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e7d719328412c7d410d5c37b1f91ee0612e4f4c5
geant4/source/geometry/solids/specific/src/G4Hype.cc
T
Gabriele Cosmo e7d7193284 Import Geant4 2.0.0 source tree
2016-06-08 15:42:07 +02:00

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// This code implementation is the intellectual property of
// the GEANT4 collaboration.
//
// By copying, distributing or modifying the Program (or any work
// based on the Program) you indicate your acceptance of this statement,
// and all its terms.
//
// $Id: G4Hype.cc,v 1.3 2000/04/19 17:56:44 davidw Exp $
// $Original: G4Hype.cc,v 1.0 1998/06/09 16:57:50 safai Exp $
// GEANT4 tag $Name: geant4-02-00 $
//
//
// --------------------------------------------------------------------
// GEANT 4 class source file
//
//
// G4Hype.cc
//
// This class implements in G4 the volume equivalent to the HYPE volume
// in Geant 3.21, i.e. a tube with hyperbolic profile.
// For further informations, please read G4Hype.history and G4Hype.doc,
// and the G4Hype.hh header.
//
// --------------------------------------------------------------------
//
// Authors:
// Ernesto Lamanna (Ernesto.Lamanna@roma1.infn.it) &
// Francesco Safai Tehrani (Francesco.SafaiTehrani@roma1.infn.it)
// Rome, INFN & University of Rome "La Sapienza", 9 June 1998.
//
// History:
// Updated Feb 2000 D.C. Williams
//
// --------------------------------------------------------------------
#include "G4Hype.hh"
#include "G4VoxelLimits.hh"
#include "G4AffineTransform.hh"
#include "G4SolidExtentList.hh"
#include "G4ClippablePolygon.hh"
#include "G4VPVParameterisation.hh"
#include "meshdefs.hh"
#include "G4VGraphicsScene.hh"
#include "G4Polyhedron.hh"
#include "G4VisExtent.hh"
#include "G4NURBS.hh"
#include "G4NURBStube.hh"
#include "G4NURBScylinder.hh"
#include "G4NURBStubesector.hh"
// Constructor - check parameters, and fills protected data members
G4Hype::G4Hype(const G4String& pName,
const G4double newInnerRadius,
const G4double newOuterRadius,
const G4double newInnerStereo,
const G4double newOuterStereo,
const G4double newHalfLenZ) : G4VSolid(pName)
{
// Check z-len
if (newHalfLenZ>0)
{
halfLenZ=newHalfLenZ;
}
else
{
G4Exception("Error in G4Hype::G4Hype - invalid z half-length");
}
// Check radii
if (newInnerRadius>=0 && newOuterRadius>=0)
if (newInnerRadius < newOuterRadius) {
innerRadius=newInnerRadius;
outerRadius=newOuterRadius;
}
else { // swapping radii (:-)
// innerRadius=newOuterRadius;
// outerRadius=newInnerRadius;
// DCW: swapping is fine, but what about the stereo angles???
G4Exception( "Error in G4Hype::G4Hype outer > inner radius" );
}
else
{
G4Exception("Error in G4Hype::G4Hype - invalid radii");
}
innerRadius2=innerRadius*innerRadius;
outerRadius2=outerRadius*outerRadius;
SetInnerStereo( newInnerStereo );
SetOuterStereo( newOuterStereo );
}
// Destructor
G4Hype::~G4Hype()
{;}
// Dispatch to parameterisation for replication mechanism dimension
// computation & modification.
void G4Hype::ComputeDimensions(G4VPVParameterisation* p,
const G4int n,
const G4VPhysicalVolume* pRep)
{
p->ComputeDimensions(*this,n,pRep);
}
//
// CalculateExtent
//
G4bool G4Hype::CalculateExtent( const EAxis axis,
const G4VoxelLimits &voxelLimit,
const G4AffineTransform &transform,
G4double &min, G4double &max ) const
{
G4SolidExtentList extentList( axis, voxelLimit );
//
// Choose phi size of our segment(s) based on constants as
// defined in meshdefs.hh
//
G4int numPhi = kMaxMeshSections;
G4double sigPhi = 2*M_PI/numPhi;
G4double rFudge = 1.0/cos(0.5*sigPhi);
//
// We work around in phi building polygons along the way.
// As a reasonable compromise between accuracy and
// complexity (=cpu time), the following facets are chosen:
//
// 1. If outerRadius/endOuterRadius > 0.95, approximate
// the outer surface as a cylinder, and use one
// rectangular polygon (0-1) to build its mesh.
