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 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.

Celeritas nomenclature tends toward computer science terminology.

Celeritas	Geant4	VecGeom	KENO [1]
(not used)	Solid	Unplaced	Shape
Volume	Logical volume	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	—	Hole/array element
Boundary	Skin surface	—	Hole/placement
Surface	Surface property [2]	—	—

[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]

Surface properties in Geant4 can be referenced by multiple surfaces. Celeritas will duplicate these (although lower-level data deduplication may result in the referencing the same data again at runtime).

Celeritas defines abstract geometry concepts, indexed as IDs, to support multiple geometry applications [3] 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.

[3]

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. This definition differs slightly from Geant4 and VecGeom, where the G4LogicalVolume and UnplacedVolume classes directly reference the child geometry nodes and thus implicitly include the objects embedded in a volume.

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. [4] 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.

[4] (1,2)

A volume instance has a one-to-one mapping for G4PVPlacement, but “replica” and “parameterized” volumes in Geant4 use a single physical volume object to represent multiple spatial elements. For those, we currently define a celeritas::GeantPhysicalInstance that is a tuple of physical volume and a replica instance, which corresponds to the “copy number” in a replica volume. In the future, the replica numbers will be hidden and one volume instance will map directly to a PV pointer and copy number.

• Interfaces
  • celeritas::VolumeParams
  • celeritas::SurfaceParams
  • celeritas::GeoParamsInterface
  • celeritas::GeantPhysicalInstance
• Geant4 geometry
  • celeritas::GeantGeoParams
• ORANGE
  • Construction API
  • Geant4 geometry translation
  • Runtime interfaces
• VecGeom