Geant4
10.00.p01
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#include <USphere.hh>
Public Member Functions | |
USphere (const std::string &pName, double pRmin, double pRmax, double pSPhi, double pDPhi, double pSTheta, double pDTheta) | |
~USphere () | |
double | GetInnerRadius () const |
double | GetOuterRadius () const |
double | GetStartPhiAngle () const |
double | GetDeltaPhiAngle () const |
double | GetStartThetaAngle () const |
double | GetDeltaThetaAngle () const |
void | SetInnerRadius (double newRMin) |
void | SetOuterRadius (double newRmax) |
void | SetStartPhiAngle (double newSphi, bool trig=true) |
void | SetDeltaPhiAngle (double newDphi) |
void | SetStartThetaAngle (double newSTheta) |
void | SetDeltaThetaAngle (double newDTheta) |
double | Capacity () |
double | SurfaceArea () |
VUSolid::EnumInside | Inside (const UVector3 &p) const |
bool | Normal (const UVector3 &p, UVector3 &n) const |
double | DistanceToIn (const UVector3 &p, const UVector3 &v, double aPstep=UUtils::kInfinity) const |
double | SafetyFromOutside (const UVector3 &p, bool aAccurate=false) const |
double | DistanceToOut (const UVector3 &p, const UVector3 &v, UVector3 &n, bool &validNorm, double aPstep=UUtils::kInfinity) const |
double | SafetyFromInside (const UVector3 &p, bool aAccurate=false) const |
UGeometryType | GetEntityType () const |
UVector3 | GetPointOnSurface () const |
VUSolid * | Clone () const |
std::ostream & | StreamInfo (std::ostream &os) const |
UVisExtent | GetExtent () const |
void | Extent (UVector3 &aMin, UVector3 &aMax) const |
void | GetParametersList (int, double *) const |
virtual void | ComputeBBox (UBBox *, bool) |
USphere (const USphere &rhs) | |
USphere & | operator= (const USphere &rhs) |
double | GetRmin () const |
double | GetRmax () const |
double | GetSPhi () const |
double | GetDPhi () const |
double | GetSTheta () const |
double | GetDTheta () const |
double | GetInsideRadius () const |
void | SetInsideRadius (double newRmin) |
Public Member Functions inherited from VUSolid | |
VUSolid () | |
VUSolid (const std::string &name) | |
virtual | ~VUSolid () |
double | GetCarTolerance () const |
double | GetRadTolerance () const |
double | GetAngTolerance () const |
void | SetCarTolerance (double eps) |
void | SetRadTolerance (double eps) |
void | SetAngTolerance (double eps) |
virtual void | ExtentAxis (EAxisType aAxis, double &aMin, double &aMax) const |
const std::string & | GetName () const |
void | SetName (const std::string &aName) |
virtual void | SamplePointsInside (int, UVector3 *) const |
virtual void | SamplePointsOnSurface (int, UVector3 *) const |
virtual void | SamplePointsOnEdge (int, UVector3 *) const |
double | EstimateCubicVolume (int nStat, double epsilon) const |
double | EstimateSurfaceArea (int nStat, double ell) const |
Private Types | |
enum | ESide { kNull, kRMin, kRMax, kSPhi, kEPhi, kSTheta, kETheta } |
enum | ENorm { kNRMin, kNRMax, kNSPhi, kNEPhi, kNSTheta, kNETheta } |
Private Member Functions | |
void | Initialize () |
void | CheckThetaAngles (double sTheta, double dTheta) |
void | CheckSPhiAngle (double sPhi) |
void | CheckDPhiAngle (double dPhi) |
void | CheckPhiAngles (double sPhi, double dPhi) |
void | InitializePhiTrigonometry () |
void | InitializeThetaTrigonometry () |
UVector3 | ApproxSurfaceNormal (const UVector3 &p) const |
Private Attributes | |
double | fCubicVolume |
double | fSurfaceArea |
double | fRminTolerance |
double | kTolerance |
double | kAngTolerance |
double | kRadTolerance |
double | fEpsilon |
double | fRmin |
double | fRmax |
double | fSPhi |
double | fDPhi |
double | fSTheta |
double | fDTheta |
double | sinCPhi |
double | cosCPhi |
double | cosHDPhiOT |
double | cosHDPhiIT |
double | sinSPhi |
double | cosSPhi |
double | sinEPhi |
double | cosEPhi |
double | hDPhi |
double | cPhi |
double | ePhi |
double | sinSTheta |
double | cosSTheta |
double | sinETheta |
double | cosETheta |
double | tanSTheta |
double | tanSTheta2 |
double | tanETheta |
double | tanETheta2 |
double | eTheta |
bool | fFullPhiSphere |
bool | fFullThetaSphere |
bool | fFullSphere |
Additional Inherited Members | |
Public Types inherited from VUSolid | |
enum | EnumInside { eInside =0, eSurface =1, eOutside =2 } |
enum | EAxisType { eXaxis =0, eYaxis =1, eZaxis =2 } |
Static Public Member Functions inherited from VUSolid | |
static double | Tolerance () |
Static Protected Attributes inherited from VUSolid | |
static double | fgTolerance = 1.0E-9 |
static double | frTolerance = 1.0E-9 |
static double | faTolerance = 1.0E-9 |
Definition at line 55 of file USphere.hh.
