2.5 Volume Commands

The following commands are available on the Geometry/Volume subpad.

2.5.1 Form Volume

The Form Volume command button allows you to perform the following operations.

The following sections describe the procedures and specifications required to execute the commands listed above.

Stitch Faces

The Stitch Faces command allows you to form a volume from a set of existing faces.

To form a volume by means of the Stitch Faces command, you must specify the following information:

• A set of faces that comprise the sides of the volume
• The volume type

Specifying the Faces

To stitch faces to form a volume, you must specify a set of faces that constitute the sides of the volume. The faces do not have to be planar but must possess coincident edges such that the set defines a completely closed volume.

Specifying the Volume Type

GAMBIT allows you to form a real or virtual volume by means of the Stitch Faces command. To form a real volume, you must specify only real faces. To form a virtual volume, you can specify real and/or virtual faces.

If you specify the creation of a virtual volume, you can also specify a Tolerance value. The Tolerance value allows you to form a volume from a set of faces the edges of which are not exactly coincident with each other.

Using the Stitch Faces Form

To open the Stitch Faces form (see below), click the Stitch Faces command button on the Geometry/Volume subpad.

The Stitch Faces form includes the following specifications.

The Sweep Real Faces command allows you to form volumes by sweeping real faces along a specified path.

To create a volume by means of the Sweep Real Faces command, you must specify the following parameters.

• Profile
• Path
• Type

Specifying the Sweep Profile

The sweep profile consists of a set of one or more existing faces. GAMBIT creates a sepa­rate volume corresponding to each face in the profile. Each type of sweep operation possesses its own set of rules that govern whether or not a face con­stitutes a valid profile component. In general, however, GAMBIT does not allow you to specify profile faces that are parallel to the sweep path.

Specifying the Sweep Path

You can define the sweep path by means of either of the following specifications.

• Edge
• Vector

When you define the sweep path by specifying a vector, GAMBIT defines the path as a straight line possessing the magnitude and direction of the vector. You must define the vector by means of the Vector Definition form (see "Using the Vector Definition Form" in Section 2.1.4).

Specifying the Sweep Type

GAMBIT provides two general types of sweep operations:

• Rigid
• Perpendicular

Performing a Rigid Sweep

When you specify a rigid sweep operation, GAMBIT projects the profile along the entire length of the specified path without altering the size, shape, or orientation of the profile. The shape and orientation of any volume created by means of a rigid sweep operation depends on two factors:

• The shape of the profile face and its orientation relative to the path
• The shape and direction of the path

Specifying the Profile

The edges that bound the profile face(s) can be straight or curved, and the profile face does not have to be planar. However, GAMBIT imposes the following restrictions on profiles and paths employed in face-sweep operations:

• None of the edges that bound the profile face can be parallel to the path
• The face normal cannot be perpendicular to the path

Figure 2-83: Allowed face configurations for sweeping a face

The validities of the configurations shown in the figure are as follows.

• The configuration shown in Figure 2-83(a) is not valid, because edge AB is parallel to the path.
• The configuration shown in Figure 2-83(b) is not valid, because the normal to the face (ABC) is perpendicular to the path at its starting point (D).
• The combination shown in Figure 2-83(c) is valid, because none of its bounding edges is parallel to the path.

Specifying the Path

The sweep path can be defined by means of either an edge or a vector. If you specify an edge to define the path, the path can be straight or curved-depending on the shape of the edge. If you specify a vector to define the path, the path is straight by definition.

Example Face-Sweep Operations

Figure 2-84 and Figure 2-85 illustrate the results of the rigid face-sweep operation for two simple path/profile configurations. In each case, the profile face is planar and is bounded by three edges. The sweep paths shown in Figure 2-84 and Figure 2-85 are defined by a straight edge and a circular arc edge, respectively.

Figure 2-84: Example rigid face sweep operation—straight path

Figure 2-85: Example rigid face sweep operation—curved path

Performing a Perpendicular Sweep

Overview

Perpendicular sweep operations differ from rigid sweep operations in that, for perpendicular sweeps, the initial orientation between the profile and path is main­tained along the entire length of the sweep path. Rigid sweeps, by contrast, maintain the orientation of the profile with respect to the global coordinate system along the sweep path.

As an example of the difference between rigid and perpendicular sweep operations, consider the profile and path shown in Figure 2-86(a). In this case, the profile consists of a planar square face aligned with the y-z coordinate plane, and the path is defined by a circular arc edge aligned with the x-y plane.