//
// Otherwise, use two trapazoidal polygons that
// meet at z = 0 (0-4-1)
//
// 2. If there is no inner surface, then use one
// polygon for each entire endcap. (0) and (1)
//
// Otherwise, use a trapazoidal polygon for each
// phi segment of each endcap. (0-2) and (1-3)
//
// 3. For the inner surface, if innerRadius/endInnerRadius > 0.95,
// approximate the inner surface as a cylinder of
// radius innerRadius and use one rectangular polygon
// to build each phi segment of its mesh. (2-3)
//
// Otherwise, use one rectangular polygon centered
// at z = 0 (5-6) and two connecting trapazoidal polygons
// for each phi segment (2-5) and (3-6).
//
G4bool splitOuter = (outerRadius/endOuterRadius < 0.95);
G4bool splitInner;
if (InnerSurfaceExists()) {
splitInner = (innerRadius/endInnerRadius < 0.95);
}
//
// Vertex assignments (v and w arrays)
// [0] and [1] are mandatory
// the rest are optional
//
// + -
// [0]------[4]------[1] <--- outer radius
// | |
// | |
// [2]---[5]---[6]---[3] <--- inner radius
//
G4ClippablePolygon endPoly1, endPoly2;
G4double phi = 0,
cosPhi = cos(phi),
sinPhi = sin(phi);
G4ThreeVector v0( rFudge*endOuterRadius*cosPhi, rFudge*endOuterRadius*sinPhi, +halfLenZ ),
v1( rFudge*endOuterRadius*cosPhi, rFudge*endOuterRadius*sinPhi, -halfLenZ ),
v2, v3, v4, v5, v6,
w0, w1, w2, w3, w4, w5, w6;
transform.ApplyPointTransform( v0 );
transform.ApplyPointTransform( v1 );
G4double zInnerSplit;
if (InnerSurfaceExists()) {
if (splitInner) {
v2 = transform.TransformPoint(
G4ThreeVector( endInnerRadius*cosPhi, endInnerRadius*sinPhi, +halfLenZ ) );
v3 = transform.TransformPoint(
G4ThreeVector( endInnerRadius*cosPhi, endInnerRadius*sinPhi, -halfLenZ ) );
//
// Find intersection of line normal to inner
// surface at z = halfLenZ and line r=innerRadius
//
G4double rn = halfLenZ*tanInnerStereo2;
G4double zn = endInnerRadius;
zInnerSplit = halfLenZ + (innerRadius - endInnerRadius)*zn/rn;
//
// Build associated vertices
//
v5 = transform.TransformPoint(
G4ThreeVector( innerRadius*cosPhi, innerRadius*sinPhi, +zInnerSplit ) );
v6 = transform.TransformPoint(
G4ThreeVector( innerRadius*cosPhi, innerRadius*sinPhi, -zInnerSplit ) );
}
else {
v2 = transform.TransformPoint(
G4ThreeVector( innerRadius*cosPhi, innerRadius*sinPhi, +halfLenZ ) );
v3 = transform.TransformPoint(
G4ThreeVector( innerRadius*cosPhi, innerRadius*sinPhi, -halfLenZ ) );
}
}
if (splitOuter) {
v4 = transform.TransformPoint(
G4ThreeVector( rFudge*outerRadius*cosPhi, rFudge*outerRadius*sinPhi, 0 ) );
}
//
// Loop over phi segments
//
do {
phi += sigPhi;
if (numPhi == 1) phi = 0; // Try to avoid roundoff
cosPhi = cos(phi),
sinPhi = sin(phi);
G4double r(rFudge*endOuterRadius);
w0 = G4ThreeVector( r*cosPhi, r*sinPhi, +halfLenZ );
w1 = G4ThreeVector( r*cosPhi, r*sinPhi, -halfLenZ );
transform.ApplyPointTransform( w0 );
transform.ApplyPointTransform( w1 );
//
// Outer hyperbolic surface
//
if (splitOuter) {
r = rFudge*outerRadius;
w4 = G4ThreeVector( r*cosPhi, r*sinPhi, 0 );
transform.ApplyPointTransform( w4 );
