```// @(#)root/geom:\$Id\$
// Author: Andrei Gheata   31/01/02

/*************************************************************************
*                                                                       *
* For the licensing terms see \$ROOTSYS/LICENSE.                         *
* For the list of contributors see \$ROOTSYS/README/CREDITS.             *
*************************************************************************/

///////////////////////////////////////////////////////////////////////////////
// TGeoCompositeShape - class handling Boolean composition of shapes
//
//   Composite shapes are Boolean combination of two or more shape
// components. The supported boolean operations are union (+), intersection (*)
// and subtraction. Composite shapes derive from the base TGeoShape class,
// therefore providing all shape features : computation of bounding box, finding
// if a given point is inside or outside the combination, as well as computing the
// distance to entering/exiting. It can be directly used for creating volumes or
// used in the definition of other composite shapes.
//   Composite shapes are provided in order to complement and extend the set of
// basic shape primitives. They have a binary tree internal structure, therefore
// all shape-related geometry queries are signals propagated from top level down
// to the final leaves, while the provided answers are assembled and interpreted
// back at top. This CSG hierarchy is effective for small number of components,
// while performance drops dramatically for large structures. Building a complete
// geometry in this style is virtually possible but highly not recommended.
//
//   Structure of composite shapes
//
//   A composite shape can always be regarded as the result of a Boolean operation
// between only two shape components. All information identifying these two
// components as well as their positions with respect to the frame of the composite
// is represented by an object called Boolean node. A composite shape just have
// a pointer to such a Boolean node. Since the shape components may also be
// composites, they will also contain binary Boolean nodes branching other two
// shapes in the hierarcy. Any such branch ends-up when the final leaves are no
// longer composite shapes, but basic primitives.
//
//Begin_Html
/*
<img src="gif/t_booltree.jpg">
*/
//End_Html
//
//   Suppose that A, B, C and D represent basic shapes, we will illustrate
// how the internal representation of few combinations look like. We do this
// only for the sake of understanding how to create them in a proper way, since
// the user interface for this purpose is in fact very simple. We will ignore
// for the time being the positioning of components. The definition of a composite
// shape takes an expression where the identifiers are shape names. The
// expression is parsed and decomposed in 2 sub-expressions and the top-level
// Boolean operator.
//
// 1.     A+B+C
//   This represent the union of A, B and C. Both union operators are at the
// same level. Since:
//        A+B+C = (A+B)+C = A+(B+C)
// the first (+) is taken as separator, hence the expression split:
//        A and B+C
// A Boolean node of type TGeoUnion("A", "B+C") is created. This tries to replace
// the 2 expressions by actual pointers to corresponding shapes.
// The first expression (A) contains no operators therefore is interpreted as
// representing a shape. The shape named "A" is searched into the list of shapes
// handled by the manager class and stored as the "left" shape in the Boolean
// union node. Since the second expression is not yet fully decomposed, the "right"
// shape in the combination is created as a new composite shape. This will split
// at its turn B+C into B and C and create a TGeoUnion("B","C"). The B and C
// identifiers will be looked for and replaced by the pointers to the actual shapes
// into the new node. Finally, the composite "A+B+C" will be represented as:
//
//                 A
//                |
//   [A+B+C] = (+)             B
//                |           |
//                 [B+C] = (+)
//                            |
//                             C
//
// where [] is a composite shape, (+) is a Boolean node of type union and A, B,
// C are pointers to the corresponding shapes.
//   Building this composite shapes takes the following line :
//      TGeoCompositeShape *cs1 = new TGeoCompositeShape("CS1", "A+B+C");
//
// 2.      (A+B)\(C+D)
//   This expression means: subtract the union of C and D from the union of A and
// B. The usage of paranthesys to force operator precedence is always recommended.
