Input File: Geometry

Basic geometric shapes are created using a region block. Named regions can be embedded inside a compound region to perform boolean operations on the volumes. This can be done recursively to build up complex geometries.

The geometry can be viewed using twcad, a Python program that reads a turboWAVE input file and displays the geometry in a CAD style window.

An important distinction in creating geometries is whether an object is defined in parameter space or real space.

Parameter Space

Objects in parameter space are defined in a specific coordinate system, and become a different object when the coordinate system is changed. For example, the circle is defined in Cartesian coordinates as x^2+z^2=1. If cylindrical coordinates are used, the equation retains its form, \varrho^2+z^2=1, which implies the geometry of the object changes. This can sometimes be used to advantage, e.g., one can create a torus in real space using a circle in parameter space, (\varrho-5)^2+z^2=1.

Real Space

Objects in real space are the same object regardless of coordinates. If a sphere is created in real space, it remains a sphere no matter what the grid geometry is.

At present most objects are created in parameter space. This distinction is only important on a curvilinear grid.

When defining geometry using the input file, 3-tuples are often used to specify spatial coordinates. The meaning of the tuple components depends on the coordinate system, as shown in Table I. If a 4-tuple is used, it is the same except the first component is time.

TurboWAVE CAD Viewer

There is a Python program for viewing turboWAVE geometries in turboWAVE/tools/twcad/. If the program is run with stdin in the working directory, a 3D viewing window is created allowing the user to inspect the geometry from any angle. This program has to be run from a special Python environment. For more on how to install and run this program see the documentation in turboWAVE/tools/twcad/.

Geometry Transformations

Every region has a native position and orientation that is only modified by applying a transformation of the form

T({\rm origin})K({\rm boost})R({\rm euler angles})T({\rm translation})T({\rm window})

Note that in the active view the order would be read from left to right. Here T is a space-time translation, K is a Lorentz boost, and R is a rotation. The way the factors are specified is as follows.

origin = ( t , x , y , z )

This specifies the translation operator T({\rm origin}). In the active view this is applied before the boost-rotation.

Parameters:

  • t (float) – translation in time

  • x (float) – translation in the x direction

  • y (float) – translation in the y direction

  • z (float) – translation in the z direction

boost = ( gbx , gby , gbz )

This specifies the spatial part of the 4-velocity of the new reference frame

Parameters:

  • gbx (float) – \gamma\beta_x

  • gby (float) – \gamma\beta_y

  • gbz (float) – \gamma\beta_z

euler angles = ( a , b , c )

This specifies the rotation operation R(a,b,c). The tuple elements are in radians unless the [deg] dimension is given.

Parameters:

  • a – rotation about the z-axis that is applied last in the active view

  • b – rotation about the x-axis that is applied second

  • c – rotation about the z-axis that is applied first in the active view

translation = ( t , x , y , z )

This specifies the translation operator T({\rm translation}). In the active view this is applied after the boost-rotation.

Parameters:

  • t (float) – translation in time

  • x (float) – translation in the x direction

  • y (float) – translation in the y direction

  • z (float) – translation in the z direction

move with window = tst

This specifies the translation operator T({\rm window}). If tst is true it evaluates to a Galilean transformation that aligns the region with the current grid position. If tst is false it evaluates to the identity.

Parameters:

tst (bool) – if true, the region moves with the window

complement = tst
Parameters:

tst (bool) – if true, transforms the region into its complement

Basic Region Types

new region rect <name> { <directives> }

Creates a rectangular box.

Parameters:

  • name (str) – assigns a name to the region

  • directives (block) –

    The following directives are supported:

    Shared directives: see Geometry Transformations

    size = ( x, y, z )

    Gives the length of the box in the three spatial dimensions, the box exists for all time.

new region circ <name> { <directives> }

Creates a disc or sphere.

Parameters:

  • name (str) – assigns a name to the region

  • directives (block) –

    The following directives are supported:

    Shared directives: see Geometry Transformations

    radius = R
    Parameters:

    R (float) – defines the radius of the circle

new region prism <name> { <directives> }

Creates a prism.

Parameters:

  • name (str) – assigns a name to the region

  • directives (block) –

    The following directives are supported:

    Shared directives: see Geometry Transformations

    size = ( x, y, z )

    Defines a box in which the prism is bounded. The tip points in the +x direction.

new region ellipsoid <name> { <directives> }

Creates an ellipsoid in parameter space.

Parameters:

  • name (str) – assigns a name to the region

  • directives (block) –

    The following directives are supported:

    Shared directives: see Geometry Transformations

    size = ( x, y, z )

    Defines a box in which the ellipsoid is bounded.

new region cylinder <name> { <directives> }

Creates a cylinder in parameter space. Default orientation is centered on the z-axis.

Parameters:

  • name (str) – assigns a name to the region

  • directives (block) –

    The following directives are supported:

    Shared directives: see Geometry Transformations

    radius = R
    Parameters:

    R (float) – radius of the cylinder

    length = L
    Parameters:

    L (float) – length of cylinder

new region rounded_cylinder <name> { <directives> }

Creates a cylinder in parameter space, with hemispherical end-caps. Default orientation is centered on the z-axis.