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Enumerator | |
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kNRMin | |
kNRMax | |
kNSPhi | |
kNEPhi | |
kNSTheta | |
kNETheta |
Definition at line 179 of file USphere.hh.
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Enumerator | |
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kNull | |
kRMin | |
kRMax | |
kSPhi | |
kEPhi | |
kSTheta | |
kETheta |
Definition at line 175 of file USphere.hh.
USphere::USphere | ( | const std::string & | pName, |
double | pRmin, | ||
double | pRmax, | ||
double | pSPhi, | ||
double | pDPhi, | ||
double | pSTheta, | ||
double | pDTheta | ||
) |
Definition at line 34 of file USphere.cc.
References CheckPhiAngles(), CheckThetaAngles(), UUtils::Exception(), FatalErrorInArguments, VUSolid::faTolerance, fEpsilon, fRmax, fRmin, fRminTolerance, VUSolid::frTolerance, VUSolid::GetName(), kAngTolerance, kRadTolerance, kTolerance, and G4INCL::Math::max().
Referenced by Clone().
USphere::~USphere | ( | ) |
Definition at line 70 of file USphere.cc.
USphere::USphere | ( | const USphere & | rhs | ) |
Definition at line 78 of file USphere.cc.
Definition at line 436 of file USphere.cc.
References cosEPhi, cosETheta, cosSPhi, cosSTheta, UUtils::Exception(), fDPhi, fDTheta, fFullPhiSphere, fFullThetaSphere, fRmax, fRmin, fSPhi, fSTheta, kNEPhi, kNETheta, kNRMax, kNRMin, kNSPhi, kNSTheta, UUtils::kPi, sinEPhi, sinETheta, sinSPhi, sinSTheta, Warning, UVector3::x, UVector3::y, and UVector3::z.
Referenced by Normal().
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Implements VUSolid.
Definition at line 489 of file USphere.hh.
References fCubicVolume, fDPhi, fDTheta, fRmax, fRmin, and fSTheta.
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Definition at line 351 of file USphere.hh.
References UUtils::Exception(), FatalError, fDPhi, fFullPhiSphere, fSPhi, VUSolid::GetName(), kAngTolerance, and UUtils::kPi.
Referenced by CheckPhiAngles().
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Definition at line 379 of file USphere.hh.
References CheckDPhiAngle(), CheckSPhiAngle(), fFullPhiSphere, fFullSphere, fFullThetaSphere, and InitializePhiTrigonometry().
Referenced by SetDeltaPhiAngle(), and USphere().
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Definition at line 332 of file USphere.hh.
References fDPhi, fSPhi, and UUtils::kPi.
Referenced by CheckPhiAngles(), and SetStartPhiAngle().
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Definition at line 287 of file USphere.hh.
References UUtils::Exception(), FatalError, fDTheta, fFullPhiSphere, fFullSphere, fFullThetaSphere, fSTheta, VUSolid::GetName(), InitializeThetaTrigonometry(), and UUtils::kPi.
Referenced by SetDeltaThetaAngle(), SetStartThetaAngle(), and USphere().
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Implements VUSolid.
Definition at line 2805 of file USphere.cc.
References USphere().
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Implements VUSolid.
Definition at line 129 of file USphere.hh.
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Implements VUSolid.
Definition at line 611 of file USphere.cc.
