# Difference between revisions of "BRL-CAD Primitives"

JoelDBenson (talk | contribs) (→Arbitrary convex polyhedra: developed box subsection of arb section) |
JoelDBenson (talk | contribs) (→Arbitrary convex polyhedra: moved creation discussions to a separate article, and finished this section as an overview of arb primitives) |
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= Arbitrary convex polyhedra = | = Arbitrary convex polyhedra = | ||

− | An '''arbitrary convex polyhedron''' ('''arb''') is a geometric | + | An '''arbitrary convex polyhedron''' ('''arb''') is a geometric volume that is completely enclosed by a set of 3-dimensional planes. Each has a set of straight-edged, flat '''faces''' outlined by the intersections of those planes. The intersection of each pair of planes is a line whose intersections with other planes defines a pair of '''vertices'''. The line segment between those two vertices is an '''edge''' of the polyhedron that is shared by two faces. Each vertex is common to an equal number (at least three) of faces and edges. |

− | + | For example, a rectangular parallelepiped is enclosed by three orthagonal pairs of parallel planes. Their intersections define six faces, each with four edges and four vertices. There are a total of 12 edges (each shared by two faces) and 8 vertices (each shared by three faces and three edges). | |

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− | + | The BRL-CAD geometry file format defines two types of records for such polyhedra: | |

+ | * [[#ARB8 Records|'''arb8'''s]] are specified by a set of eight vertices. | ||

+ | * [[#ARBN Records|'''arbn'''s]] are specified by a set of intersecting planes, each defined by four coefficients. | ||

− | + | Although any polyhedron can be defined and stored as an arbn, the arb8 record type is more commonly employed because it is simpler to work with and still accommodates most constructive solid geometry applications. | |

− | == | + | == ARB8 Records == |

− | + | An '''arb8''' record is specified by a set of eight {X, Y, Z} vertices designated V1 through V8, which need not all be unique. As discussed in the [[Creating and editing arb8 primitives]] article, BRL-CAD uses such records to represent polyhedra having four, five or six faces: | |

− | + | * '''arb8''' shapes represent '''hexahedra''' (six-sided polyhedra) whose sides are all quadrilaterals. They thus have eight edges and eight unique vertices. In addition to simply specifying the {X, Y, Z} coordinates of those vertices, MGED provides easier ways to create the following specific types of hexahedra: | |

+ | ** '''3ptarb''' shapes represent '''right quadrilateral prisms''', which are extruded quadrilaterals having parallel ends connected by four rectangular sides. | ||

+ | ** '''box''' shapes represent '''parallelepipeds''', whose faces comprise three pairs of equal parallelograms. Unlike a common box, those faces need not be rectangular—if they are, the enclosed volume is a rectangular parallelepiped. | ||

+ | ** '''rpp''' shapes represent '''rectangular parallelepipeds''' (also known as '''cuboids''' and '''rectangular prisms'''), whose faces comprise three pairs of equal rectangles. If one pair of faces are squares, the volume is a '''square prism'''. If all of them are squares, the volume is a '''cube''' (geometrically, there cannot be just two pairs of square faces). | ||

− | + | * '''arb7''' shapes represent hexahedra with four quadrilateral and two triangular faces. They have a total of eleven edges with seven unique vertices, one of which is shared by the two triangular faces. They can only be created by specifying the {X, Y, Z} coordinates of those vertices. | |

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− | + | * '''arb6''' shapes represent '''triangular prisms''' and '''truncated tetrahedra''', both of which have two triangular ends connected by three quadrilateral sides (its seems they should be called quintahedra but that term seems to be rarely used). Either has a total of nine edges with six unique vertices. In addition to simply specifying the {X, Y, Z} coordinates of their vertices, MGED provides an easier way to create one specific type of hexahedron: | |

+ | ** '''raw''' ('''right angle wedge''') shapes are '''triangular prisms''' whose ends are parallel to each other. Interestingly enough, they don't have to incorporate any right angles. If the ends are perpendicular to the connecting edges, the shape is a '''right triangular prism''' with rectangular sides. Presumably two of the rectangular sides of an actual right-angle wedge would also be perpendicular to each other. Such a shape could easily be created as a BRL-CAD raw primitive. | ||

− | + | * '''arb5''' shapes represent '''quadrahedra''', which are polyhedra with five faces—a quadrilateral base and the three triangular sides with a total of f. If such a volume has a rectangular base it is a '''rectangular pyramid''', one with a square base is a '''square pyramid'''. | |

− | + | * '''arb4''' shapes represent tetrahedra, which are polyhedra with four triangular faces. If all four faces are equilateral triangles, the shape is a '''regular tetrahedron'''. | |

− | + | == ARBN Records == | |

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− | + | An '''arbn''' record is specified by N sets of intersecting planes, each defined by four coefficients: | |

− | + | * the {X, Y, Z} coefficients of the plane's normal vector pointing outward from the center of the arbn shape, and | |

− | + | * the perpendicular distance of that plane from the origin. | |

− | + | As discussed in the [[Creating and editing arbn primitives]] article, BRL-CAD uses such primitives to represent polyhedra having any number of sides, edges and vertices. | |

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=Ellipsoids= | =Ellipsoids= |

## Revision as of 00:18, 10 June 2013

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:

- Creating_primitive_objects
- Determining_the_properties_of_primitive objects
- Changing_the_properties_of_primitive objects

also see:

## Contents

# Arbitrary convex polyhedra

An **arbitrary convex polyhedron** (**arb**) is a geometric volume that is completely enclosed by a set of 3-dimensional planes. Each has a set of straight-edged, flat **faces** outlined by the intersections of those planes. The intersection of each pair of planes is a line whose intersections with other planes defines a pair of **vertices**. The line segment between those two vertices is an **edge** of the polyhedron that is shared by two faces. Each vertex is common to an equal number (at least three) of faces and edges.

