| 1665 | <table border=1 cellpadding=8>
|
|---|
| 1666 | <tr>
|
|---|
| 1667 | <TD><tt>G4FacetVertexType</tt> <td><tt>ABSOLUTE</tt> in which case <tt>Pt0</tt>,
|
|---|
| 1668 | <tt>vt1</tt>, <tt>vt2</tt> and <tt>vt3</tt> are the four vertices required
|
|---|
| 1669 | in anti-clockwise order when looking from the outside.
|
|---|
| 1670 | <tr>
|
|---|
| 1671 | <TD><tt>G4FacetVertexType</tt> <td><tt>RELATIVE</tt> in which case the first
|
|---|
| 1672 | vertex is <tt>Pt0</tt>, the second vertex is <tt>Pt0+vt</tt>, the third
|
|---|
| 1673 | vertex is <tt>Pt0+vt2</tt> and the fourth vertex is <tt>Pt0+vt3</tt>, in
|
|---|
| 1674 | anti-clockwise order when looking from the outside.
|
|---|
| 1675 | </table>
|
|---|
| 1676 | </P>
|
|---|
| 1677 |
|
|---|
| 1678 | <hr><a href="../../../../Authors/html/subjectsToAuthors.html">
|
|---|
| 1679 | <i>About the authors</a></i> </P>
|
|---|
| 1680 |
|
|---|
| 1681 | </body>
|
|---|
| 1682 | </html>
|
|---|
