Geometry

Detector geometry descriptions for HEP are almost universally defined using a hierarchy of fully nested volumes, often saved as a GDML file [Chytracek et al., 2006]. These user-defined volumes can be represented as a directed acyclic graph (DAG): the nodes are the geometric elements, and the edges are an instantiation of the volume below inside the volume above. This instantiation is associated with a transformation and other metadata. In HEP geometries, child nodes may not overlap each other or their enclosing parent volume.

Approximately equivalent geometry structure terminology for Celeritas, Geant4, VecGeom, and SCALE.

Celeritas	Geant4	VecGeom	KENO/SCALE [1]
Object [2]	Solid	Unplaced	Shape
Volume	Logical volume [3]	Logical volume	Unit/array/media
Volume instance	Physical volume [4]	Placed volume	Hole/array element
Child	Daughter	Daughter	Hole/placement
Parent	Mother	Mother	—
Interface	Border surface	—	—
Boundary	Skin surface	—	—
Surface	Logical surface	—	—

[1]

The KENO geometry package in SCALE [Wieselquist and Lefebvre, 2024] differs substantially from Geant4 geometry definitions. In KENO-VI [Hollenbach, DF et al., 1993] geometry, parent units mask (rather than strictly contain) child units.

[2]

Objects are used strictly for ORANGE construction in ORANGE and are not identifiable during runtime.

[3]

The G4LogicalVolume class is equivalent to a volume except that points inside the children are not considered to be part of the volume. The same is true for VecGeom::LogicalVolume.

[4]

One G4PVReplica volume is expanded into several volume instances, one per “multiplicity”.

Celeritas defines abstract geometry concepts, indexed as IDs, to support multiple geometry applications [5] and to make the code backend-agnostic for integrating with physics. These include “volumes” (known in some other fields as “cells”) and “surfaces” defined by the relationships between volumes.

[5]

In the future the use of these abstract concepts will enable detector descriptions, and geometry models for other applications, that are not Geant4 hierarchies.

Volume

A volume corresponds to a homogeneous physical object that can have multiple instances but is treated identically. It has a specific shape, material, metadata, and associated scoring/sensitive region. Each volume is simply a node in the detector geometry graph; it does not include its children. The Celeritas codebase sometimes refers to user-defined volumes as canonical to differentiate them from implementation volumes.

Volume instance

An instance of a volume is defined in conjunction with a transform and an enclosing object (or, in the special case of the outermost or “world” volume instance, no enclosing object). In Geant4 this roughly corresponds to a “physical volume,” except that Celeritas generates distinct volume instance IDs for every copy provided by a G4PVReplica. VecGeom refers to volume instances as placed volumes. In a user-provided (or SCALE-generated) ORANGE geometry, a volume instance might correspond to a particular hole placement (i.e., a universe daughter), an array element, or a media entry (i.e., a cell). The volume instance is an edge in the graph of volumes.

Unique instance

A unique instance of a volume refers to the logical definition of a specific region of global space in the geometry model. It is the full directed path [Bender and Williamson, 2010] from the root volume node (world volume) to a node (logical volume) somewhere in the graph, thereby describing all enclosing volumes and their locations. This path can be encoded uniquely as a single integer by pre-calculating the number of direct and indirect children for each node. Celeritas always uses 64-bit integers to store the VolumeUniqueInstanceId.

Surface

A surface is defined as a contiguous area on the boundary of a volume, sometimes on only a single side of the volume. Note that this definition differs from the infinite surfaces of ORANGE and the surface frames of VecGeom. Surfaces currently are defined in two ways: Interface surfaces (“border” surfaces in Geant4) are one-directional surfaces defined as the interface from one volume instance to another. Boundary surfaces (“skin” surfaces in Geant4) surround an entire volume, and their properties apply symmetrically to tracks entering or exiting.

ImplVolume

An implementation volume is a low-level detail used by each separate geometry representation/navigation implementation. They may correspond more or less to volumes, volume instances, unique volume instances, or anywhere in between. Use of these outside an individual geometry is discouraged; some parts of the code use these to map between Geant4 pointers and the geometry state. Use the volume/instance/unique volume instead, relying on the cpp:class:celeritas::VolumeParams and global celeritas::GeantGeoParams to convert between the local geometry state and the Geant4 navigation.

• Interfaces
  • celeritas::VolumeParams
  • celeritas::SurfaceParams
  • celeritas::GeoParamsInterface
  • build_volume_collection()
  • celeritas::VolumeMapFiller
• Geant4 geometry
  • celeritas::GeantGeoParams
• ORANGE
  • Construction API
  • Geant4 geometry translation
  • Runtime interfaces
• VecGeom