Figure 2-86: Example Rigid and Perpendicular sweep operations—curved path

The differences between the created faces can be summarized as follows.

• If you perform a rigid sweep, GAMBIT maintains the orientation of the profile with respect to the global coordinate system, thereby creating the volume shown in Figure 2-86(b).
• If you perform a perpendicular sweep with a zero draft angle (see below), GAMBIT maintains the orientation between the path and profile and creates the volume shown in Figure 2-86(c).

Perpendicular Sweep Methods

GAMBIT provides two options for perpendicular face-sweep operations:

• Draft
• Twist

NOTE: In order to constitute a valid configuration for either a Draft or Twist operation, the profile and path must meet the following conditions. The profile must be planar. The face normal cannot be perpendicular to the path.

Draft Option

When you create a volume by means of the draft method, GAMBIT allows you to expand or contract the projected face by a specified angle along the path. Figure 2-87 shows a perpendicular draft sweep involving a profile and path identical to those shown in Figure 2-86(a). In this case the draft angle is specified as +10^o, therefore the profile expands as it is swept along the profile curve.

Figure 2-87: Perpendicular face sweep—draft option, 10^o draft angle

The Effect of Draft Angle

As noted above, when you perform a perpendicular face sweep operation by means of the draft method, GAMBIT allows you to specify a draft angle for the created volume. The draft angle represents the extent to which the swept edges of the volume are expanded or contracted relative to those of the original profile.

Figure 2-88 shows the effect of draft angle on the shape of a volume created by sweeping a square profile along a straight path that is perpendicular to the face. In this case, the profile face is a square, planar face aligned with the y-z plane, the path is defined by a straight edge aligned with the x axis, and the draft angle is specified as 10^o.

If you specify a positive draft angle, the profile expands along the length of the path (see Figure 2-88(c)). If you specify a negative draft angle, the profile contracts along the length of the path (see Figure 2-88(d)).

Figure 2-88: Perpendicular draft face sweep—effect of draft angle

The Effect of Draft Type

When you sweep a face by means of the perpendicular draft method and expand the profile by means of a positive draft angle, GAMBIT allows you to specify the following options for the expanded profile type:

• Extended
• Round
• Mixed

Figure 2-89: Perpendicular face sweep, draft method—effect of draft type

Twist Method

When you perform a perpendicular sweep operation by means of the twist method, GAMBIT revolves the profile through a specified angle along the length of the path. The profile and path can be straight or curved.

As an example of the effects of the twist sweep procedure, consider the profile/path configurations shown in Figure 2-90. In each case, the profile consists of a square planar face aligned with the y-z plane. The paths shown in Figure 2-90(a) and (b) are defined by straight and circular arc edges, respectively.

NOTE: When you employ a twist sweep procedure, GAMBIT twists the profile face about the specified path—rather than projecting the path start location onto the face surface geometry. Consequently, the results of the twist face-sweep operation depend, in part, on the orientation and distance between the profile and path.

Figure 2-90: Twist-method face sweep—example profiles and paths

Figure 2-91 and Figure 2-92 show the results of a perpendicular twist face-sweep procedure applied to the profiles and paths shown in Figure 2-90(a) and (b), respectively. Figure 2-91 shows results for draft-angle values of +90^oand +360^o. Figure 2-92 shows results for draft-angle values of +90^o and +180^o.

Figure 2-91: Twist-method face sweep—straight path results

Figure 2-92: Twist-method face sweep—curved path results

Using the Sweep Real Faces Form

To open the Sweep Real Faces form (see below), click the Sweep Real Faces command button on the Geometry/Volume subpad.

The Sweep Real Faces form includes the following specifications.

Revolve Real Faces

The Revolve Real Faces command allows you to form a volume by revolving a face through a specified angle

To create a volume by means of the Revolve Real Faces option, you must specify the following parameters:

• One or more faces to be revolved
• The axis of rotation
• The angle through which the face is revolved about the axis
• Draft angle and type

The rotational axis does not have to be coincident with one of the edges of the face to be swept, but it must lie in the same plane as the profile face (see Figure 2-93).

Figure 2-93: Face revolve parameters

Specifying Faces to Be Revolved

To create a volume by means of the Revolve Real Faces form, you must specify one or more faces to be revolved about the axis of rotation. Each specified face can include any combination of straight and curved edges as long as all the edges comprising the face lie in a single plane.