AddPolyToExtent( v0, v4, w4, w0, voxelLimit, axis, extentList );
AddPolyToExtent( v4, v1, w1, w4, voxelLimit, axis, extentList );
}
else {
AddPolyToExtent( v0, v1, w1, w0, voxelLimit, axis, extentList );
}
if (InnerSurfaceExists()) {
//
// Inner hyperbolic surface
//
if (splitInner) {
w2 = G4ThreeVector( endInnerRadius*cosPhi, endInnerRadius*sinPhi, +halfLenZ );
w3 = G4ThreeVector( endInnerRadius*cosPhi, endInnerRadius*sinPhi, -halfLenZ );
transform.ApplyPointTransform( w2 );
transform.ApplyPointTransform( w3 );
w5 = G4ThreeVector( innerRadius*cosPhi, innerRadius*sinPhi, +zInnerSplit );
w6 = G4ThreeVector( innerRadius*cosPhi, innerRadius*sinPhi, -zInnerSplit );
transform.ApplyPointTransform( w5 );
transform.ApplyPointTransform( w6 );
AddPolyToExtent( v3, v6, w6, w3, voxelLimit, axis, extentList );
AddPolyToExtent( v6, v5, w5, w6, voxelLimit, axis, extentList );
AddPolyToExtent( v5, v2, w2, w5, voxelLimit, axis, extentList );
}
else {
w2 = G4ThreeVector( innerRadius*cosPhi, innerRadius*sinPhi, +halfLenZ );
w3 = G4ThreeVector( innerRadius*cosPhi, innerRadius*sinPhi, -halfLenZ );
transform.ApplyPointTransform( w2 );
transform.ApplyPointTransform( w3 );
AddPolyToExtent( v3, v2, w2, w3, voxelLimit, axis, extentList );
}
//
// Endplate segments
//
AddPolyToExtent( v1, v3, w3, w1, voxelLimit, axis, extentList );
AddPolyToExtent( v2, v0, w0, w2, voxelLimit, axis, extentList );
}
else {
//
// Continue building endplate polygons
//
endPoly1.AddVertexInOrder( v0 );
endPoly2.AddVertexInOrder( v1 );
}
//
// Next phi segments
//
v0 = w0;
v1 = w1;
if (InnerSurfaceExists()) {
v2 = w2;
v3 = w3;
if (splitInner) {
v5 = w5;
v6 = w6;
}
}
if (splitOuter) v4 = w4;
} while( --numPhi > 0 );
//
// Don't forget about the endplate polygons, if
// we use them
//
if (!InnerSurfaceExists()) {
if (endPoly1.PartialClip( voxelLimit, axis )) {
static const G4ThreeVector normal(0,0,+1);
endPoly1.SetNormal( transform.TransformAxis(normal) );
extentList.AddSurface( endPoly1 );
}
if (endPoly2.PartialClip( voxelLimit, axis )) {
static const G4ThreeVector normal(0,0,-1);
endPoly2.SetNormal( transform.TransformAxis(normal) );
extentList.AddSurface( endPoly2 );
}
}
//
// Return min/max value
//
return extentList.GetExtent( min, max );
}
//
// AddPolyToExtent (static)
//
// Utility function for CalculateExtent
//
void G4Hype::AddPolyToExtent( const G4ThreeVector &v0,
const G4ThreeVector &v1,
const G4ThreeVector &w1,
const G4ThreeVector &w0,
const G4VoxelLimits &voxelLimit,
const EAxis axis,
G4SolidExtentList &extentList )
{
G4ClippablePolygon phiPoly;
phiPoly.AddVertexInOrder( v0 );
phiPoly.AddVertexInOrder( v1 );
phiPoly.AddVertexInOrder( w1 );
phiPoly.AddVertexInOrder( w0 );
if (phiPoly.PartialClip( voxelLimit, axis )) {
phiPoly.SetNormal( (v1-v0).cross(w0-v0).unit() );
extentList.AddSurface( phiPoly );
}
}
//
// Decides whether point is inside,outside or on the surface
//
EInside G4Hype::Inside(const G4ThreeVector& p) const
{
static const G4double halfTol = 0.5*kCarTolerance;
//
// Check z extents: are we outside?
