This article provides an overview of various types of geometric primitive objects that can be added to a BRL-CAD geometry file. The shape, size, location and orientation of each such object are defined by a set of parameters/properties that are specific to its type, which are discussed in the corresponding section below.

For general discussions on using MGED to create primitive objects, view their properties, and modify or move them, see:

also see:

# Arbitrary convex polyhedra

An arbitrary convex polyhedron (arb) is a geometric solid that is completely enclosed by a set of 3-dimensional planes. Each has a set of straight-edged, flat faces/facets defined by those planes and their intersections. For example, a rectangular parallelpiped (rpp) is enclosed by six planes--two perpendicular/normal to the X-axis, two normal to the Y-axis, and two normal to the Z-axis.

The BRL-CAD geometry file format defines two types of arb object records:

• arb8s are specified by a set of eight vertices (V1 through V8) that collectively define up to six facets.
• arbns are specified by a set of intersecting planes, each defined by four coefficients.

Although any arb object could be defined and stored as an arbn, the arb8 record type is used to store all of the special-case arbs discussed below (that is, all except the explicitly arbn type).

## Box

Each box is enclosed by three pairs of parallel planes defined by a vertex [an (Xv,Yv,Zv) vector relative to the origin] and depth, width and height vectors [(Xd,Yd,Zd), (Xw,Yw,Zw), (Xh,Yh,Zh)]. Those vectors not only do not have to be normal to the X, Y and Z axes, they need not even be orthogonal (mutually perpendicular to each other). Thus, those vectors merely define the box's opposing faces as pairs of similar parallelograms. If they are parallel to the X, Y, Z axes, the box will have the same characteristics as an rpp (see below).

Each box is stored as an arb8 record whose eight vertices are calculated from its defining vectors as:

1. (X1, Y1, Z1) = (Xv, Yv, Zv)
2. (X1+Xw, Y1+Yw, Z1+Zw) = (Xv+Xw, Yv+Yw, Zv+Zw)
3. (X2+Xh, Y2+Yh, Z2+Zh) = (Xv+Xw+Xh, Yv+Yw+Yh, Zv+Zw+Zh)
4. (X3-Xw, Y3-Yw, Z3-Zw) = (Xv+Xh, Yv+Yh, Zv+Zh)
5. (X1+Xd, Y1+Yd, Z1+Zd) = (Xv+Xd, Yv+Yd, Zv+Zd)
6. (X5+Xw, Y5+Yw, Z5+Zw) = (Xv+Xd+Xw, Yv+Xd+Yw, Zv+Zd+Zw)
7. (X6+Xh, Y6+Yh, Z6+Zh) = (Xv+Xd+Xw+Xh, Yv+Xd+Yw+Yh, Zv+Zd+Zw+Zh)
8. (X7-Xw, Y7-Yw, Z7-Zw) = (Xv+Xd+Xh, Yv+Xd+Yh, Zv+Zd+Zh)

## Rectangular parallelpiped (rpp)

Each rectangular parallelpiped (rpp) is enclosed by two planes normal to the X-axis (mathematically defined by X=Xmin and X=Xmax), two normal to the Y-axis (Y=Ymin and Y=Ymax), and two normal to the Z-axis (Z=Zmin and Z=Zmax). The opposing faces of any such arb are thus pairs of similar rectangles. If Xmax-Xmin = Ymax-Ymin = Zmax-Zmin, as they are for the default rpp created by MGED's make and create commands, the resulting ppp would be a cube with edges parallel to the three axes.

Each rpp is stored as an arb8 record whose eight vertices are calculated from its six planar coefficients as:

1. (Xmax, Ymin, Zmin)
2. (Xmax, Ymax, Zmin)
3. (Xmax, Ymax, Zmax)
4. (Xmax, Ymin, Zmax)
5. (Xmin, Ymin, Zmin)
6. (Xmin, Ymax, Zmin)
7. (Xmin, Ymax, Zmax)
8. (Xmin, Ymin, Zmax)

Note that the rpp primitive type is actually a special case of the box type. Thus, you can also create an rpp by specifying a box whose depth, width and height vectors are parallel to the X, Y and Z axes.

## Right angle wedge (raw)

Right Angle Wedge, special case of arb6

Handled by
in form(arb8)
Arguments
Vertex of first corner, direction vectors for height, width, and depth

## arb8

Arbitrary straight-edged shape with 8 vertices.

Handled by
make in form create
Arguments
8 Vertices in the following order: 1234 vertices for the front face, starting at bottom left, counterclockwise; then 5678 vertices for the rear face, starting at bottom left, counterclockwise.
Example
```in unitcube.s arb8  0 0 0  1 0 0  1 0 1  0 0 1  0 1 0  1 1 0  1 1 1  0 1 1
```

creates the unit cube (first vertex at the origin, extends for 1 unit in x, y and z direction).