// The representation of the corresponding composite shape looks like:
//
//                                   A
//                                  |
//                       [A+B] = (+)
//                      |           |
//   [(A+B)\(C+D)] = (\)           C B
//                      |         |
//                       [C+D]=(+)
//                                |
//                                 D
//
//      TGeoCompositeShape *cs2 = new TGeoCompositeShape("CS2", "(A+B)\(C+D)");
//
//   Building composite shapes as in the 2 examples above is not always quite
// usefull since we were using unpositioned shapes. When suplying just shape
// names as identifiers, the created boolean nodes will assume that the shapes
// are positioned with an identity transformation with respect to the frame of
// the created composite. In order to provide some positioning of the combination
// components, we have to attach after each shape identifier the name of an
// existing transformation, separated by a colon. Obviously all transformations
// created for this purpose have to be objects with unique names in order to be
// properly substituted during parsing.
//   Let's look at the code implementing the second example :
//
//      TGeoTranslation *t1 = new TGeoTranslation("T1",0,0,-20);
//      TGeoTranslation *t2 = new TGeoTranslation("T2",0,0, 20);
//      TGeoRotation *r1 = new TGeoRotation("R1"); // transformations need names
//      r1->SetAngles(90,30,90,120,0,0); // rotation with 30 degrees about Z
//      TGeoTube *a = new TGeoTube(0, 10,20);
//      a->SetName("A");                 // shapes need names too
//      TGeoTube *b = new TGeoTube(0, 20,20);
//      b->SetName("B");
//      TGeoBBox *c = new TGeoBBox(10,10,50);
//      c->SetName("C");
//      TGeoBBox *d = new TGeoBBox(50,10,10);
//      d->SetName("D");
//
//      TGeoCompositeShape *cs;
//      cs = new TGeoCompositeShape("CS", "(A:t1+B:t2)\(C+D:r1)");
//
//   The newly created composite looks like 2 cylinders of different radii sitting
// one on top of the other and having 2 rectangular holes : a longitudinal one
// along Z axis corresponding to C and an other one in the XY plane due to D.
//   One should have in mind that the same shape or matrix identifier can be
// used many times in the same expression. For instance:
//
//      (A:t1-A:t2)*B:t1
//
// is a valid expression. Expressions that cannot be parsed or identifiers that
// cannot be substituted by existing objects generate error messages.
//   Composite shapes can be subsequently used for defining volumes. Moreover,
// these volumes may have daughters but these have to obbey overlapping/extruding
// rules (see TGeoVolume). Volumes created based on composite shapes cannot be
// divided. Visualization of such volumes is currently not implemented.

#include "Riostream.h"
#include "TRandom3.h"

#include "TGeoManager.h"
#include "TGeoMatrix.h"
#include "TGeoBoolNode.h"
#include "TVirtualGeoPainter.h"

#include "TVirtualViewer3D.h"
#include "TBuffer3D.h"
#include "TBuffer3DTypes.h"

#include "TGeoCompositeShape.h"
ClassImp(TGeoCompositeShape)

//______________________________________________________________________________
{
// Needed just for cleanup.
}

//______________________________________________________________________________
{
// Needed just for cleanup.
}

//_____________________________________________________________________________
TGeoCompositeShape::TGeoCompositeShape()
:TGeoBBox(0, 0, 0)
{
// Default constructor
SetShapeBit(TGeoShape::kGeoComb);
fNode  = 0;
}

//_____________________________________________________________________________
TGeoCompositeShape::TGeoCompositeShape(const char *name, const char *expression)
:TGeoBBox(0, 0, 0)
{
// Default constructor
SetShapeBit(TGeoShape::kGeoComb);
SetName(name);
fNode  = 0;
MakeNode(expression);
if (!fNode) {
Error("ctor", "Composite %s: cannot parse expression: %s", name, expression);
return;
}
ComputeBBox();
}

//_____________________________________________________________________________
TGeoCompositeShape::TGeoCompositeShape(const char *expression)
:TGeoBBox(0, 0, 0)
{
// Default constructor
SetShapeBit(TGeoShape::kGeoComb);
fNode  = 0;
MakeNode(expression);
if (!fNode) {
TString message = TString::Format("Composite (no name) could not parse expression %s", expression);
Error("ctor", "%s", message.Data());
return;
}
ComputeBBox();
}

//_____________________________________________________________________________
TGeoCompositeShape::TGeoCompositeShape(const char *name, TGeoBoolNode *node)
:TGeoBBox(0,0,0)
{
// Constructor with a Boolean node
SetName(name);
fNode = node;
if (!fNode) {
Error("ctor", "Composite shape %s has null node", name);
return;
}
ComputeBBox();
}

//_____________________________________________________________________________
TGeoCompositeShape::~TGeoCompositeShape()
{
// destructor
if (fNode) delete fNode;
}

//_____________________________________________________________________________
Double_t TGeoCompositeShape::Capacity() const
{
// Computes capacity of this shape [length^3] by sampling with 1% error.