//
const G4double absZ(fabs(p.z()));
if (absZ > halfLenZ + halfTol) return kOutside;
//
// Check outer radius
//
const G4double oRad2(HypeOuterRadius2(absZ));
const G4double xR2( p.x()*p.x()+p.y()*p.y() );
if (xR2 > oRad2 + kCarTolerance*endOuterRadius) return kOutside;
if (xR2 > oRad2 - kCarTolerance*endOuterRadius) return kSurface;
if (InnerSurfaceExists()) {
//
// Check inner radius
//
const G4double iRad2(HypeInnerRadius2(absZ));
if (xR2 < iRad2 - kCarTolerance*endInnerRadius) return kOutside;
if (xR2 < iRad2 + kCarTolerance*endInnerRadius) return kSurface;
}
//
// We are inside in radius, now check endplate surface
//
if (absZ > halfLenZ - halfTol) return kSurface;
return kInside;
}
//
// return the normal unit vector to the Hyperbolical Surface at a point
// p on (or nearly on) the surface
//
G4ThreeVector G4Hype::SurfaceNormal( const G4ThreeVector& p) const
{
//
// Which of the three or four surfaces are we closest to?
//
const G4double absZ(fabs(p.z()));
const G4double distZ(absZ - halfLenZ);
const G4double dist2Z(distZ*distZ);
const G4double xR2( p.x()*p.x()+p.y()*p.y() );
const G4double dist2Outer( fabs(xR2 - HypeOuterRadius2(absZ)) );
if (InnerSurfaceExists()) {
//
// Has inner surface: is this closest?
//
const G4double dist2Inner( fabs(xR2 - HypeInnerRadius2(absZ)) );
if (dist2Inner < dist2Z && dist2Inner < dist2Outer)
return G4ThreeVector( -p.x(), -p.y(), p.z()*tanInnerStereo2 ).unit();
}
//
// Do the "endcaps" win?
//
if (dist2Z < dist2Outer)
return G4ThreeVector( 0.0, 0.0, p.z() < 0 ? -1.0 : 1.0 );
//
// Outer surface wins
//
return G4ThreeVector( p.x(), p.y(), -p.z()*tanOuterStereo2 ).unit();
}
//
// Calculate distance to shape from outside, along normalised vector
// - return kInfinity if no intersection, or intersection distance <= tolerance
//
// Calculating the intersection of a line with the surfaces
// is fairly straight forward. The difficult problem is dealing
// with the intersections of the surfaces in a consistent manner,
// and this accounts for the complicated logic.
//
G4double G4Hype::DistanceToIn(const G4ThreeVector& p,
const G4ThreeVector& v ) const
{
static const G4double halfTol = 0.5*kCarTolerance;
//
// Quick test. Beware! This assumes v is a unit vector!
//
if (fabs(p.x()*v.y() - p.y()*v.x()) > endOuterRadius+kCarTolerance) return kInfinity;
//
// Take advantage of z symmetry, and reflect throught the
// z=0 plane so that pz is always positive
//
G4double pz(p.z()), vz(v.z());
if (pz < 0) {
pz = -pz;
vz = -vz;
}
//
// We must be very careful if we don't want to
// create subtle leaks at the edges where the
// hyperbolic surfaces connect to the endplate.
// The only reliable way to do so is to make sure
// that the decision as to when a track passes
// over the edge of one surface is exactly the
// same decision as to when a track passes into the
// other surface. By "exact", we don't mean algebraicly
// exact, but we mean the same machine instructions
// should be used.
//
G4bool couldMissOuter(true),
couldMissInner(true),
cantMissInnerCylinder(false);
//
// Check endplate intersection
//
G4double sigz = pz-halfLenZ;
if (sigz > -halfTol) { // equivalent to: if (pz > halfLenZ - halfTol)
//
// We start in front of the endplate (within roundoff)
// Correct direction to intersect endplate?
//
if (vz >= 0) {
//
// Nope. As long as we are far enough away, we
// can't intersect anything
//
if (sigz > 0) return kInfinity;
//
// Otherwise, we may still hit a hyperbolic surface
// if the point is on the hyperbolic surface (within tolerance)
//
G4double pr2 = p.x()*p.x() + p.y()*p.y();
if (pr2 > endOuterRadius2 + kCarTolerance*endOuterRadius) return kInfinity;
if (InnerSurfaceExists()) {
if (pr2 < endInnerRadius2 - kCarTolerance*endInnerRadius) return kInfinity;
if (pr2 < endOuterRadius2 - kCarTolerance*endOuterRadius &&
pr2 > endInnerRadius2 + kCarTolerance*endInnerRadius ) return kInfinity;
}
else {
if (pr2 < endOuterRadius2 - kCarTolerance*endOuterRadius) return kInfinity;
}
}
else {
//
// Where do we intersect at z = halfLenZ?
