# class TGeoCompositeShape: public TGeoBBox

``` 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.

```
/* */
```
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 splitted:
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.
```

## Function Members (Methods)

public:
protected:
 TGeoCompositeShape(const TGeoCompositeShape& gcs) virtual void TObject::DoError(int level, const char* location, const char* fmt, va_list va) const virtual void TGeoBBox::FillBuffer3D(TBuffer3D& buffer, Int_t reqSections, Bool_t localFrame) const virtual void TGeoShape::FillBuffer3D(TBuffer3D& buffer, Int_t reqSections, Bool_t localFrame) const Int_t TGeoShape::GetBasicColor() const void TObject::MakeZombie() TGeoCompositeShape& operator=(const TGeoCompositeShape& gcs) void TGeoShape::SetOnBoundary(Bool_t) void TGeoShape::TransformPoints(Double_t* points, UInt_t NbPoints) const

## Data Members

private:
 enum TGeoShape::EShapeType { kBitMask32 kGeoNoShape kGeoBad kGeoRSeg kGeoPhiSeg kGeoThetaSeg kGeoVisX kGeoVisY kGeoVisZ kGeoRunTimeShape kGeoInvalidShape kGeoTorus kGeoBox kGeoPara kGeoSph kGeoTube kGeoTubeSeg kGeoCone kGeoConeSeg kGeoPcon kGeoPgon kGeoArb8 kGeoEltu kGeoTrap kGeoCtub kGeoTrd1 kGeoTrd2 kGeoComb kGeoClosedShape kGeoXtru kGeoParaboloid kGeoHalfSpace kGeoHype kGeoSavePrimitive }; enum TObject::EStatusBits { kCanDelete kMustCleanup kObjInCanvas kIsReferenced kHasUUID kCannotPick kNoContextMenu kInvalidObject }; enum TObject::[unnamed] { kIsOnHeap kNotDeleted kZombie kBitMask kSingleKey kOverwrite kWriteDelete };
protected:
 Double_t TGeoBBox::fDX X half-length Double_t TGeoBBox::fDY Y half-length Double_t TGeoBBox::fDZ Z half-length TString TNamed::fName object identifier Double_t TGeoBBox::fOrigin[3] box origin UInt_t TGeoShape::fShapeBits shape bits Int_t TGeoShape::fShapeId shape id TString TNamed::fTitle object title
private:
 TGeoBoolNode* fNode top boolean node

## Function documentation

``` Default constructor
```
TGeoCompositeShape(const char *name, const char *expression)
``` Default constructor
```
TGeoCompositeShape(const char *expression)
``` Default constructor
```
TGeoCompositeShape(const char *name, TGeoBoolNode *node)
``` Constructor with a Boolean node
```

``` destructor
```
Double_t Capacity() const
``` Computes capacity of this shape [length^3] by sampling with 1% error.
```
void ComputeBBox()
``` compute bounding box of the sphere
```
void ComputeNormal(Double_t* point, Double_t* dir, Double_t* norm)
``` Computes normal vector in POINT to the composite shape.
```
Bool_t Contains(Double_t* point) const
``` Tests if point is inside the shape.
```
Double_t DistFromOutside(Double_t* point, Double_t* dir, Int_t iact = 1, Double_t step = TGeoShape::Big(), Double_t* safe = 0) const
``` Compute distance from outside point to this composite shape.
Check if the bounding box is crossed within the requested distance
```
Double_t DistFromInside(Double_t* point, Double_t* dir, Int_t iact = 1, Double_t step = TGeoShape::Big(), Double_t* safe = 0) const
``` Compute distance from inside point to outside of this composite shape.
```
TGeoVolume * 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
```
void GetMeshNumbers(Int_t& nvert, Int_t& nsegs, Int_t& npols) const
``` Returns numbers of vertices, segments and polygons composing the shape mesh.
```
void InspectShape() const
``` print shape parameters
```
void 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);
```
Bool_t 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
```
void RegisterYourself()
``` Register the shape and all components to TGeoManager class.
```
Double_t Safety(Double_t* point, Bool_t in = kTRUE) const
``` computes the closest distance from given point to this shape, according
to option. The matching point on the shape is stored in spoint.
```
void SavePrimitive(ostream& out, Option_t* option = "")
``` Save a primitive as a C++ statement(s) on output stream "out".
```
void SetPoints(Double_t *points)
``` create points for a composite shape
```
void SetPoints(Float_t *points)
``` create points for a composite shape
```
void Sizeof3D() const
``` compute size of this 3D object
```
Int_t GetNmeshVertices() const
``` Return number of vertices of the mesh representation
```
TGeoCompositeShape(const TGeoCompositeShape& gcs)
`{ }`
TGeoCompositeShape& operator=(const TGeoCompositeShape& gcs)
TGeoBoolNode * GetBoolNode() const
`{return fNode;}`
void GetBoundingCylinder(Double_t* ) const
`{;}`
TGeoShape * GetMakeRuntimeShape(TGeoShape* , TGeoMatrix* ) const
`{return 0;}`
Bool_t GetPointsOnSegments(Int_t , Double_t* ) const
`{return kFALSE;}`
Bool_t IsComposite() const
`{return kTRUE;}`
Bool_t IsCylType() const
`{return kFALSE;}`
void SetDimensions(Double_t* )
`{;}`