## arb7

Special case of arb8, except with point 8 merged into point 5, making the left face triangular

Handled by
make in form(arb8) create

## arb6

Arbitrary straight-edged shape with 6 vertices, special case of arb8.

Handled by
make in form(arb8) create
Arguments
6 Vertices in the following order: 1234 vertices for the front face, starting at bottom left, counterclockwise; then back edge is 5 on bottom, 6 on top. Top and bottom faces are triangles.
Example
```in arb6.s arb6 1 -1 -1   1 1 -1   1 1 1  1 -1 1  -1 0 -1  -1 0 1
```

## arb5

special case of arb8.

Handled by
make in form(arb8) create

## arb4

special case of arb8.

Handled by
make in form(arb8) create

## arbn

Arbitrary solid bounded by N planes.

The solid is constructed by N sets of plane coefficients and distance magnitudes, that define space which is ~outside~ the solid. The coefficients define a vector whose normal is a plane parallel to the face of the solid. The surface of the solid is at the perscribed distance along this vector.

The distances may be negative and are used when a face lies on the opposite side of the origin as the tip of its vector. An example is if the left side of a box lies on the positive X axis. In this case, because the left side is being defined, the vector points left (coefficients -1 0 0), but since the point is on the positive X axis its distance is opposite its vector and therefore negative.

Handled by
make in create
Arguments
Number of planes
xyz direction vector and distance for each plane
Example
in arbn.s arbn 8 1 0 1 1 -1 0 0 1 0 1 0 1 0 -1 0 1 0 0 1 1 0 0 -1 1 0.5 0.5 0.5 1 -0.5 -0.5 -0.5 1
Example with negative distance
in arbn2.s arbn 6 1 0 0 100 -1 0 0 -10 0 1 0 200 0 -1 0 -10 0 0 -1 0 0 0 1 1.5
...is equivalent to...
in rpp.s rpp 10 100 10 200 0 1.5

# Ellipsoids

## ell

Ellipsoid

Handled by
make in form create
Arguments
vertex point, at the center
vectors A B C describing the radii of the ellipses; A points front, B points right, C points up.

Example:

```in ell.s ell 0 0 0  0 -1 0  1 0 0  0 0 1
```

## sph

Sphere, special case of the ellipsoid, with vectors A B and C all the same magnitude (radius).

Handled by
make in form(ell) create

Arguments:

vertex point, at the center

## ellg

Special case of ellipsoid

Handled by
in form(ell)
Arguments
two foci points, and axis length

## ell1

Special case of ellipsoid

Handled by
in make form(ell) create
Arguments
vertex, vector A, radius of revolution

## ehy

Elliptical hyperboloid

Handled by
make in form create
Arguments
vertex, perpendicular vectors Height and (A,r_1) major axis, (r_2) magnitude of vector B, (c) apex to asymptotes distance

## epa

Elliptical paraboloid

Handled by
in make form create

# Cones and Cylinders

## tgc

Truncated general cone

Handled by
in make form create
Arguments
vertex, vectors H A B, magnitudes of vectors C D

## rcc

Right circular cylinder, special case of tgc

Handled by
in make form(tgc) create
Arguments

Example:

``` in rcc1.s rcc 0 0 0  1 1 1  0.5
```

## rec

Right elliptical cylinder, special case of tgc

Handled by
in make form(tgc) create
Arguments

## rhc

Right hyperbolic cylinder

Handled by
in make form create
Arguments
vertex, perpendicular vectors for Height and B, (r) rectangular half width, (c) apex to asymptote distance,

## rpc

Right parabolic cylinder

Handled by
in make form create
Arguments
vertex, perpendicular vectors for Height and B, (r) rectangular half width

## tec

Truncated elliptical cone, special case of tgc

Handled by
in make form(tgc) create
Arguments
Vertex, vectors Height, A, B

## trc

Truncated right circular cone, special case of tgc

Handled by
in make form(tgc) create
Arguments
Vertex, Height vector, radius of base and top

# derived from 2d

## extrude

Extrusion of a 2-d sketch

Handled by
in make form(?) create
Arguments
vertex, perpendicular vectors Height A B, sketch, K

## revolve

Revolution of a 2-d sketch

Handled by
in
Arguments
vertex, revolution axis, vector in start plane, angle, sketch

## dsp

Handled by
in create
Arguments
data type (f|o), datasource, count of length and width, interpolation type, cut direction, cell size, unit elevation

## ebm

extruded bit map

Handled by
in form create
Arguments
filename, width and height in cells, extrusion distance,

The extruded bitmap (also referred to as EBM) is a solid based on a greyscale bitmap. The bitmap is an array of unsigned char values, see bw(5), and is extruded by some distance. The EBM solid requires the dimensions of the bitmap file (height and width in bytes), an extrusion length, and a transformation matrix to position the EBM. Each byte in the bitmap file is treated as the base of a cell that is extruded by the specified extrusion length. If the value of the byte is non­zero, then that cell is considered solid.