//
G4double s = -sigz/vz;
G4double xi = p.x() + s*v.x(),
yi = p.y() + s*v.y();
//
// Is this on the endplate? If so, return s, unless
// we are on the tolerant surface, in which case return 0
//
G4double pr2 = xi*xi + yi*yi;
if (pr2 <= endOuterRadius2) {
if (InnerSurfaceExists()) {
if (pr2 >= endInnerRadius2) return (sigz < halfTol) ? 0 : s;
//
// This test is sufficient to ensure that the
// trajectory cannot miss the inner hyperbolic surface
// for z > 0, if the normal is correct.
//
G4double dot1 = (xi*v.x() + yi*v.y())*endInnerRadius/sqrt(pr2);
couldMissInner = (dot1 - halfLenZ*tanInnerStereo2*vz <= 0);
if (pr2 > endInnerRadius2*(1 - 2*DBL_EPSILON) ) {
//
// There is a potential leak if the inner
// surface is a cylinder
//
if (innerStereo < DBL_MIN &&
(fabs(v.x()) > DBL_MIN || fabs(v.y()) > DBL_MIN))
cantMissInnerCylinder = true;
}
}
else {
return (sigz < halfTol) ? 0 : s;
}
}
else {
G4double dotR( xi*v.x() + yi*v.y() );
if (dotR >= 0) {
//
// Otherwise, if we are traveling outwards, we know
// we must miss the hyperbolic surfaces also, so
// we need not bother checking
//
return kInfinity;
}
else {
//
// This test is sufficient to ensure that the
// trajectory cannot miss the outer hyperbolic surface
// for z > 0, if the normal is correct.
//
G4double dot1 = dotR*endOuterRadius/sqrt(pr2);
couldMissOuter = (dot1 - halfLenZ*tanOuterStereo2*vz>= 0);
}
}
}
}
//
// Check intersection with outer hyperbolic surface, save
// distance to valid intersection into "best".
//
G4double best = kInfinity;
G4double s[2];
G4int n = IntersectHype( p, v, outerRadius2, tanOuterStereo2, s );
if (n > 0) {
//
// Potential intersection: is p on this surface?
//
if (pz < halfLenZ+halfTol) {
G4double dr2 = p.x()*p.x() + p.y()*p.y() - HypeOuterRadius2(pz);
if (fabs(dr2) < kCarTolerance*endOuterRadius) {
//
// Sure, but make sure we're traveling inwards at
// this point
//
if (p.x()*v.x() + p.y()*v.y() - pz*tanOuterStereo2*vz < 0) return 0;
}
}
//
// We are now certain that p is not on the tolerant surface.
// Accept only position distance s
//
G4int i;
for( i=0; i<n; i++ ) {
if (s[i] >= 0) {
//
// Check to make sure this intersection point is
// on the surface, but only do so if we haven't
// checked the endplate intersection already
//
G4double zi = pz + s[i]*vz;
if (zi < -halfLenZ) continue;
if (zi > +halfLenZ && couldMissOuter) continue;
//
// Check normal
//
G4double xi = p.x() + s[i]*v.x(),
yi = p.y() + s[i]*v.y();
if (xi*v.x() + yi*v.y() - zi*tanOuterStereo2*vz > 0) continue;
best = s[i];
break;
}
}
}
if (!InnerSurfaceExists()) return best;
//
// Check intersection with inner hyperbolic surface
//
n = IntersectHype( p, v, innerRadius2, tanInnerStereo2, s );
if (n == 0) {
if (cantMissInnerCylinder) return (sigz < halfTol) ? 0 : -sigz/vz;
return best;
}
//
// P on this surface?
//
if (pz < halfLenZ+halfTol) {
G4double dr2 = p.x()*p.x() + p.y()*p.y() - HypeInnerRadius2(pz);
if (fabs(dr2) < kCarTolerance*endInnerRadius) {
//
// Sure, but make sure we're traveling outwards at
// this point
//
if (p.x()*v.x() + p.y()*v.y() - pz*tanInnerStereo2*vz > 0) return 0;
}
}
//
// No, so only positive s is valid. Search for a valid intersection
// that is closer than the outer intersection (if it exists)
//
G4int i;
for( i=0; i<n; i++ ) {
if (s[i] > best) break;
if (s[i] >= 0) {
//
// Check to make sure this intersection point is
// on the surface, but only do so if we haven't
// checked the endplate intersection already
//
G4double zi = pz + s[i]*vz;
if (zi < -halfLenZ) continue;
if (zi > +halfLenZ && couldMissInner) continue;
//
// Check normal
//
G4double xi = p.x() + s[i]*v.x(),
yi = p.y() + s[i]*v.y();
if (xi*v.x() + yi*v.y() - zi*tanOuterStereo2*vz < 0) continue;
best = s[i];
break;
}
}
//
// Done
//
return best;
}
//
// Calculate distance to shape from outside, along perpendicular direction
// (if one exists). May be an underestimate.