For example, a rectangular parallelepiped is enclosed by three orthagonal pairs of parallel planes. Their intersections define six faces, each with four edges and four vertices. There are a total of 12 edges (each shared by two faces) and 8 vertices (each shared by three faces and three edges).

The BRL-CAD geometry file format defines two types of records for such polyhedra:

**arb8**s are specified by a set of eight vertices.**arbn**s are specified by a set of intersecting planes, each defined by four coefficients.

Although any polyhedron can be defined and stored as an arbn, the arb8 record type is more commonly employed because it is simpler to work with and still accommodates most constructive solid geometry applications.

## ARB8 Records

An **arb8** record is specified by a set of eight {X, Y, Z} vertices designated V1 through V8, which need not all be unique. As discussed in the Creating and editing arb8 primitives article, BRL-CAD uses such records to represent polyhedra having four, five or six faces:

**arb8**shapes represent**hexahedra**(six-sided polyhedra) whose sides are all quadrilaterals. They thus have eight edges and eight unique vertices. In addition to simply specifying the {X, Y, Z} coordinates of those vertices, MGED provides easier ways to create the following specific types of hexahedra:**3ptarb**shapes represent**right quadrilateral prisms**, which are extruded quadrilaterals having parallel ends connected by four rectangular sides.**box**shapes represent**parallelepipeds**, whose faces comprise three pairs of equal parallelograms. Unlike a common box, those faces need not be rectangular—if they are, the enclosed volume is a rectangular parallelepiped.**rpp**shapes represent**rectangular parallelepipeds**(also known as**cuboids**and**rectangular prisms**), whose faces comprise three pairs of equal rectangles. If one pair of faces are squares, the volume is a**square prism**. If all of them are squares, the volume is a**cube**(geometrically, there cannot be just two pairs of square faces).

**arb7**shapes represent hexahedra with four quadrilateral and two triangular faces. They have a total of eleven edges with seven unique vertices, one of which is shared by the two triangular faces. They can only be created by specifying the {X, Y, Z} coordinates of those vertices.

**arb6**shapes represent**triangular prisms**and**truncated tetrahedra**, both of which have two triangular ends connected by three quadrilateral sides (its seems they should be called quintahedra but that term seems to be rarely used). Either has a total of nine edges with six unique vertices. In addition to simply specifying the {X, Y, Z} coordinates of their vertices, MGED provides an easier way to create one specific type of hexahedron:**raw**(**right angle wedge**) shapes are**triangular prisms**whose ends are parallel to each other. Interestingly enough, they don't have to incorporate any right angles. If the ends are perpendicular to the connecting edges, the shape is a**right triangular prism**with rectangular sides. Presumably two of the rectangular sides of an actual right-angle wedge would also be perpendicular to each other. Such a shape could easily be created as a BRL-CAD raw primitive.

**arb5**shapes represent**quadrahedra**, which are polyhedra with five faces—a quadrilateral base and the three triangular sides with a total of f. If such a volume has a rectangular base it is a**rectangular pyramid**, one with a square base is a**square pyramid**.

**arb4**shapes represent tetrahedra, which are polyhedra with four triangular faces. If all four faces are equilateral triangles, the shape is a**regular tetrahedron**.

## ARBN Records

An **arbn** record is specified by N sets of intersecting planes, each defined by four coefficients:

- the {X, Y, Z} coefficients of the plane's normal vector pointing outward from the center of the arbn shape, and
- the perpendicular distance of that plane from the origin.

As discussed in the Creating and editing arbn primitives article, BRL-CAD uses such primitives to represent polyhedra having any number of sides, edges and vertices.

# Ellipsoids

## ell

Ellipsoid

- Handled by
- make in form create
- Arguments

- V
- 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:

- V
- vertex point, at the center
- radius

## 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
- vertex, height vector, radius

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
- vertex, height vector, radius

## 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

See also DSP tutorial.

## ebm

extruded bit map

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

See also EBM tutorial.

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.

## hf

Height field

- Handled by
- none?
- Status
- depreciated, use dsp instead

# Other solids

## tor

Torus

- Handled by
- in make form create
- Arguments
- vertex, normal vector, radius of revolution, tube radius

## 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
- vertex, height vector, radius at v, radius at h

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

- for each 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.

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?

## spline

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
- See also
- BoT

## poly

polysolid

- Handled by
- none?
- Status
- depreciated, use bot instead

# Other

## Sketch

2d outline

- Handled by
- make form(sketch editor) create
- See also
- sketch

## grip

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

- Handled by
- in make form create

Arguments:

- C
- Center
- N
- normal vector
- L
- 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