CAD & Geometric Primitives
The CAD/Geom panel provides access to facilities which can be
used to complete
the development of the analysis model if such has not been fully
defined. This will typically involve the creation of one or more
geometric primitives to define the enclosing domain of interest followed
by a series of volume operations to incorporate the desired geometry
model. In any event, it is assumed that the configuration geometry
is adequately defined and possesses no holes, gaps, or mismatched edges
as the facilities available herein simply provide a means to define the
domain far-field boundary and the resulting solid model. In other
words, geometry used by GridEx must be a "water-tight"
valid manifold solid, and the software performs no interrogation of the
model to ensure that is the case.
primitives consisting of a Box, Sphere, Cone,
and Cylinder may be created to represent the domain's far-field
boundary by simply providing the appropriate defining data in the
appropriate dialog window. These entities may be positioned
arbitrarily in three-dimensional space as prescribed by the user via
a series of dialog windows which accept the relevant input
parameters. Currently, all primitives are Cartesian aligned with
the subject geometry. As the primitives are generated, they are
also listed in the Structure Tree.
For the Box, a Corner Reference
Point is first specified to anchor the entity in space.
The Box Dimensions are then specified as the coordinates of
the opposite corner thus defining an appropriately sized box.
Note that each of the latter coordinates must be specified such that
the resulting body has non-zero volume.
For the Sphere, the Center Reference
Point anchors the center of the sphere in space. The radius
of the Sphere completes the definition and must be greater than
zero to produce a body with non-zero volume.
For the Cone, the Apex
Reference Point is first specified to anchor the apex of the cone
in space. The orientation of the Cone is then prescribed
by specifying coordinates for the Base Center. The cone
angle is then specified indirectly through the specification of the
Radius, which is the radius of the cone in the base plane.
Like the Box, specification of the Apex Reference
Point and Base Center must not be coincident so as to produce
a body with non-zero volume.
For the Cylinder, the First Axis
Reference Point represents the coordinate along the axis at one end
of the cylinder. The orientation of the cylinder is then fixed in
space by specification of the Second Axis Point which corresponds
to a point on the axis at the opposite end of the cylinder.
Finally, the Radius completes the definition of the cylinder.
As for the other primitives, specification of the axis points must be
unique and the radius must be greater than zero to provide a
The Torus is a surface of revolution. The
first three parameters define the rotation:
the Center Reference Point
anchors the center of the torus in space, the Sweep Curve Radius
represents the distance from the center reference point to the center of
the torus cross-section, and the Rotation Axis Direction is a
vector about which the cross-section is rotated.
The final parameter is the Cross Section Radius which defines the
radius of the circle cross-section.
Solid operations consisting of Unite, Subtract, and
Intersect may be performed on the geometric entities to complete
the definition of the solid model or to define intermediate entities
required to build a more complex model. In any event, each
operation requires the selection of a target volume followed
by a single tool volume. If successfully executed, the
resulting entity will be rendered in the Working Display and
entered in the Structure Tree. Each operation will conclude
by transparently redefining the rendering mode for the target and
tool volumes to off such that
they are no longer visible within the Working Display. They are,
however, not deleted and will remain within the Structure Tree
for subsequent use.
The Unite operation combines the target
volume with the tool volume to create a third volume defined by
the sum of the initial volumes. The operation will fail if the
initial volumes do not overlap. This operation may also fail if
the bodies simply abut depending on the capabilities of the underlying
modeling kernel. The Unite capability is useful for
assembling simple primitives into complex volumes.
The Subtract operation determines
that portion of the target volume external to the tool
volume. This facility will frequently be employed as a last step to
define the solid model as this effectively "carves" the domain occupied by
the configuration out of the volume whose boundaries define the extent
of the analysis domain. It can also be viewed as imprinting
the tool in a clay facsimile of the target
The Intersect operation determines
that portion of the target volume which is also occupied by the
tool volume. If the volumes do indeed overlap, a new volume
is created and displayed within the Working Display defined by
the region common to both bodies.
The solid operations tutorial provides a graphic
description of the use of the facilities described above.