Specifying the Axis of Rotation

In order to constitute a valid axis of rotation for the face-revolve operation, the axis must lie in the plane of the face. To specify the axis of rotation, you must define the axis by means of the Vector Definition form. For a description of the Vector Definition form and its operation, see "Using the Vector Definition Form" in Section 2.1.4. The conventions regarding the angle of rotation for the Revolve Real Faces operation are identical to those described in "Rotating an Entity" in Section 2.1.4.

Specifying the Angle of Rotation

The angle of rotation is defined according to the right-hand rule relative to the direction of the axis vector. That is, when the rotational axis is oriented such that its vector points away from the observer, angles swept in the clockwise direction are defined as positive (see Figure 2-91, above).

Specifying Draft Angle and Type

When you create a volume by revolving a face, GAMBIT allows you to specify a draft angle and type to be applied in conjunction with the revolution of the face. The draft angle represents the extent to which the profile is expanded or contracted as the face is revolved. The draft type determines whether or not the edges of an expanded profile are rounded in the process of creating the volume.

Figure 2-94 shows two volumes created by revolving a rectangular face and specifying a positive draft angle—that is, an expansion of the profile. In Figure 2-94(a), the draft type is extended, therefore the basic shape of the face does not change as it is revolved. In Figure 2-94(b), the draft type is round, therefore the corners of the revolved face are rounded with respect to the original profile.

Figure 2-94: Revolving faces—effect of draft angle and type

Using the Revolve Real Faces Form

To open the Revolve Real Faces form (see below), click the Revolve Real Faces command button on the Geometry/Volume subpad.

The Revolve Real Faces form includes the following specifications.

Form Real Volume From Wireframe

The Form Real Volume From Wireframe command allows you to form a volume from a set of existing edges.

To create a volume by means of the Form Real Volume From Wireframe option, you must specify a set of edges that define the volume. The edge specifications are subject to the following restrictions:

• The set of edges must describe an entire closed volume
• All specified edges must possess at least one endpoint vertex that is coincident with that of one other edge in the set
• All edge loops must be joined to the overall set of loops

GAMBIT does not require that edges specified for the wireframe are connected at their endpoints. During the creation process, GAMBIT deletes coincident vertices, thereby connecting the edges used to form the volume.

Figure 2-95 shows four different sets of edges, only one of which constitutes a valid wireframe for the creation of a volume by means of the Form Real Volume From Wireframe form. Each set represents a slight variation on a set of edges that constitutes the wireframe of a cube. The sets shown in Figure 2-95 are allowed or not allowed for the following reasons:

1. Allowed—All of the edges possess at least one endpoint vertex that is coincident with that of at least one other edge; there are no edges that are wholly internal to the cube
2. Not allowed—The circular edges of the cylindrical region cannot be joined to any part of the edges that comprise the cube
3. Not allowed—There are four edges in the set that cannot be joined in to the edges of the cube
4. Not allowed—The edges of the pyramidal region exist entirely within the volume represented by the edges of the cube

Figure 2-95: Allowable wireframe configurations

If GAMBIT cannot resolve the specified set of edges into a valid volume, it completes as much as the creation process as is possible-including the creation of faces-and displays a warning in the Transcript window.

Using the Form Real Volume From Wireframe Form

To open the Form Real Volume From Wireframe form (see below), click the Form Real Volume From Wireframe command button on the Geometry/ Volume subpad.

The Form Real Volume From Wireframe form includes the following specifications.

2.5.2 Create Volume

The Create Volume command button allows you to perform the following operations.

Create Real Brick

The Create Real Brick command allows you to create a volume in the shape of a rectangular brick.

To create a volume by means of the Create Real Brick command, you must specify the following parameters:

• The dimensions of the brick
• The reference coordinate system
• The position of the brick relative to the origin of the reference coordinate system

Specifying the Dimensions

When you create a rectangular brick volume by means of the Create Real Brick option, GAMBIT applies the width, depth, and height specifications to the x, y, and z directions, respectively. To define the locations of the brick edges relative the origin of the reference coordinate system, you must specify the position of the brick (see below).

Specifying the Position of the Brick

To orient the brick relative to the reference coordinate system, you must specify the directions in which to apply the dimensions of the edges—that is, whether GAMBIT applies the width, depth, and height dimension parameters in the positive or negative direction with respect to each of the coordinate axes. The nine allowable direction options are as follows:

• +X +Y +Z
• +X +Y -Z
• +X -Y +Z
• +X -Y -Z
• -X +Y +Z
• -X +Y -Z
• -X -Y +Z
• -X -Y -Z
• Centered

Figure 2-96 shows the effect of four different direction options on the position of a cube created by means of the Create Real Brick form.