References cosCPhi, cosEPhi, cosHDPhiIT, cosHDPhiOT, cosSPhi, d2, eTheta, fFullPhiSphere, fFullThetaSphere, fRmax, fRmin, fRminTolerance, fSTheta, UUtils::Infinity(), kAngTolerance, UUtils::kPi, kTolerance, sinCPhi, sinEPhi, sinSPhi, tanETheta2, tanSTheta2, VUSolid::Tolerance(), UVector3::x, UVector3::y, and UVector3::z.
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Implements VUSolid.
Definition at line 1651 of file USphere.cc.
References cosCPhi, cosEPhi, cosSPhi, d2, ePhi, eTheta, UUtils::Exception(), fDPhi, fFullPhiSphere, fFullThetaSphere, fRmax, fRmin, fRminTolerance, fSPhi, fSTheta, UUtils::Infinity(), kAngTolerance, kEPhi, kETheta, kNull, UUtils::kPi, kRMax, kRMin, kSPhi, kSTheta, kTolerance, sinCPhi, sinEPhi, sinETheta, sinSPhi, tanETheta, tanETheta2, tanSTheta, tanSTheta2, VUSolid::Tolerance(), Warning, UVector3::x, UVector3::y, and UVector3::z.
Implements VUSolid.
Definition at line 2983 of file USphere.cc.
References fRmax, and UVector3::Set().
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Definition at line 230 of file USphere.hh.
References fDPhi.
Referenced by G4USphere::GetDeltaPhiAngle(), GetDPhi(), and GetParametersList().
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Definition at line 241 of file USphere.hh.
References fDTheta.
Referenced by G4USphere::GetDeltaThetaAngle(), GetDTheta(), and GetParametersList().
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Definition at line 471 of file USphere.hh.
References GetDeltaPhiAngle().
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Definition at line 483 of file USphere.hh.
References GetDeltaThetaAngle().
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Implements VUSolid.
Definition at line 2796 of file USphere.cc.
UVisExtent USphere::GetExtent | ( | ) | const |
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Definition at line 212 of file USphere.hh.
References fRmin.
Referenced by G4USphere::GetInnerRadius(), and GetParametersList().
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Definition at line 206 of file USphere.hh.
References fRmin.
Referenced by GetRmin().
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Definition at line 218 of file USphere.hh.
References fRmax.
Referenced by G4USphere::GetOuterRadius(), GetParametersList(), and GetRmax().
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Implements VUSolid.
Definition at line 2989 of file USphere.cc.
References GetDeltaPhiAngle(), GetDeltaThetaAngle(), GetInnerRadius(), GetOuterRadius(), GetStartPhiAngle(), and GetStartThetaAngle().
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Implements VUSolid.
Definition at line 2838 of file USphere.cc.
References cosEPhi, cosETheta, cosSPhi, cosSTheta, ePhi, eTheta, fDPhi, fDTheta, fFullPhiSphere, fRmax, fRmin, fSPhi, fSTheta, UUtils::GetRadiusInRing(), UUtils::kPi, UUtils::Random(), sinEPhi, sinETheta, sinSPhi, sinSTheta, UUtils::sqr(), tanETheta, and tanSTheta.
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Definition at line 459 of file USphere.hh.
References GetOuterRadius().
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Definition at line 453 of file USphere.hh.
References GetInsideRadius().
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Definition at line 465 of file USphere.hh.
References GetStartPhiAngle().
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Definition at line 224 of file USphere.hh.
References fSPhi.
Referenced by GetParametersList(), GetSPhi(), and G4USphere::GetStartPhiAngle().
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Definition at line 236 of file USphere.hh.
References fSTheta.
Referenced by GetParametersList(), G4USphere::GetStartThetaAngle(), and GetSTheta().
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Definition at line 477 of file USphere.hh.
References GetStartThetaAngle().
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Definition at line 247 of file USphere.hh.
References fCubicVolume, and fSurfaceArea.
Referenced by SetDeltaPhiAngle(), SetDeltaThetaAngle(), SetInsideRadius(), SetOuterRadius(), SetStartPhiAngle(), and SetStartThetaAngle().
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Definition at line 254 of file USphere.hh.
References cosCPhi, cosEPhi, cosHDPhiIT, cosHDPhiOT, cosSPhi, cPhi, ePhi, fDPhi, fSPhi, hDPhi, kAngTolerance, sinCPhi, sinEPhi, and sinSPhi.
