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In these drawings the points of the various volumes and their coordinate systems are marked with names. The CATIA drawings were then converted to IGES format. A special interface analyzed these files and wrote the points and coordinate systems of the volumes into the database Oracle.

The hope was, that any change in the technical drawings could be easily converted into a new geometry for GEANT.

But this way was quite time consuming (somebody had to mark these points). Furthermore actual drawings (AUTOCAT drawings )of the inner parts of the detectors were not yet imported into CATIA for all detectors.

Additionally the requirements for GEANT imply some simplifications and modifications, which cannot be retrieved from the drawings. Therefore the final geometry definitions was written directly into ASCII files and with an interface program stored in Oracle.

The transformation describes the transformation of the local coordinate system of the daughter relative to the local coordinate system of the mother.

Some shapes are defined by a list of points (BOX, TRAP, TRD1, ...). This makes it easier to transfer the data from technical drawings into the file format, in especially for trapezes.

The geometry interface calculates automatically the parameters and transformations needed to create the volume in GEANT or ROOT.

In GEANT3 and ROOT the volume parameters are specified

The transformation therefore not only depends on the positioning of a daughter relative to the mother, but also from the size of both volumes.

In case the size of the mother changes asymmetrically, all daughter volumes need new transformations.

- A simple (artificial) example:

In the HADES input file one would not change the local coordinate system of the beam tube, but only change the volume parameters.

In the GEANT and ROOT definition one must change additionally the transformations of all three targets, because the center of the beam tube has moved.

- name of the volume
- name of the mother volume
- GEANT shape of the volume
- name of the medium (= material)
- points or parameters from technical drawings (depends on the shape)
- position (x y z) of the coordinate system, in which the points are given, in the coordinate system of the mother
- 3x3 rotational matrix of the coordinate system listed row-wise as a vector

Each volume has a name with at least 4 characters (upper case letters). Only the first 4 characters are used in GEANT (the name of the volume).

All volumes of which several copies exist (several nodes of the same volume) have names with 5 or more characters. These additionally characters are always digits ranging from 1 to the maximum number of volumes with the same 4-character GEANT name.

For example TOF 22 (the outermost TOF) contains 8 identical cells T22S1 ... T22S8. The volume T22S is created only once via GSVOLU(...) but positioned 8 times via GSPOS(...).

The names of the sensitive volumes must have a special structure defined for each detector.

This medium must be defined in the medium file (if not initialized from Oracle).

The predefined media in GEANT are

The number of these parameters and their meaning depend on the shape of the volume.

This is explained in chapter Shapes.

Its position and orientation relative to the coordinate system of the mother volume is described by a translation vector T and a 3x3 rotation matrix R according to the equation x=R*x'+T, where x is the vector in the coordinate system of the mother, and x' the vector in the coordinate system of the daughter.

The matrix R is listed row-wise as a vector with 9 components.

Each shape has its own intrinsic orientation, which is defined similar to the GEANT definition except for TRAP and TRD1 (see chapter Shapes).

The rotation matrix should be given with a precision of at least 10**-6. Otherwise you would get a lot of warnings from GEANT that the coordinate system is not orthogonal.

As long as all volumes in a module are not rotated you may use the coordinate system of the module as the base coordinate system in which all points are given.

More information about the coordinate transformations you can find in the document [[???][Hades Geometry and Database] of Michael Dahlinger. Volumes of which several copies exist may use a shortened input structure in the ASCII file:

For the first volume all information above is defined. For the other copies one must only specify

- name of the volume
- name of the mother
- translation vector of the coordinate transformation
- rotation matrix of the coordinate transformation

Apart from the shapes with 8 corners (BOX , TRAP, TRD1) the parameter are at least very similar to the ones in GEANT.

Each shape has an intrinsic coordinate system. They are the same as in GEANT except for a TRAP and a TRD1.

point 0 | NZ number of planes perpendicular to the z-axis where the section is given |

point 1 | azimuthal angle PHI1 at which the volume begins opening angle DPHI of the volume number NPDV of sides of the cross section between the phi limits |

point 2ff | z coordinate Z of the section inner radius RMIN at position z outer radius RMAX at position z |

point 0 | NZ number of planes perpendicular to the z-axis where the section is given |

point 1 | azimuthal angle PHI1 at which the volume begins opening angle DPHI of the volume |

point 2ff | z coordinate Z of the section inner radius RMIN at position z outer radius RMAX at position z |

point 0 | inner radius RMIN of the shell outer radius RMAX of the shell |

point 1 | starting polar angle THE1 of the shell ending polar angle THE2 of the shell |

point 2 | starting azimuthal angle PHI1 of the shell ending azimuthal angle PHI2 of the shell |

point 0 | x, y, z coordinate of the center of the circle at the beginning of the tube |

point 1 | nner radius RMIN of the tube outer radius RMAX of the tube |

point 2 | x, y, z coordinate of the center of the circle at the end of the tube |

point 0 | x, y, z coordinate of the center of the circle at the beginning of the tubs |

point 1 | inner radius RMIN of the tubs outer radius RMAX of the tubs |

point 2 | x, y, z coordinate of the center of the circle at the end of the tubs |

point 3 | starting angle PHI1 of the segment ending angle PHI2 of the segment |

point 0 | x, y, z coordinate of the center of the circle at the beginning of the cone |

point 1 | inner radius RMIN at the beginning of the cone outer radius RMAX at the beginning of the cone |

point 2 | x, y, z coordinate of the center of the circle at the end of the cone |

point 3 | inner radius RMN2 at the end of the cone outer radius RMX2 at the end of the cone |

Point 0 | x, y, z coordinate of the center of the circle at the beginning of the cons |

point 1 | inner radius RMN1 at the beginning of the cons outer radius RMX1 at the beginning of the cons |

point 2 | x, y, z coordinate of the center of the circle at the end of the cons |

point 3 | inner radius RMIN at the end of the cons outer radius RMAX at the end of the cons |

point 4 | starting angle PHI1 of the segment ending angle PHI2 of the segment |

point 0 | x, y, z coordinate of the center of the ellipsoid at the beginning of the eltu |

point 1 | semi-axis P1 along x semi-axis P2 along y |

point 2 | x, y, z coordinate of the center of the ellipsoid at the end of the eltu |

A rotation can only be defined by a rotation matrix. -- IlseKoenig - 16 Jul 2007

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