Figure 2-96: Effect of direction option on brick position

Using the Create Real Brick Form

To open the Create Real Brick form (see below), click the Create Real Brick command button on the Geometry/Volume subpad.

The Create Real Brick form includes the following specifications.

Create Real Cylinder

The Create Real Cylinder command allows you to create a circular or elliptical cylinder possessing a constant cross-sectional area.

To create a volume by means of the Create Real Cylinder command, you must specify the following parameters:

• The height of the cylinder
• The radii that define the cylinder cross section
• The reference coordinate system
• The axis location

Specifying the Cylinder Height

The height of the cylinder represents length of the cylinder along its axis. By default, the cylinder axis coincides with the z axis of the reference coordinate system. To change the orientation of the cylinder, you must specify the axis location (see below).

Specifying the Cylinder Radii

To define the cross section of the cylinder, you must specify its major and minor axes. To do so, you must specify two radii-Radius 1 and Radius 2-each of which is aligned with a coordinate axis. Either radius can constitute the major axis of the cylinder cross section. If you do not specify Radius 2, GAMBIT creates a circular cylinder of radius Radius 1.

By default, Radius 1 is aligned with the x axis, and Radius 2 is aligned with the y axis. If you change the orientation of the cylinder by specifying the axis location (see below), the axes corresponding to Radius 1 and Radius 2 change as well. The following table summarizes the relationship between axis location, Radius 1, and Radius 2.

Specifying the Axis Location

To locate and orient the cylinder, you must specify its axis location relative to the reference coordinate system. The axis location specification includes a coordinate axis and a direction. There are nine possible options for the axis location, each of which represents a different combination of three directions (positive, centered, and negative) and three coordinate axes (x, y, and z). The default axis location is Positive Z.

Figure 2-97 shows the effects of four different axis locations on the position of an elliptical cylinder created by means of the Create Real Cylinder form. In this example, the cylinder Height, Radius 1, and Radius 2 specifications are 7, 3, and 2, respectively.

Figure 2-97: Effect of axis location on cylinder position and orientation

Using the Create Real Cylinder Form

To open the Create Real Cylinder form (see below), click the Create Real Cylinder command button on the Geometry/Volume subpad.

The Create Real Cylinder form includes the following specifications.

Create Real Prism

The Create Real Prism command allows you to create a regular prism possessing a constant cross-sectional area. Each side of the prism is parallel to the prism axis.

To create a volume by means of the Create Real Prism command, you must specify the following parameters:

• The height of the prism
• The number of sides of the prism
• Two radii that define an ellipse that circumscribes the prism cross section
• The reference coordinate system
• The axis location

Specifying the Prism Height

The height of the prism represents length of the prism along its axis—that is, perpendicular to its cross section. By default, the prism axis coincides with the z axis of the reference coordinate system. To change the orientation of the prism, you must specify the axis location (see below).

Specifying the Number of Prism Sides

To create a prism, you must specify the number of its sides (n >= 3). GAMBIT constructs the prism such that each side is parallel to the prism axis.

The positions of the prism sides depend, in part, on whether you specify an odd number or even number of sides. If you specify an odd number of sides, GAMBIT constructs the prism such that one of its corner vertices lies within a coordinate plane of the reference coordinate system. If you specify an even number of vertices, GAMBIT constructs the prism such that one of its sides is parallel to a coordinate plane of the reference system.

Figure 2-98 shows the cross sections (in the x-y plane) of four prisms, each of which is circumscribed by a circular cylinder. In Figure 2-98(a), each prism possesses an odd number of sides. In Figure 2-98(b), each prism possesses an even number of sides. Note the following characteristics:

• The uppermost vertices of the triangle and pentagon in Figure 2-98(a) are coincident and lie in the y-z plane
• The uppermost sides of the square and hexagon in Figure 2-98(b) are parallel to the x-z plane.

Figure 2-98: Effect of the number of prism sides

Specifying the Prism Radii

To define the dimensions of the prism, you must specify the major and minor axes of an ellipse by which its cross section is circumscribed. To do so, you must specify two radii-Radius 1 and Radius 2-each of which is aligned with a coordinate axis. Either radius can constitute the major axis of the ellipse. If you do not specify Radius 2, GAMBIT circumscribes the prism by a circular cylinder of radius Radius 1.

