5 Geometry

A geometry in Radiant is represented by the Radiant.Geometry object. Once instantiated, its dimension, region layout, voxelization, material map and boundary conditions are configured, and the structure is finalized with a call to build(...).

5.1 Cartesian Geometries

Radiant currently treats Cartesian geometries in 1D, 2D and 3D. The geometry is described region by region along each axis:

• In 1D the only axis is "x".
• In 2D the axes are "x" and "y".
• In 3D the axes are "x", "y" and "z".

5.1.1 Instantiating and Setting the Dimension

geo = Geometry()
geo.set_type("cartesian")
geo.set_dimension(1)        # 1D Cartesian geometry

set_dimension only accepts 1, 2 or 3.

5.1.2 Defining Regions and Voxelization

For each axis, the user specifies:

1. The number of regions, with set_number_of_regions(axis,N).
2. The region boundaries, in ascending order, with set_region_boundaries(axis,bnds). The length of the boundary vector must be N+1.
3. The number of voxels used to discretize each region, with set_voxels_per_region(axis,nvox). The length of nvox must be N.

For a 1D slab of three regions (Al, Au, Al) sharing the same voxel count:

geo.set_number_of_regions("x",3)
geo.set_region_boundaries("x",[0.0,0.2,0.4,0.6])
geo.set_voxels_per_region("x",[20,20,20])

The same pattern is used along "y" and "z" in higher dimensions.

5.1.3 Material Map

set_material_per_region takes a multi-dimensional array of Material objects, with one entry per region:

# 1D: a row vector of length Nx
geo.set_material_per_region([al,au,al])

# 2D: a matrix of size (Nx, Ny)
geo.set_material_per_region([al au al ; au al au])

# 3D: a 3-D array of size (Nx, Ny, Nz)

The materials placed in this array must be among those that were given to the corresponding Cross_Sections object.

5.1.4 Boundary Conditions

A boundary condition is set independently on each face of the domain. The face is identified by a string "x-", "x+", "y-", "y+", "z-", "z+", and the condition can be "void", "reflective" or "periodic":

geo.set_boundary_conditions("x-","void")
geo.set_boundary_conditions("x+","void")

In 2D and 3D, the conditions on the additional boundaries must also be set.

5.1.5 Building the Geometry

After the inputs are complete, the geometry is finalized with:

geo.build(cs)

build(cs) validates the inputs and pre-computes voxel widths, midpoint positions, boundaries, the material index in each voxel and the voxel volumes. The Cross_Sections argument is used to match the material objects from the geometry to those stored in the library.

5.2 Inspecting the Geometry

After build(...), the following getters expose the discretization:

geo.get_type()                          # "cartesian"
geo.get_dimension()                     # 1, 2 or 3
geo.get_axis()                          # ["x"], ["x","y"], or ["x","y","z"]
geo.get_number_of_voxels()              # Vector with the number of voxels along each axis
geo.get_voxels_width()                  # Voxel widths along each axis
geo.get_voxels_position("x")            # Midpoint positions along the x-axis
geo.get_voxels_boundaries("x")          # Voxel boundaries along the x-axis
geo.get_material_per_voxel()            # Material index in each voxel
geo.get_boundary_conditions()           # All boundary conditions as integer codes
geo.get_boundary_conditions("x-")       # Boundary condition string at x-

5.3 Complete Example (1D Al-Au-Al slab)

geo = Geometry()
geo.set_type("cartesian")
geo.set_dimension(1)
geo.set_number_of_regions("x",3)
geo.set_region_boundaries("x",[0.0,0.2,0.4,0.6])
geo.set_voxels_per_region("x",[20,20,20])
geo.set_boundary_conditions("x-","void")
geo.set_boundary_conditions("x+","void")
geo.set_material_per_region([al,au,al])
geo.build(cs)

5.4 Other Kinds of Geometries

5.5 Summary of the Geometry API