Double_t pt[3];
if (!gRandom) gRandom = new TRandom3();
Double_t vbox = 8*fDX*fDY*fDZ; // cm3
Int_t igen=0;
Int_t iin = 0;
while (iin<10000) {
pt[0] = fOrigin[0]-fDX+2*fDX*gRandom->Rndm();
pt[1] = fOrigin[1]-fDY+2*fDY*gRandom->Rndm();
pt[2] = fOrigin[2]-fDZ+2*fDZ*gRandom->Rndm();
igen++;
if (Contains(pt)) iin++;
}
Double_t capacity = iin*vbox/igen;
return capacity;
}

//_____________________________________________________________________________
void TGeoCompositeShape::ComputeBBox()
{
// compute bounding box of the sphere
if(fNode) fNode->ComputeBBox(fDX, fDY, fDZ, fOrigin);
}

//_____________________________________________________________________________
void TGeoCompositeShape::ComputeNormal(const Double_t *point, const Double_t *dir, Double_t *norm)
{
// Computes normal vector in POINT to the composite shape.
if (fNode) fNode->ComputeNormal(point,dir,norm);
}

//_____________________________________________________________________________
Bool_t TGeoCompositeShape::Contains(const Double_t *point) const
{
// Tests if point is inside the shape.
if (fNode) return fNode->Contains(point);
return kFALSE;
}

//_____________________________________________________________________________
Int_t TGeoCompositeShape::DistancetoPrimitive(Int_t px, Int_t py)
{
// Compute closest distance from point px,py to each corner.
const Int_t numPoints = GetNmeshVertices();
return ShapeDistancetoPrimitive(numPoints, px, py);
}

//_____________________________________________________________________________
Double_t TGeoCompositeShape::DistFromOutside(const Double_t *point, const Double_t *dir, Int_t iact,
Double_t step, Double_t *safe) const
{
// Compute distance from outside point to this composite shape.
// Check if the bounding box is crossed within the requested distance
Double_t sdist = TGeoBBox::DistFromOutside(point,dir, fDX, fDY, fDZ, fOrigin, step);
if (sdist>=step) return TGeoShape::Big();
if (fNode) return fNode->DistFromOutside(point, dir, iact, step, safe);
return TGeoShape::Big();
}

//_____________________________________________________________________________
Double_t TGeoCompositeShape::DistFromInside(const Double_t *point, const Double_t *dir, Int_t iact,
Double_t step, Double_t *safe) const
{
// Compute distance from inside point to outside of this composite shape.
if (fNode) return fNode->DistFromInside(point, dir, iact, step, safe);
return TGeoShape::Big();
}

//_____________________________________________________________________________
TGeoVolume *TGeoCompositeShape::Divide(TGeoVolume  * /*voldiv*/, const char * /*divname*/, Int_t /*iaxis*/,
Int_t /*ndiv*/, Double_t /*start*/, Double_t /*step*/)
{
// Divide all range of iaxis in range/step cells
Error("Divide", "Composite shapes cannot be divided");
return 0;
}

//_____________________________________________________________________________
void TGeoCompositeShape::GetMeshNumbers(Int_t &nvert, Int_t &nsegs, Int_t &npols) const
{
// Returns numbers of vertices, segments and polygons composing the shape mesh.
nvert = GetNmeshVertices();
nsegs = 0;
npols = 0;
}

//_____________________________________________________________________________
void TGeoCompositeShape::InspectShape() const
{
// print shape parameters
printf("*** TGeoCompositeShape : %s = %s\n", GetName(), GetTitle());
printf(" Bounding box:\n");
TGeoBBox::InspectShape();
}

//_____________________________________________________________________________
void TGeoCompositeShape::MakeNode(const char *expression)
{
// Make a booleann node according to the top level boolean operation of expression.
