1 | <html> |
---|
2 | <head> |
---|
3 | <title>ADG: Geometry</title> |
---|
4 | <script language="JavaScript"> |
---|
5 | function remote_win(urlnum) |
---|
6 | { |
---|
7 | var url = "geometry.src/pic" + urlnum + ".html"; |
---|
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") |
---|
9 | RemoteWin.creator=self |
---|
10 | } |
---|
11 | </script> |
---|
12 | </head> |
---|
13 | |
---|
14 | <!-- Changed by: Gabriele Cosmo, 18-Apr-2005 --> |
---|
15 | <!-- $Id: geomSolids.html,v 1.8 2006/11/23 16:36:33 gcosmo Exp $ --> |
---|
16 | <!-- $Name: $ --> |
---|
17 | <body> |
---|
18 | <table WIDTH="100%"><TR> |
---|
19 | <td> |
---|
20 | <a href="../../../../Overview/html/index.html"> |
---|
21 | <IMG SRC="../../../../resources/html/IconsGIF/Overview.gif" ALT="Overview"></a> |
---|
22 | <a href="geometry.html"> |
---|
23 | <IMG SRC="../../../../resources/html/IconsGIF/Contents.gif" ALT="Contents"></a> |
---|
24 | <a href="geomIntro.html"> |
---|
25 | <IMG SRC="../../../../resources/html/IconsGIF/Previous.gif" ALT="Previous"></a> |
---|
26 | <a href="geomLogical.html"> |
---|
27 | <IMG SRC="../../../../resources/html/IconsGIF/Next.gif" ALT="Next"></a> |
---|
28 | </td> |
---|
29 | <td ALIGN="Right"> |
---|
30 | <font SIZE="-1" COLOR="#238E23"> |
---|
31 | <b>Geant4 User's Guide</b> |
---|
32 | <br> |
---|
33 | <b>For Application Developers</b> |
---|
34 | <br> |
---|
35 | <b>Geometry</b> |
---|
36 | </font> |
---|
37 | </td> |
---|
38 | </tr></table> |
---|
39 | <br><br> |
---|
40 | |
---|
41 | <a name="4.1.2"> |
---|
42 | <h2>4.1.2 Solids</h2></a> |
---|
43 | |
---|
44 | <p> |
---|
45 | The STEP standard supports multiple solid representations. Constructive |
---|
46 | Solid Geometry (CSG) representations and Boundary Represented Solids (BREPs) |
---|
47 | are available. Different representations are suitable for different |
---|
48 | purposes, applications, required complexity, and levels of detail. |
---|
49 | CSG representations are easy to use and normally give superior performance, |
---|
50 | but they cannot reproduce complex solids such as those used in CAD systems. |
---|
51 | BREP representations can handle more extended topologies and reproduce the |
---|
52 | most complex solids, thus allowing the exchange of models with CAD systems. |
---|
53 | <br> |
---|
54 | All constructed solids can stream out their contents via appropriate methods |
---|
55 | and streaming operators. |
---|
56 | </p> |
---|
57 | |
---|
58 | <p> |
---|
59 | For all solids it is possible to estimate the geometrical volume and the |
---|
60 | surface area by invoking the methods: |
---|
61 | <pre> |
---|
62 | G4double GetCubicVolume() |
---|
63 | G4double GetSurfaceArea() |
---|
64 | </pre> |
---|
65 | which return an estimate of the solid volume and total area in internal |
---|
66 | units respectively. For elementary solids the functions compute the exact |
---|
67 | geometrical quantities, while for composite or complex solids an estimate |
---|
68 | is made using Monte Carlo techniques. |
---|
69 | </p> |
---|
70 | |
---|
71 | <p> |
---|
72 | For all solids it is also possible to generate pseudo-random points lying |
---|
73 | on their surfaces, by invoking the method |
---|
74 | <pre> |
---|
75 | G4ThreeVector GetPointOnSurface() const |
---|
76 | </pre> |
---|
77 | which returns the generated point in local coordinates relative to the solid. |
---|
78 | </p> |
---|
79 | |
---|
80 | <a name="4.1.2.1"> |
---|
81 | <H4>4.1.2.1 Constructed Solid Geometry (CSG) Solids</H4></a> |
---|
82 | |
---|
83 | CSG solids are defined directly as three-dimensional primitives. They are |
---|