Referenced by CheckPhiAngles(), and SetStartPhiAngle().
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Definition at line 271 of file USphere.hh.
References cosETheta, cosSTheta, eTheta, fDTheta, fSTheta, sinETheta, sinSTheta, tanETheta, tanETheta2, tanSTheta, and tanSTheta2.
Referenced by CheckThetaAngles().
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Implements VUSolid.
Definition at line 164 of file USphere.cc.
References VUSolid::eInside, VUSolid::eOutside, ePhi, VUSolid::eSurface, eTheta, fFullPhiSphere, fFullThetaSphere, fRmax, fRmin, fRminTolerance, fSPhi, fSTheta, kAngTolerance, UUtils::kPi, kTolerance, G4INCL::Math::max(), UVector3::x, UVector3::y, and UVector3::z.
Referenced by SafetyFromInside().
Implements VUSolid.
Definition at line 273 of file USphere.cc.
References ApproxSurfaceNormal(), cosEPhi, cosETheta, cosSPhi, cosSTheta, ePhi, eTheta, UUtils::Exception(), fFullPhiSphere, fFullSphere, fFullThetaSphere, fRmax, fRmin, fSPhi, fSTheta, UUtils::Infinity(), kAngTolerance, UUtils::kPi, sinEPhi, sinETheta, sinSPhi, sinSTheta, VUSolid::Tolerance(), UVector3::Unit(), Warning, UVector3::x, UVector3::y, and UVector3::z.
Definition at line 103 of file USphere.cc.
References cosCPhi, cosEPhi, cosETheta, cosHDPhiIT, cosHDPhiOT, cosSPhi, cosSTheta, cPhi, ePhi, eTheta, fCubicVolume, fDPhi, fDTheta, fEpsilon, fFullPhiSphere, fFullSphere, fFullThetaSphere, fRmax, fRmin, fRminTolerance, fSPhi, fSTheta, fSurfaceArea, hDPhi, kAngTolerance, kRadTolerance, kTolerance, sinCPhi, sinEPhi, sinETheta, sinSPhi, sinSTheta, tanETheta, tanETheta2, tanSTheta, and tanSTheta2.
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Implements VUSolid.
Definition at line 2557 of file USphere.cc.
References cosCPhi, cosEPhi, cosSPhi, VUSolid::eOutside, eTheta, UUtils::Exception(), fFullPhiSphere, fRmax, fRmin, fSTheta, Inside(), UUtils::kPi, sinCPhi, sinEPhi, sinSPhi, Warning, UVector3::x, UVector3::y, and UVector3::z.
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Implements VUSolid.
Definition at line 1546 of file USphere.cc.
References cosCPhi, cosEPhi, cosSPhi, eTheta, fFullPhiSphere, fFullThetaSphere, fRmax, fRmin, fSTheta, hDPhi, UUtils::kPi, sinCPhi, sinEPhi, sinSPhi, UVector3::x, UVector3::y, and UVector3::z.
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Definition at line 430 of file USphere.hh.
References CheckPhiAngles(), fSPhi, and Initialize().
Referenced by G4USphere::SetDeltaPhiAngle().
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Definition at line 444 of file USphere.hh.
References CheckThetaAngles(), fSTheta, and Initialize().
Referenced by G4USphere::SetDeltaThetaAngle().
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Definition at line 401 of file USphere.hh.
References SetInsideRadius().
Referenced by G4USphere::SetInnerRadius().
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Definition at line 393 of file USphere.hh.
References fEpsilon, fRmin, fRminTolerance, Initialize(), kRadTolerance, and G4INCL::Math::max().
Referenced by SetInnerRadius().
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Definition at line 407 of file USphere.hh.
References fEpsilon, fRmax, Initialize(), kRadTolerance, kTolerance, and G4INCL::Math::max().
Referenced by G4USphere::SetOuterRadius().
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Definition at line 415 of file USphere.hh.
References CheckSPhiAngle(), fFullPhiSphere, Initialize(), and InitializePhiTrigonometry().
Referenced by G4USphere::SetStartPhiAngle().
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Definition at line 437 of file USphere.hh.
References CheckThetaAngles(), fDTheta, and Initialize().
Referenced by G4USphere::SetStartThetaAngle().
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Implements VUSolid.
Definition at line 2814 of file USphere.cc.