// Propagates signal to branches until expression is fully decomposed.
//   printf("Making node for : %s\n", expression);
if (fNode) delete fNode;
fNode = 0;
SetTitle(expression);
TString sleft, sright, smat;
Int_t boolop;
boolop = TGeoManager::Parse(expression, sleft, sright, smat);
if (boolop<0) {
// fail
Error("MakeNode", "parser error");
return;
}
if (smat.Length())
Warning("MakeNode", "no geometrical transformation allowed at this level");
switch (boolop) {
case 0:
Error("MakeNode", "Expression has no boolean operation");
return;
case 1:
fNode = new TGeoUnion(sleft.Data(), sright.Data());
return;
case 2:
fNode = new TGeoSubtraction(sleft.Data(), sright.Data());
return;
case 3:
fNode = new TGeoIntersection(sleft.Data(), sright.Data());
}
}

//_____________________________________________________________________________
Bool_t TGeoCompositeShape::PaintComposite(Option_t *option) const
{
// Paint this composite shape into the current 3D viewer
// Returns bool flag indicating if the caller should continue to
// paint child objects

TVirtualGeoPainter *painter = gGeoManager->GetGeomPainter();
if (!painter || !viewer) return kFALSE;

if (fNode) {
// Fill out the buffer for the composite shape - nothing extra
// over TGeoBBox
Bool_t preferLocal = viewer->PreferLocalFrame();
if (TBuffer3D::GetCSLevel()) preferLocal = kFALSE;
static TBuffer3D buffer(TBuffer3DTypes::kComposite);
FillBuffer3D(buffer, TBuffer3D::kCore|TBuffer3D::kBoundingBox,
preferLocal);

Bool_t paintComponents = kTRUE;

// Start a composite shape, identified by this buffer
if (!TBuffer3D::GetCSLevel())

TBuffer3D::IncCSLevel();

// Paint the boolean node - will add more buffers to viewer
TGeoHMatrix *matrix = (TGeoHMatrix*)TGeoShape::GetTransform();
TGeoHMatrix backup(*matrix);
if (preferLocal) matrix->Clear();
if (paintComponents) fNode->Paint(option);
if (preferLocal) *matrix = backup;
// Close the composite shape
if (!TBuffer3D::DecCSLevel())
viewer->CloseComposite();
}

}

//_____________________________________________________________________________
void TGeoCompositeShape::RegisterYourself()
{
// Register the shape and all components to TGeoManager class.
if (gGeoManager->GetListOfShapes()->FindObject(this)) return;
TGeoMatrix *matrix;
TGeoShape  *shape;
TGeoCompositeShape *comp;
if (fNode) {
matrix = fNode->GetLeftMatrix();
if (!matrix->IsRegistered()) matrix->RegisterYourself();
else if (!gGeoManager->GetListOfMatrices()->FindObject(matrix)) {
}
matrix = fNode->GetRightMatrix();
if (!matrix->IsRegistered()) matrix->RegisterYourself();
else if (!gGeoManager->GetListOfMatrices()->FindObject(matrix)) {
}
shape = fNode->GetLeftShape();
if (!gGeoManager->GetListOfShapes()->FindObject(shape)) {
if (shape->IsComposite()) {
comp = (TGeoCompositeShape*)shape;
comp->RegisterYourself();
} else {
}
}
shape = fNode->GetRightShape();
if (!gGeoManager->GetListOfShapes()->FindObject(shape)) {
if (shape->IsComposite()) {
comp = (TGeoCompositeShape*)shape;
comp->RegisterYourself();
} else {
}
}
}
}

//_____________________________________________________________________________
Double_t TGeoCompositeShape::Safety(const Double_t *point, Bool_t in) const
{
// computes the closest distance from given point to this shape, according
// to option. The matching point on the shape is stored in spoint.