84 | described by a minimal set of parameters necessary to define the shape and |
---|
85 | size of the solid. CSG solids are Boxes, Tubes and their sections, Cones |
---|
86 | and their sections, Spheres, Wedges, and Toruses. |
---|
87 | <P> |
---|
88 | <HR width=40% align=center noshade> |
---|
89 | </P> |
---|
90 | To create a <b>box</b> one can use the constructor: |
---|
91 | |
---|
92 | <table border="0" width="100%" id="table1"> |
---|
93 | <tr> |
---|
94 | <td width="480" valign="top"> |
---|
95 | <font face="Courier"> |
---|
96 | G4Box(const G4String& pName,<br> |
---|
97 | |
---|
98 | G4double pX,<br> |
---|
99 | |
---|
100 | G4double pY,<br> |
---|
101 | |
---|
102 | G4double pZ) |
---|
103 | </font> |
---|
104 | <P> |
---|
105 | by giving the box a name and its half-lengths along the |
---|
106 | X, Y and Z axis: |
---|
107 | </P> |
---|
108 | <P> |
---|
109 | <table border=1 cellpadding=8> |
---|
110 | <tr> |
---|
111 | <td><tt>pX</tt><td>half length in X |
---|
112 | <td><tt>pY</tt><td>half length in Y |
---|
113 | <td><tt>pZ</tt><td>half length in Z |
---|
114 | </tr> |
---|
115 | </table> |
---|
116 | </P> |
---|
117 | <P> |
---|
118 | This will create a box that extends from <tt>-pX</tt> to |
---|
119 | <tt>+pX</tt> in X, from <tt>-pY</tt> to <tt>+pY</tt> in Y, |
---|
120 | and from <tt>-pZ</tt> to <tt>+pZ</tt> in Z. |
---|
121 | </P> |
---|
122 | <P> </P><P> </P> |
---|
123 | <P> |
---|
124 | <div align="right"><font size=-1><I> |
---|
125 | <U>In the picture</U>: pX = 30, pY = 40, pZ = 60 |
---|
126 | </I></font></div> |
---|
127 | </P> |
---|
128 | <P> |
---|
129 | For example to create a box that is 2 by 6 by 10 centimeters |
---|
130 | in full length, and called <tt>BoxA</tt> one should use the |
---|
131 | following code: |
---|
132 | </P> |
---|
133 | </td> |
---|
134 | <td> |
---|
135 | <a href="javascript:remote_win(1)" |
---|
136 | onMouseOver="window.status='Get alive picture...'; return true"> |
---|
137 | <img src="geometry.src/aBox.jpg" border=0></a> |
---|
138 | </td> |
---|
139 | </tr> |
---|
140 | </table> |
---|
141 | |
---|
142 | <PRE> |
---|
143 | G4Box* aBox = new G4Box("BoxA", 1.0*cm, 3.0*cm, 5.0*cm); |
---|
144 | </PRE> |
---|
145 | </P> |
---|
146 | <P> |
---|
147 | <HR width=40% align=center noshade> |
---|
148 | </P> |
---|
149 | <P> |
---|
150 | <table border="0" width="100%" id="table2"> |
---|
151 | <tr> |
---|
152 | <td width="480" valign="top"> |
---|
153 | Similarly to create a <b>cylindrical section</b> or <b>tube</b>, |
---|
154 | one would use the constructor: |
---|
155 | <P> |
---|
156 | <font face="Courier"> |
---|
157 | G4Tubs(const G4String& pName,<br> |
---|
158 | |
---|
159 | G4double pRMin,<br> |
---|
160 | |
---|
161 | G4double pRMax,<br> |
---|
162 | |
---|
163 | G4double pDz,<br> |
---|
164 | |
---|
165 | G4double pSPhi,<br> |
---|
166 | |
---|
167 | G4double pDPhi) |
---|
168 | </font> |
---|
169 | <P> </P><P> </P><P> </P><P> </P> |
---|
170 | <P> |
---|
171 | <div align="right"><font size=-1><I> |
---|
172 | <U>In the picture</U>: pRMin = 10, pRMax = 15, pDz = 20<br> |
---|
173 | pSPhi = 0*Degree, pDPhi = 90*Degree |
---|
174 | </I></font></div> |
---|
175 | </P> |
---|
176 | </td> |
---|
177 | <td> |
---|
178 | <a href="javascript:remote_win(2)" |
---|
179 | onMouseOver="window.status='Get alive picture...'; return true"> |
---|
180 | <img src="geometry.src/aTubs.jpg" border=0 height=380></a> |
---|
181 | </td> |
---|
182 | </tr> |
---|
183 | </table> |
---|
184 | |
---|
185 | giving its name <tt>pName</tt> and its parameters which are:</P> |
---|
186 | <p> |
---|
187 | <table border=1 cellpadding=8> |
---|