References fDPhi, fDTheta, fRmax, fRmin, fSPhi, fSTheta, VUSolid::GetName(), and UUtils::kPi.
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Implements VUSolid.
Definition at line 2935 of file USphere.cc.
References cosETheta, cosSTheta, eTheta, fDPhi, fDTheta, fFullPhiSphere, fRmax, fRmin, fSTheta, fSurfaceArea, UUtils::kPi, sinETheta, and sinSTheta.
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Definition at line 190 of file USphere.hh.
Referenced by DistanceToIn(), DistanceToOut(), InitializePhiTrigonometry(), operator=(), SafetyFromInside(), and SafetyFromOutside().
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Definition at line 190 of file USphere.hh.
Referenced by ApproxSurfaceNormal(), DistanceToIn(), DistanceToOut(), GetPointOnSurface(), InitializePhiTrigonometry(), Normal(), operator=(), SafetyFromInside(), and SafetyFromOutside().
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Definition at line 195 of file USphere.hh.
Referenced by ApproxSurfaceNormal(), GetPointOnSurface(), InitializeThetaTrigonometry(), Normal(), operator=(), and SurfaceArea().
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Definition at line 190 of file USphere.hh.
Referenced by DistanceToIn(), InitializePhiTrigonometry(), and operator=().
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Definition at line 190 of file USphere.hh.
Referenced by DistanceToIn(), InitializePhiTrigonometry(), and operator=().
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Definition at line 190 of file USphere.hh.
Referenced by ApproxSurfaceNormal(), DistanceToIn(), DistanceToOut(), GetPointOnSurface(), InitializePhiTrigonometry(), Normal(), operator=(), SafetyFromInside(), and SafetyFromOutside().
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Definition at line 195 of file USphere.hh.
Referenced by ApproxSurfaceNormal(), GetPointOnSurface(), InitializeThetaTrigonometry(), Normal(), operator=(), and SurfaceArea().
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Definition at line 190 of file USphere.hh.
Referenced by InitializePhiTrigonometry(), and operator=().
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Definition at line 190 of file USphere.hh.
Referenced by DistanceToOut(), GetPointOnSurface(), InitializePhiTrigonometry(), Inside(), Normal(), and operator=().
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Definition at line 195 of file USphere.hh.
Referenced by DistanceToIn(), DistanceToOut(), GetPointOnSurface(), InitializeThetaTrigonometry(), Inside(), Normal(), operator=(), SafetyFromInside(), SafetyFromOutside(), and SurfaceArea().
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Definition at line 148 of file USphere.hh.
Referenced by Capacity(), Initialize(), and operator=().
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Definition at line 186 of file USphere.hh.
Referenced by ApproxSurfaceNormal(), Capacity(), CheckDPhiAngle(), CheckSPhiAngle(), DistanceToOut(), GetDeltaPhiAngle(), GetPointOnSurface(), InitializePhiTrigonometry(), operator=(), StreamInfo(), and SurfaceArea().
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Definition at line 186 of file USphere.hh.
Referenced by ApproxSurfaceNormal(), Capacity(), CheckThetaAngles(), GetDeltaThetaAngle(), GetPointOnSurface(), InitializeThetaTrigonometry(), operator=(), SetStartThetaAngle(), StreamInfo(), and SurfaceArea().
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Definition at line 181 of file USphere.hh.
Referenced by operator=(), SetInsideRadius(), SetOuterRadius(), and USphere().
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Definition at line 200 of file USphere.hh.
Referenced by ApproxSurfaceNormal(), CheckDPhiAngle(), CheckPhiAngles(), CheckThetaAngles(), DistanceToIn(), DistanceToOut(), GetPointOnSurface(), Inside(), Normal(), operator=(), SafetyFromInside(), SafetyFromOutside(), SetStartPhiAngle(), and SurfaceArea().
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Definition at line 200 of file USphere.hh.
Referenced by CheckPhiAngles(), CheckThetaAngles(), Normal(), and operator=().
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Definition at line 200 of file USphere.hh.
Referenced by ApproxSurfaceNormal(), CheckPhiAngles(), CheckThetaAngles(), DistanceToIn(), DistanceToOut(), Inside(), Normal(), operator=(), and SafetyFromOutside().
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Definition at line 186 of file USphere.hh.