Height field

Handled by
none?
Status

# Other solids

## tor

Torus

Handled by
in make form create
Arguments

## eto

Elliptical torus

Handled by
in make form create
Arguments
vertex, normal vector, radius of revolution, vector C, (r_d) magnitude of semi-minor axis

## part

Conical particle

Handled by
in make create
Arguments

The particle solid is a lozenge-shaped object defined by a vertex, a height vector and radii at both ends. The body of the particle is either a cylinder or a truncated cone, depending on the values of the radii. Each end of the particle is a hemisphere of the specified radius.

## nmg

n-Manifold geometry solid (non-manifold geometry)

Handled by
make create

## pipe

Hollow and solid pipes and wires

Handled by
in make create
Arguments
# points, for each point: location, inner and outer diameters, bend radius

## ars

Arbitrary rectangular solid

Handled by
in make create

Solids of type 'ars' (Arbitrary Faceted Solids) are defined using "waterlines". The following figure consists of a start point, some number of intermediate polygons, and an ending point. Each of the intermediate polygons have the same number of vertices and the vertices are numbered 1 thru N. In addition to the intermediate polygons a line will be created that begins at the start point, goes through each polygon at its vertex numbered 1, and terminates at the end point. This is repeated for each polygon vertex 2 thru N. The start point, polygons, and end point are each a "waterline".

<need an image here to illustrate the concept>

the ars shape takes the following values as input:

• The number of points per waterline (the number of vertices on each intermediate polygon)
• The number of waterlines (the number of intermediate polygons plus 2)
• X, Y, and Z for a starting point (the first waterline)
• for each interior polygon (an intermediate waterline)
• for each point on the polygon
• X, Y, and Z for the point on the polygon
• X, Y, and Z for an ending point (the last waterline)

For example, the command:

in x.1 ars 4 6 0 0 3 1 1 3 1 -1 3 -1 -1 3 -1 1 3 1 1 1 1 -1 1 -1 -1 1 -1 1 1 1 0 -1 0 -1 -1 -1 0 -1 0 1 -1 1 0 -3 0 -1 -3 -1 0 -3 0 1 -3 0 0 -3

Will produce a square bar with a tapered 1/8 turn twist in the middle. Of course, more waterlines in the twist and more points per waterline would make the twist smoother.

Example ARS

The parameters to the above ars command can be dissected as:

4 : number of points per waterline (i.e. intermediate polygons have 4 vertices)
6 : number of waterlines (four intermediate polygons plus the two endpoints)
0 0 3 - the center of the top end of the bar
1 1 3 1 -1 3 -1 -1 3 -1 1 3 : a 2x2 square in the xy plane at z offset 3
1 1 1 1 -1 1 -1 -1 1 -1 1 1 : a 2x2 square oriented the same as the first but at z offset 1
1 0 -1 0 -1 -1 -1 0 -1 0 1 -1 : a 2x2 square at a 45 degree rotation from the first squares at z offset -1
1 0 -3 0 -1 -3 -1 0 -3 0 1 -3 : a 2x2 square at a 45 degree rotation from the first squares at z offset -3
0 0 -3 : the center of the bottom end of the bar

## metaball

Handled by
in make form(*) create
Arguments
render method, threshold, number of points, location and field strength for each point (and blobbiness/goo factor)

## nurb

Non-uniform rational b-spline

Handled by
none?

surface splines

Handled by
?

## vol

volume / voxel

Handled by
in
Arguments
filename, xyz dimensions of file (in voxels), lower and upper threasholds, xyz dimensions of a cell

The vol solid is defined by a 3-dimensional array of unsigned char values. The solid requires a file of these values, the extent of the file (in bytes) in each dimension, the size of each cell, and high and low thresholds. Any value in the file that is between the thresholds (inclusive) represents a solid cell.

## bot

Bag of triangles

Handled by
in make create (not edit!)
Arguments
number of verticies, number of triangles, mode (1=surface 2=solid 3=plate), triangle orientation mode (1=unoriented 2=counter-clockwise 3=clockwise), each vertex, vertex index of each triangle
BoT

polysolid

Handled by
none?
Status

# Other

## Sketch

2d outline

Handled by
make form(sketch editor) create
sketch

## grip

Grip -- support for joints, non-geometric (does not show in rt)

Handled by
in make form create

Arguments:

Center
normal vector
magnitude

## half

halfspace

Handled by
in make form create
Arguments
Normal, distance from origin

A half space is the portion of space on one side of a plane. It is represented by its boundary (the plane) and its outward-pointing normal vector.

## binunif

Uniform-array binary object

Handled by
in create (not edit!)
Arguments
minor type (fdcsiLCSIL), data file, number of values