Parameters:

  • name (str) – assigns a name to the region

  • directives (block) –

    The following directives are supported:

    Shared directives: see Geometry Transformations

    radius = R
    Parameters:

    R (float) – radius of the cylinder

    length = L
    Parameters:

    L (float) – length of cylinder, does not count the end-caps

new region cylindrical_shell <name> { <directives> }

Creates a cylindrical shell, or “tube”, in parameter space. Default orientation is centered on the z-axis.

Parameters:

  • name (str) – assigns a name to the region

  • directives (block) –

    The following directives are supported:

    Shared directives: see Geometry Transformations

    inner radius = R1
    Parameters:

    R1 (float) – inner radius of the tube

    outer radius = R2
    Parameters:

    R2 (float) – outer radius of the tube

    length = L
    Parameters:

    L (float) – length of tube

new region torus <name> { <directives> }

Creates a torus in parameter space. Default orientation is centered on the z-axis.

Parameters:

  • name (str) – assigns a name to the region

  • directives (block) –

    The following directives are supported:

    Shared directives: see Geometry Transformations

    minor radius = R1
    Parameters:

    R1 (float) – radius of tube that is bent to make the torus

    major radius = R2
    Parameters:

    R2 (float) – distance from the torus center to the tube center

new region cone <name> { <directives> }

Creates a cone in parameter space. Default orientation is centered on the z-axis, i.e., the origin is mid-way between the base and the tip.

Parameters:

  • name (str) – assigns a name to the region

  • directives (block) –

    The following directives are supported:

    Shared directives: see Geometry Transformations

    tip radius = R1
    Parameters:

    R1 (float) – radius of blunted tip

    base radius = R2
    Parameters:

    R2 (float) – radius of the cone base

    length = L
    Parameters:

    L (float) – distance between base and tip

new region tangent_ogive <name> { <directives> }

Creates a spherically blunted tangent ogive in parameter space. Default orientation is centered on the z-axis, with the tip on the +z side.

Parameters:

  • name (str) – assigns a name to the region

  • directives (block) –

    The following directives are supported:

    Shared directives: see Geometry Transformations

    tip radius = R1
    Parameters:

    R1 (float) – radius of blunted tip

    base radius = R2
    Parameters:

    R2 (float) – radius of the cone base

    length = L
    Parameters:

    L (float) – distance between base and spherical tip

new region box_array <name> { <directives> }

Creates an infinite array of box shaped regions.

Parameters:

  • name (str) – assigns a name to the region

  • directives (block) –

    The following directives are supported:

    Shared directives: see Geometry Transformations

    size = ( dx , dy , dz )

    size of each box

    spacing = ( lx , ly , lz )

    center-to-center distance between boxes

Compound Regions

new region union <name> { <directives> }

Create the union of several other regions. This is the boolean or, i.e., if the union has elements A, B, and C, then a point in the union must be in A or in B or in C. If C is the complement of D, then the point must be in A or in B or not in D.

Parameters:

  • name (str) – assigns a name to the region

  • directives (block) –

    The following directives are supported:

    Shared directives: see Geometry Transformations

    elements = { R1 , R2 , R3 , ... }

    variable length list of names of regions forming the union

new region intersection <name> { <directives> }

Create the intersection of several other regions. This is the boolean and, i.e., if the intersection has elements A, B, and C, then a point in the intersection must be in A and in B and in C. If C is the complement of D, then the point must be in A and in B and not in D.

Parameters:

  • name (str) – assigns a name to the region

  • directives (block) –

    The following directives are supported:

    Shared directives: see Geometry Transformations

    elements = { R1 , R2 , R3 , ... }

    variable length list of names of regions forming the intersection

new region difference <name> { <directives> }

Create the difference of one region with several other regions. This is an intersection except that the complement of every region but the first one is automatically taken, i.e., if the difference has elements A, B, and C, then a point in the difference must be in A and not in B and not in C.

Parameters:

  • name (str) – assigns a name to the region

  • directives (block) –

    The following directives are supported:

    Shared directives: see Geometry Transformations

    elements = { R1 , R2 , R3 , ... }

    variable length list of names of regions forming the difference

Specific Example in 2D

In this example we make a square with a rounded top in the x-z plane, with a hole in it. First define the elements of the compound region:

new region rect 'r1'
{
        size = ( 2, 2, 2 )
}

new region circ 'c1'
{
        translation = ( 0, 0, 1 )
        radius = 1.0
}

new region circ 'c2'
{
        radius = 0.5
}

Now make the square with rounded top:

new region union 'u1'
{
        elements = { r1 , c1 }
}

Now put a hole in it and rotate the whole thing:

new region difference 'thing'
{
        elements = { u1 , c2 }
        euler angles = ( 90[deg], 20[deg], -90[deg] ) // amounts to a rotation about y
}

The named region “thing” can now be used as the clipping region in Matter Loading, in certain diagnostics, or in Conducting Regions.