Referenced by ApproxSurfaceNormal(), Capacity(), DistanceToIn(), DistanceToOut(), Extent(), GetOuterRadius(), GetPointOnSurface(), Inside(), Normal(), operator=(), SafetyFromInside(), SafetyFromOutside(), SetOuterRadius(), StreamInfo(), SurfaceArea(), and USphere().
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Definition at line 186 of file USphere.hh.
Referenced by ApproxSurfaceNormal(), Capacity(), DistanceToIn(), DistanceToOut(), GetInnerRadius(), GetInsideRadius(), GetPointOnSurface(), Inside(), Normal(), operator=(), SafetyFromInside(), SafetyFromOutside(), SetInsideRadius(), StreamInfo(), SurfaceArea(), and USphere().
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Definition at line 181 of file USphere.hh.
Referenced by DistanceToIn(), DistanceToOut(), Inside(), operator=(), SetInsideRadius(), and USphere().
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Definition at line 186 of file USphere.hh.
Referenced by ApproxSurfaceNormal(), CheckDPhiAngle(), CheckSPhiAngle(), DistanceToOut(), GetPointOnSurface(), GetStartPhiAngle(), InitializePhiTrigonometry(), Inside(), Normal(), operator=(), SetDeltaPhiAngle(), and StreamInfo().
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Definition at line 186 of file USphere.hh.
Referenced by ApproxSurfaceNormal(), Capacity(), CheckThetaAngles(), DistanceToIn(), DistanceToOut(), GetPointOnSurface(), GetStartThetaAngle(), InitializeThetaTrigonometry(), Inside(), Normal(), operator=(), SafetyFromInside(), SafetyFromOutside(), SetDeltaThetaAngle(), StreamInfo(), and SurfaceArea().
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Definition at line 149 of file USphere.hh.
Referenced by Initialize(), operator=(), and SurfaceArea().
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Definition at line 190 of file USphere.hh.
Referenced by InitializePhiTrigonometry(), operator=(), and SafetyFromOutside().
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Definition at line 181 of file USphere.hh.
Referenced by CheckDPhiAngle(), DistanceToIn(), DistanceToOut(), InitializePhiTrigonometry(), Inside(), Normal(), operator=(), and USphere().
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Definition at line 181 of file USphere.hh.
Referenced by operator=(), SetInsideRadius(), SetOuterRadius(), and USphere().
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Definition at line 181 of file USphere.hh.
Referenced by DistanceToIn(), DistanceToOut(), Inside(), operator=(), SetOuterRadius(), and USphere().
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Definition at line 190 of file USphere.hh.
Referenced by DistanceToIn(), DistanceToOut(), InitializePhiTrigonometry(), operator=(), SafetyFromInside(), and SafetyFromOutside().
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Definition at line 190 of file USphere.hh.
Referenced by ApproxSurfaceNormal(), DistanceToIn(), DistanceToOut(), GetPointOnSurface(), InitializePhiTrigonometry(), Normal(), operator=(), SafetyFromInside(), and SafetyFromOutside().
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Definition at line 195 of file USphere.hh.
Referenced by ApproxSurfaceNormal(), DistanceToOut(), GetPointOnSurface(), InitializeThetaTrigonometry(), Normal(), operator=(), and SurfaceArea().
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Definition at line 190 of file USphere.hh.
Referenced by ApproxSurfaceNormal(), DistanceToIn(), DistanceToOut(), GetPointOnSurface(), InitializePhiTrigonometry(), Normal(), operator=(), SafetyFromInside(), and SafetyFromOutside().
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Definition at line 195 of file USphere.hh.
Referenced by ApproxSurfaceNormal(), GetPointOnSurface(), InitializeThetaTrigonometry(), Normal(), operator=(), and SurfaceArea().
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Definition at line 195 of file USphere.hh.
Referenced by DistanceToOut(), GetPointOnSurface(), InitializeThetaTrigonometry(), and operator=().
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Definition at line 195 of file USphere.hh.
Referenced by DistanceToIn(), DistanceToOut(), InitializeThetaTrigonometry(), and operator=().
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Definition at line 195 of file USphere.hh.
Referenced by DistanceToOut(), GetPointOnSurface(), InitializeThetaTrigonometry(), and operator=().
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Definition at line 195 of file USphere.hh.
Referenced by DistanceToIn(), DistanceToOut(), InitializeThetaTrigonometry(), and operator=().