## ARB

The ARB is a planar-faced convex solid with between four and eight unique vertices. The specific type of ARB is often referred to by adding the number of unique vertices to the word ARB. For example, an ARB8 is the usual solid block, an ARB4 is a tetrahedron, and an ARB6 may be a wedge shape.

## arbitrary faceted solid

The arbitrary faceted solid (Also referred to as ARS) is a planar-faced solid defined by any number of curves (more precisely closed polylines). These curves are typically planar waterline or station curves, but they are not restricted to being planar. Each curve in a particular ARS must have the same number of points. The first and last curves are normally degenerate, each consisting of repetitions of a single point to make up the correct number of points for a curve. Faces are built by connecting corresponding points on adjacent curves. Since the curves are assumed to be closed, the last point on any curve is implicitly connected to the first point on the same curve

## ARBN

The ARBN is a planar faced convex solid defined by any number of bounding planes.

## BOT

The BOT solid is a collection of triangular facets. It may represent a zero thickness surface, a finite thickness plate, or a solid volume bounded by the triangles. The surface normal for each triangle may be unoriented, oriented according to the right-hand rule, or oriented according to the left-hand rule.

## ellipsoid

The ellipsoid is a solid defined by three mutually perpendicular semi­axes. When the axes are of unequal length, an ellipsoid is generated. When the axes are all the same length, a sphere is generated.

## elliptical hyperboloid

The elliptical hyperboloid (also referred to as EHY) is a solid with an elliptical base the remainder of the surface of which is defined by hyperbolas that run from any point on the ellipse through a common vertex at a specified distance from the ellipse and back to the ellipse at the point diametrically opposite the starting point. Further control of the surface may be obtained by specifying the distance from the hyperbolas to the vertex of the asymptotes.

## elliptical paraboloid

The elliptical paraboloid (also referred to as EPA) is a solid with an elliptical base the remainder of the surface of which is defined by parabolas that run from any point on the ellipse through a common vertex at a specified distance from the ellipse and back to the ellipse at a point diametrically opposite the starting point.

## elliptical torus

The Elliptical Torus (Also referred to as ETO) is defined by sweeping an ellipse through a circular path. The plane of the ellipse and the plane of the circular path are mutually perpendicular.

## extruded bitmap

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.

## half space

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.

## height field

The height field is a solid defined by a series of height measurements on a regular grid. In addition to a file of height measurements, this solid also requires a location vector, width and height direction vectors, and some scale factors.

## n­manifold geometry

(also referred to as NMG) The n­manifold geometry solid, sometimes known as a non­manifold geometry, is based on the description by Kevin Weiler in "The Radial Edge Structure: A Topological Representation for Non­Manifold Geometric Modeling" from Geometric Modeling for CAD Applications (Springer Verlag, 1987). A useful reference for the NMG solid is Combinatorial Solid Geometry, Boundary Representations, and Non_Manifold Geometry.

## particle

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.

## pipe

The pipe solid is defined by a sequence of control points, each with values for inner radius, outer radius, and bend radius. The actual pipe starts at the first control point and ends at the last control point. The intervening control points are replaced by circular bends with the specified bend radius, so the pipe is not likely to actually pass through these points. An inner radius of zero indicates a solid pipe or wire.

## polysolid

The polysolid is defined by a set of planar polygons. Each polygon may have up to 5 unique vertices. The vertices of each polygon must be in counter­clockwise order when viewed from outside the solid. The set of polygons must completely enclose the interior of the polysolid.

## right hyperbolic cylinder

The right hyperbolic cylinder (also referred to as RHC) is a solid built by extruding a truncated hyperbola through a height vector.

## right parabolic cylinder

The right parabolic cylinder (also referred to as RPC) is a solid built by extruding a truncated parabola through a height vector.

## spline

The spline solid is defined by a set of non­uniform rational B­spline surfaces (NURBS). There are no trimming curves in the spline solid, so each NURB surface must exactly adjoin its neighbor so that the interior of the spline solid is completely enclosed and no parts of any NURB surface are dangling outside the solid.

## torus

The torus is defined by sweeping one circle through a larger circular path. The planes of the circles are mutually perpendicular.

## truncated general con (also referred to as TGC)

The TGC solid is a truncated cone with elliptical (or circular) base and top. The base and top must be parallel, but the height vector connecting the center of the base with the center of the top does not need to be perpendicular to them.

## vol

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.