//
// There are five (r,z) regions:
// 1. a point that is beyond the endcap but within the
// endcap radii
// 2. a point with r > outer endcap radius and with
// a z position that is beyond the cone formed by the
// normal of the outer hyperbolic surface at the
// edge at which it meets the endcap.
// 3. a point that is outside the outer surface and not in (1 or 2)
// 4. a point that is inside the inner surface and not in (5)
// 5. a point with radius < inner endcap radius and
// with a z position beyond the cone formed by the
// normal of the inner hyperbolic surface at the
// edge at which it meets the endcap.
// (regions 4 and 5 only exist if there is an inner surface)
//
G4double G4Hype::DistanceToIn(const G4ThreeVector& p) const
{
static const G4double halfTol(0.5*kCarTolerance);
G4double absZ(fabs(p.z()));
//
// Check region
//
G4double r2 = p.x()*p.x() + p.y()*p.y();
G4double r = sqrt(r2);
G4double sigz = absZ - halfLenZ;
if (r < endOuterRadius) {
if (sigz > -halfTol) {
if (InnerSurfaceExists()) {
if (r > endInnerRadius)
return sigz < halfTol ? 0 : sigz; // Region 1
G4double dr = endInnerRadius - r;
if (sigz > dr*tanInnerStereo2) {
//
// In region 5
//
G4double answer = sqrt( dr*dr + sigz*sigz );
return answer < halfTol ? 0 : answer;
}
}
else {
//
// In region 1 (no inner surface)
//
return sigz < halfTol ? 0 : sigz;
}
}
}
else {
G4double dr = r - endOuterRadius;
if (sigz > -dr*tanOuterStereo2) {
//
// In region 2
//
G4double answer = sqrt( dr*dr + sigz*sigz );
return answer < halfTol ? 0 : answer;
}
}
if (InnerSurfaceExists()) {
if (r2 < HypeInnerRadius2(absZ)+kCarTolerance*endInnerRadius) {
//
// In region 4
//
G4double answer = ApproxDistInside( r, absZ, innerRadius, tanInnerStereo2 );
return answer < halfTol ? 0 : answer;
}
}
//
// We are left by elimination with region 3
//
G4double answer = ApproxDistOutside( r, absZ, outerRadius, tanOuterStereo );
return answer < halfTol ? 0 : answer;
}
//
// Calculate distance to surface of shape from `inside', allowing for tolerance
//
// The situation here is much simplier than DistanceToIn(p,v). For
// example, there is no need to even check whether an intersection
// point is inside the boundary of a surface, as long as all surfaces
// are checked and the smallest distance is used.
//
G4double G4Hype::DistanceToOut( const G4ThreeVector& p,const G4ThreeVector& v,
const G4bool calcNorm,
G4bool *validNorm, G4ThreeVector *norm ) const
{
static const G4double halfTol = 0.5*kCarTolerance;
static const G4ThreeVector normEnd1(0.0,0.0,+1.0);
static const G4ThreeVector normEnd2(0.0,0.0,-1.0);
//
// Keep track of closest surface
//
G4double sBest; // distance to
const G4ThreeVector *nBest; // normal vector
G4bool vBest; // whether "valid"
//
// Check endplate, taking advantage of symmetry.
// Note that the endcap is the only surface which
// has a "valid" normal, i.e. is a surface of which
// the entire solid is behind.
//
G4double pz(p.z()), vz(v.z());
if (vz < 0) {
pz = -pz;
vz = -vz;
nBest = &normEnd2;
}
else
nBest = &normEnd1;
//
// Possible intercept. Are we on the surface?
//
if (pz > halfLenZ-halfTol) {
if (calcNorm) { *norm = *nBest; *validNorm = true; }
return 0;
}
//
// Nope. Get distance.
//
sBest = (halfLenZ - pz)/vz;
vBest = true;
//
// Check outer surface
//
G4double r2 = p.x()*p.x() + p.y()*p.y();
G4double s[2];
G4int n = IntersectHype( p, v, outerRadius2, tanOuterStereo2, s );
G4ThreeVector norm1, norm2;
if (n > 0) {
//
// We hit somewhere. Are we on the surface?