188 | <tr> |
---|
189 | <td><tt>pRMin</tt> <td>Inner radius |
---|
190 | <td><tt>pRMax</tt> <td>Outer radius |
---|
191 | <tr> |
---|
192 | <td><tt>pDz</tt> <td> half length in z |
---|
193 | <td><tt>pSPhi</tt> <td>the starting phi angle in radians |
---|
194 | <tr> |
---|
195 | <td><tt>pDPhi</tt> <td>the angle of the segment in radians |
---|
196 | <td> <td>&n |
---|
197 | </table> |
---|
198 | </P> |
---|
199 | <P> |
---|
200 | <HR width=40% align=center noshade> |
---|
201 | </P> |
---|
202 | <P> |
---|
203 | <table border="0" width="100%" id="table3"> |
---|
204 | <tr> |
---|
205 | <td width="480" valign="top"> |
---|
206 | Similarly to create a <b>cone</b>, or <b>conical section</b>, |
---|
207 | one would use the constructor: |
---|
208 | <P> |
---|
209 | <font face="Courier"> |
---|
210 | G4Cons(const G4String& pName,<br> |
---|
211 | |
---|
212 | G4double pRmin1,<br> |
---|
213 | |
---|
214 | G4double pRmax1,<br> |
---|
215 | |
---|
216 | G4double pRmin2,<br> |
---|
217 | |
---|
218 | G4double pRmax2,<br> |
---|
219 | |
---|
220 | G4double pDz,<br> |
---|
221 | |
---|
222 | G4double pSPhi,<br> |
---|
223 | |
---|
224 | G4double pDPhi) |
---|
225 | </font> |
---|
226 | <P> |
---|
227 | <div align="right"><font size=-1><I> |
---|
228 | <U>In the picture</U>: pRmin1 = 5, pRmax1 = 10,<br> |
---|
229 | pRmin2 = 20, pRmax2 = 25<br> |
---|
230 | pDz = 40, pSPhi = 0, pDPhi = 4/3*Pi |
---|
231 | </I></font></div> |
---|
232 | </P> |
---|
233 | </td> |
---|
234 | <td><a href="javascript:remote_win(3)" |
---|
235 | onMouseOver="window.status='Get alive picture...'; return true"> |
---|
236 | <img src="geometry.src/aCons.jpg" border="0"></a> |
---|
237 | </td> |
---|
238 | </tr> |
---|
239 | </table> |
---|
240 | |
---|
241 | giving its name <tt>pName</tt>, and its parameters which are:</P> |
---|
242 | <P> |
---|
243 | <table border=1 cellpadding=8> |
---|
244 | <tr> |
---|
245 | <TD><tt>pRmin1 <td>inside radius at <tt>-pDz</tt> |
---|
246 | <TD><tt>pRmax1 <td>outside radius at <tt>-pDz</tt> |
---|
247 | <tr> |
---|
248 | <TD><tt>pRmin2 <td>inside radius at <tt>+pDz</tt> |
---|
249 | <TD><tt>pRmax2 <td>outside radius at <tt>+pDz</tt> |
---|
250 | <tr> |
---|
251 | <TD><tt>pDz </tt> <td> half length in z |
---|
252 | <TD><tt>pSPhi</tt> <td> starting angle of the segment in radians |
---|
253 | <tr> |
---|
254 | <TD><tt>pDPhi</tt> <td> the angle of the segment in radians |
---|
255 | <td> <td> |
---|
256 | </table> |
---|
257 | </P> |
---|
258 | <P> |
---|
259 | <HR width=40% align=center noshade> |
---|
260 | </P> |
---|
261 | <P> |
---|
262 | <table border="0" width="100%" id="table4"> |
---|
263 | <tr> |
---|
264 | <td width="480" valign="top"> |
---|
265 | A <b>parallelepiped</b> is constructed using: |
---|
266 | <P> |
---|
267 | <font face="Courier"> |
---|
268 | G4Para(const G4String& pName,<br> |
---|
269 | |
---|
270 | G4double dx,<br> |
---|
271 | |
---|
272 | G4double dy,<br> |
---|
273 | |
---|
274 | G4double dz,<br> |
---|
275 | |
---|
276 | G4double alpha,<br> |
---|
277 | |
---|
278 | G4double theta,<br> |
---|
279 | |
---|
280 | G4double phi) |
---|
281 | </font> |
---|
282 | <P> |
---|
283 | <div align="right"><font size=-1><I> |
---|
284 | <U>In the picture</U>: dx = 30, dy = 40, dz = 60<br> |
---|
285 | alpha = 10*Degree, theta = 20*Degree,<br> |
---|
286 | phi = 5*Degree |
---|
287 | </I></font></div> |
---|
288 | </P> |
---|
289 | </td> |
---|
290 | <td><a href="javascript:remote_win(4)" |
---|
291 | onMouseOver="window.status='Get alive picture...'; return true"> |
---|
292 | <img src="geometry.src/aPara.jpg" border="0"></a> |
---|
293 | </td> |
---|