if (fNode) return fNode->Safety(point,in);
return 0.;
}

//_____________________________________________________________________________
void TGeoCompositeShape::SavePrimitive(std::ostream &out, Option_t *option /*= ""*/)
{
// Save a primitive as a C++ statement(s) on output stream "out".
if (TObject::TestBit(kGeoSavePrimitive)) return;
if (fNode) fNode->SavePrimitive(out,option);
out << "   // Shape: " << GetName() << " type: " << ClassName() << std::endl;
out << "   TGeoShape *" << GetPointerName() << " = new TGeoCompositeShape(\"" << GetName() << "\", pBoolNode);" << std::endl;
if (strlen(GetTitle())) out << "   " << GetPointerName() << "->SetTitle(\"" << GetTitle() << "\");" << std::endl;
TObject::SetBit(TGeoShape::kGeoSavePrimitive);
}

//_____________________________________________________________________________
void TGeoCompositeShape::SetPoints(Double_t *points) const
{
// create points for a composite shape
if (fNode) fNode->SetPoints(points);
}

//_____________________________________________________________________________
void TGeoCompositeShape::SetPoints(Float_t *points) const
{
// create points for a composite shape
if (fNode) fNode->SetPoints(points);
}

//_____________________________________________________________________________
void TGeoCompositeShape::Sizeof3D() const
{
// compute size of this 3D object
if (fNode) fNode->Sizeof3D();
}

//_____________________________________________________________________________
Int_t TGeoCompositeShape::GetNmeshVertices() const
{
// Return number of vertices of the mesh representation
if (!fNode) return 0;
return fNode->GetNpoints();
}

//_____________________________________________________________________________
void TGeoCompositeShape::Contains_v(const Double_t *points, Bool_t *inside, Int_t vecsize) const
{
// Check the inside status for each of the points in the array.
// Input: Array of point coordinates + vector size
// Output: Array of Booleans for the inside of each point
for (Int_t i=0; i<vecsize; i++) inside[i] = Contains(&points[3*i]);
}

//_____________________________________________________________________________
void TGeoCompositeShape::ComputeNormal_v(const Double_t *points, const Double_t *dirs, Double_t *norms, Int_t vecsize)
{
// Compute the normal for an array o points so that norm.dot.dir is positive
// Input: Arrays of point coordinates and directions + vector size
// Output: Array of normal directions
for (Int_t i=0; i<vecsize; i++) ComputeNormal(&points[3*i], &dirs[3*i], &norms[3*i]);
}

//_____________________________________________________________________________
void TGeoCompositeShape::DistFromInside_v(const Double_t *points, const Double_t *dirs, Double_t *dists, Int_t vecsize, Double_t* step) const
{
// Compute distance from array of input points having directions specisied by dirs. Store output in dists
for (Int_t i=0; i<vecsize; i++) dists[i] = DistFromInside(&points[3*i], &dirs[3*i], 3, step[i]);
}

//_____________________________________________________________________________
void TGeoCompositeShape::DistFromOutside_v(const Double_t *points, const Double_t *dirs, Double_t *dists, Int_t vecsize, Double_t* step) const
{
// Compute distance from array of input points having directions specisied by dirs. Store output in dists
for (Int_t i=0; i<vecsize; i++) dists[i] = DistFromOutside(&points[3*i], &dirs[3*i], 3, step[i]);
}

//_____________________________________________________________________________
void TGeoCompositeShape::Safety_v(const Double_t *points, const Bool_t *inside, Double_t *safe, Int_t vecsize) const
{
// Compute safe distance from each of the points in the input array.
// Input: Array of point coordinates, array of statuses for these points, size of the arrays
// Output: Safety values
for (Int_t i=0; i<vecsize; i++) safe[i] = Safety(&points[3*i], inside[i]);
}
```
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