//
G4double dr2 = r2 - HypeOuterRadius2(pz);
if (fabs(dr2) < endOuterRadius*kCarTolerance) {
G4ThreeVector normHere( p.x(), p.y(), -p.z()*tanOuterStereo2 );
//
// Sure. But are we going the right way?
//
if (normHere.dot(v) > 0) {
if (calcNorm) { *norm = normHere.unit(); *validNorm = false; }
return 0;
}
}
//
// Nope. Check closest positive intercept.
//
G4int i;
for( i=0; i<n; i++ ) {
if (s[i] > sBest) break;
if (s[i] > 0) {
//
// Make sure normal is correct (that this
// solution is an outgoing solution)
//
G4ThreeVector pi(p+s[i]*v);
norm1 = G4ThreeVector( pi.x(), pi.y(), -pi.z()*tanOuterStereo2 );
if (norm1.dot(v) > 0) {
sBest = s[i];
nBest = &norm1;
vBest = false;
break;
}
}
}
}
if (InnerSurfaceExists()) {
//
// Check inner surface
//
n = IntersectHype( p, v, innerRadius2, tanInnerStereo2, s );
if (n > 0) {
//
// On surface?
//
G4double dr2 = r2 - HypeInnerRadius2(pz);
if (fabs(dr2) < endInnerRadius*kCarTolerance) {
G4ThreeVector normHere( -p.x(), -p.y(), p.z()*tanInnerStereo2 );
if (normHere.dot(v) > 0) {
if (calcNorm) {*norm = normHere.unit(); *validNorm = false;}
return 0;
}
}
//
// Check closest positive
//
G4int i;
for( i=0; i<n; i++ ) {
if (s[i] > sBest) break;
if (s[i] > 0) {
G4ThreeVector pi(p+s[i]*v);
norm2 = G4ThreeVector( -pi.x(), -pi.y(), pi.z()*tanInnerStereo2 );
if (norm2.dot(v) > 0) {
sBest = s[i];
nBest = &norm2;
vBest = false;
break;
}
}
}
}
}
//
// Done!
//
if (calcNorm) {
*validNorm = vBest;
if (nBest == &norm1 || nBest == &norm2)
*norm = nBest->unit();
else
*norm = *nBest;
}
return sBest;
}
//
// Calculate distance (<=actual) to closest surface of shape from inside
//
// May be an underestimate
//
G4double G4Hype::DistanceToOut(const G4ThreeVector& p) const
{
//
// Try each surface and remember the closest
//
G4double absZ(fabs(p.z()));
G4double r(p.perp());
G4double sBest = halfLenZ - absZ;
G4double tryOuter = ApproxDistInside( r, absZ, outerRadius, tanOuterStereo2 );
if (tryOuter < sBest) sBest = tryOuter;
if (InnerSurfaceExists()) {
G4double tryInner = ApproxDistOutside( r, absZ, innerRadius, tanInnerStereo );
if (tryInner < sBest) sBest = tryInner;
}
return sBest < 0.5*kCarTolerance ? 0 : sBest;
}
void G4Hype::DescribeYourselfTo (G4VGraphicsScene& scene) const
{
scene.AddThis (*this);
}
G4VisExtent G4Hype::GetExtent() const
{
// Define the sides of the box into which the G4Tubs instance would fit.
return G4VisExtent( -endOuterRadius, endOuterRadius,
-endOuterRadius, endOuterRadius,
-halfLenZ, halfLenZ );
}
G4Polyhedron* G4Hype::CreatePolyhedron () const
{
// return new G4PolyhedronHype (fRMin, fRMax, fDz, fSPhi, fDPhi);
return 0;
}
G4NURBS* G4Hype::CreateNURBS () const
{
return new G4NURBStube(endInnerRadius, endOuterRadius, halfLenZ); // Tube for now!!!
}
//
// IntersectHype (static)
//
// Decide if and where a line intersects with a hyperbolic
// surface (of infinite extent)
//
// Arguments:
// p - (in) Point on trajectory
// v - (in) Vector along trajectory
// r2 - (in) Square of radius at z = 0
// tan2phi - (in) tan(phi)**2
// s - (out) Up to two points of intersection, where the
// intersection point is p + s*v, and if there are
// two intersections, s[0] < s[1]. May be negative.
// Returns:
// The number of intersections. If 0, the trajectory misses.