294 | </tr> |
---|
295 | </table> |
---|
296 | |
---|
297 | giving its name <tt>pName</tt> and its parameters which are:</P> |
---|
298 | <P> |
---|
299 | <table border=1 cellpadding=8> |
---|
300 | <tr> |
---|
301 | <TD><tt>dx,dy,dz</tt> <td> Half-length in x,y,z |
---|
302 | <tr> |
---|
303 | <TD valign=top><tt>alpha</tt> <td>Angle formed by the y axis and by the |
---|
304 | plane joining the centre of the faces <i>parallel</i> to |
---|
305 | the z-x plane at -dy and +dy |
---|
306 | <tr> |
---|
307 | <TD valign=top><tt>theta</tt> <td>Polar angle of the line joining the |
---|
308 | centres of the faces at -dz and +dz in z |
---|
309 | <tr> |
---|
310 | <TD valign=top><tt>phi</tt> <td>Azimuthal angle of the line joining the |
---|
311 | centres of the faces at -dz and +dz in z |
---|
312 | </table> |
---|
313 | </P> |
---|
314 | <P> |
---|
315 | <HR width=40% align=center noshade> |
---|
316 | </P> |
---|
317 | <P> |
---|
318 | <table border="0" width="100%" id="table5"> |
---|
319 | <tr> |
---|
320 | <td width="480" valign="top"> |
---|
321 | To construct a <b>trapezoid</b> use: |
---|
322 | <P> |
---|
323 | <font face="Courier"> |
---|
324 | G4Trd(const G4String& pName,<br> |
---|
325 | |
---|
326 | G4double dx1,<br> |
---|
327 | |
---|
328 | G4double dx2,<br> |
---|
329 | |
---|
330 | G4double dy1,<br> |
---|
331 | |
---|
332 | G4double dy2,<br> |
---|
333 | |
---|
334 | G4double dz) |
---|
335 | </font> |
---|
336 | <P> </P><P> </P> |
---|
337 | <P> |
---|
338 | <div align="right"><font size=-1><I> |
---|
339 | <U>In the picture</U>: dx1 = 30, dx2 = 10<br> |
---|
340 | dy1 = 40, dy2 = 15<br> |
---|
341 | dz = 60 |
---|
342 | </I></font></div> |
---|
343 | </P> |
---|
344 | </td> |
---|
345 | <td><a href="javascript:remote_win(5)" |
---|
346 | onMouseOver="window.status='Get alive picture...'; return true"> |
---|
347 | <img src="geometry.src/aTrd.jpg" border="0"></a> |
---|
348 | </td> |
---|
349 | </tr> |
---|
350 | </table> |
---|
351 | |
---|
352 | to obtain a solid with name <tt>pName</tt> and parameters</P> |
---|
353 | <P> |
---|
354 | <table border=1 cellpadding=8> |
---|
355 | <tr> |
---|
356 | <TD><tt>dx1</tt> <td>Half-length along x at the surface positioned at <tt>-dz</tt> |
---|
357 | <tr> |
---|
358 | <TD><tt>dx2</tt> <td>Half-length along x at the surface positioned at <tt>+dz</tt> |
---|
359 | <tr> |
---|
360 | <TD><tt>dy1</tt> <td>Half-length along y at the surface positioned at <tt>-dz</tt> |
---|
361 | <tr> |
---|
362 | <TD><tt>dy2</tt> <td>Half-length along y at the surface positioned at <tt>+dz</tt> |
---|
363 | <tr> |
---|
364 | <TD><tt>dz</tt> <td>Half-length along z axis |
---|
365 | </table> |
---|
366 | </P> |
---|
367 | <P> |
---|
368 | <HR width=40% align=center noshade> |
---|
369 | </P> |
---|
370 | <P> |
---|
371 | <table border="0" width="100%" id="table6"> |
---|
372 | <tr> |
---|
373 | <td width="480" valign="top"> |
---|
374 | To build a <b>generic trapezoid</b>, the <tt>G4Trap</tt> class is provided. |
---|
375 | Here are the two costructors for a Right Angular Wedge and for the general |
---|
376 | trapezoid for it: |
---|
377 | <P> |
---|
378 | <font face="Courier"> |
---|
379 | G4Trap(const G4String& pName,<br> |
---|
380 | |
---|
381 | G4double pZ,<br> |
---|
382 | |
---|
383 | G4double pY,<br> |
---|
384 | |
---|
385 | G4double pX,<br> |
---|
386 | |
---|
387 | G4double pLTX) |
---|
388 | <P></P> |
---|
389 | G4Trap(const G4String& pName,<br> |
---|
390 | |
---|
391 | G4double pDz, |
---|
392 | G4double pTheta,<br> |
---|
393 | |
---|
394 | G4double pPhi, |
---|
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> |
---|