//
//
// Equation of a line:
//
// x = x0 + s*tx y = y0 + s*ty z = z0 + s*tz
//
// Equation of a hyperbolic surface:
//
// x**2 + y**2 = r**2 + (z*tanPhi)**2
//
// Solution is quadratic:
//
// a*s**2 + b*s + c = 0
//
// where:
//
// a = tx**2 + ty**2 - (tz*tanPhi)**2
//
// b = 2*( x0*tx + y0*ty - z0*tz*tanPhi**2 )
//
// c = x0**2 + y0**2 - r**2 - (z0*tanPhi)**2
//
//
G4int G4Hype::IntersectHype( const G4ThreeVector &p, const G4ThreeVector &v,
const G4double r2, const G4double tan2Phi, G4double s[2] )
{
G4double x0 = p.x(), y0 = p.y(), z0 = p.z();
G4double tx = v.x(), ty = v.y(), tz = v.z();
G4double a = tx*tx + ty*ty - tz*tz*tan2Phi;
G4double b = 2*( x0*tx + y0*ty - z0*tz*tan2Phi );
G4double c = x0*x0 + y0*y0 - r2 - z0*z0*tan2Phi;
if (fabs(a) < DBL_MIN) {
//
// The trajectory is parallel to the asympotic limit of
// the surface: single solution
//
if (fabs(b) < DBL_MIN) return 0; // Unless we travel through exact center
s[0] = c/b;
return 1;
}
G4double radical = b*b - 4*a*c;
if (radical < -DBL_MIN) return 0; // No solution
if (radical < DBL_MIN) {
//
// Grazes surface
//
s[0] = -b/a/2.0;
return 1;
}
radical = sqrt(radical);
G4double q = -0.5*( b + (b < 0 ? -radical : +radical) );
G4double sa = q/a;
G4double sb = c/q;
if (sa < sb) { s[0] = sa; s[1] = sb; } else { s[0] = sb; s[1] = sa; }
return 2;
}
//
// ApproxDistOutside (static)
//
// Find the approximate distance of a point outside
// (greater radius) of a hyperbolic surface. The distance
// must be an underestimate. It will also be nice (although
// not necesary) that the estimate is always finite no
// matter how close the point is.
//
// Our hyperbola approaches the asymptotic limit at z = +/- infinity
// to the lines r = z*tanPhi. We call these lines the
// asymptotic limit line.
//
// We need the distance of the 2d point p(r,z) to the
// hyperbola r**2 = r0**2 + (z*tanPhi)**2. Find two
// points that bracket the true normal and use the
// distance to the line that connects these two points.
// The first such point is z=p.z. The second point is
// the z position on the asymptotic limit line that
// contains the normal on the line through the point p.
//
G4double G4Hype::ApproxDistOutside( const G4double pr, const G4double pz,
const G4double r0, const G4double tanPhi )
{
if (tanPhi < DBL_MIN) return pr-r0;
G4double tan2Phi = tanPhi*tanPhi;
//
// First point
//
G4double z1 = pz;
G4double r1 = sqrt( r0*r0 + z1*z1*tan2Phi );
//
// Second point
//
G4double z2 = (pr*tanPhi + pz)/(1 + tan2Phi);
G4double r2 = sqrt( r0*r0 + z2*z2*tan2Phi );
//
// Line between them
//
G4double dr = r2-r1;
G4double dz = z2-z1;
G4double len = sqrt(dr*dr + dz*dz);
if (len < DBL_MIN) {
//
// The two points are the same?? I guess we
// must have really bracketed the normal
//
dr = pr-r1;
dz = pz-z1;
return sqrt( dr*dr + dz*dz );
}
//
// Distance
//
return fabs((pr-r1)*dz - (pz-z1)*dr)/len;
}
//
// ApproxDistInside (static)
//
// Find the approximate distance of a point inside
// of a hyperbolic surface. The distance
// must be an underestimate. It will also be nice (although
// not necesary) that the estimate is always finite no
// matter how close the point is.
//
// This estimate uses the distance to a line tangent to
// the hyperbolic function. The point of tangent is chosen
// by the z position point
//
// Assumes pr and pz are positive
//
G4double G4Hype::ApproxDistInside( const G4double pr, const G4double pz,
const G4double r0, const G4double tan2Phi )
{
if (tan2Phi < DBL_MIN) return r0 - pr;
//
// Corresponding position and normal on hyperbolic
//
G4double rh = sqrt( r0*r0 + pz*pz*tan2Phi );
G4double dr = -rh;
G4double dz = pz*tan2Phi;
G4double len = sqrt(dr*dr + dz*dz);
//
// Answer
//
return fabs((pr-rh)*dr)/len;
}
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