By default, Radius 1 is aligned with the x axis, and Radius 2 is aligned with the y axis. If you change the orientation of the cylinder by specifying the axis location (see below), the axes corresponding to Radius 1 and Radius 2 change, as well. The following table summarizes the relationship between axis location, Radius 1, and Radius 2 with respect to the corresponding coordinate axes.

The Effect of Radii Specifications

If you specify values for Radius 1 and Radius 2 that are identical to each other (or do not specify a value for Radius 2) GAMBIT creates a prism the cross section of which is circumscribed by a circle (see Figure 2-98, above). If you specify values for Radius 1 and Radius 2 that differ from each other, GAMBIT creates a prism the cross section of which is circumscribed by an ellipse.

The procedure by which GAMBIT creates a prism circumscribed by an ellipse can be thought of as a two-step process:

1. Construct a prism circumscribed by a circular cylinder the radius of which is equal to the minor axis of the ellipse
2. Reposition the corner vertices of the cross section along lines parallel to the major axis of the ellipse

Figure 2-99 shows the effect of specifying an elliptical boundary on the cross section of a five-sided prism oriented with an axis location in the Positive Z direction. In Figure 2-99(a), Radius 1 constitutes the major axis of the ellipse, therefore GAMBIT locates the corner vertices of the cross section along lines parallel to its corresponding axis—that is, the x axis. In Figure 2-99(b), Radius 2 constitutes the major axis, therefore GAMBIT locates the corner vertices along lines parallel to the y axis.

Figure 2-99: Effect of radii on prism cross section

Specifying the Axis Location

To locate the prism in the model domain, you must specify its axis location relative to the reference coordinate system. The axis location specification includes a coordinate axis and a direction. For a description of the axis location specification, see "Create Real Cylinder," above.

Using the Create Real Prism Form

To open the Create Real Prism form (see below), click the Create Real Prism command button on the Geometry/Volume subpad.

The Create Real Prism form includes the following specifications.

Create Real Pyramid

The Create Real Pyramid command allows you to create a volume in the shape of a pyramid—that is, a prism possessing a non-constant cross-sectional area.

To create a volume by means of the Create Real Pyramid command, you must specify the following parameters:

• The height of the pyramid
• The number of sides of the pyramid
• Two radii that define an ellipse that circumscribes the cross section at the base of the pyramid
• One radius that defines the size of the top of the pyramid relative to its base
• The reference coordinate system
• The axis location

Specifying the General Pyramid Parameters

Four of the seven parameters required to specify a pyramid are identical to those required to specify a prism. The identical parameters are as follows:

• Height
• Number of sides
• Reference coordinate system
• Axis location

For a description of how to specify these parameters, see "Create Real Prism," above.

Specifying the Pyramid Radii

When you create a pyramid by means of the Create Real Pyramid form, GAMBIT constructs a volume in the shape of a prism the base and top of which differ only in size. To define size and shape of the base and top, you must specify three radii-Radius 1, Radius 2, and Radius 3.

Radius 1 and Radius 2 constitute the axes of an ellipse that circumscribes the base of the pyramid. They are specified according to the same procedure used to specify the radii of a prism (see "Create Real Prism," above). Radius 3 specifies the size of the top of the pyramid relative to Radius 1.

Figure 2-100 shows a three-sided prism with an elliptical base defined by Radius 1 (minor axis) and Radius 2 (major axis). The top of the pyramid is identical in shape to the pyramid base, but the sizes of its edges differ from those of the base by the ratio Radius 3:Radius 1.

Figure 2-100: Pyramid radii specifications

Using the Create Real Pyramid Form

To open the Create Real Pyramid form (see below), click the Create Real Pyramid command button on the Geometry/Volume subpad.

The Create Real Pyramid form includes the following specifications.

Create Real Frustum

The Create Real Frustum command allows you to create a volume in the shape of a frustum—that is, a cylinder of non-constant cross-sectional area.

To create a volume by means of the Create Real Frustum command, you must specify the following parameters:

• The height of the frustum
• Two radii that define an ellipse that constitutes the base of the frustum
• One radius that defines the size of the top of the frustum relative to its base
• The reference coordinate system
• The axis location

Specifying the General Frustum Parameters

Three of the six parameters required to specify a frustum are identical to those required to specify a cylinder. The identical parameters include the following:

• Height
• Reference coordinate system
• Axis location

For a description of how to specify these parameters, see "Create Real Cylinder," above.

Specifying the Frustum Radii

When you create a frustum by means of the Create Real Frustum form, GAMBIT constructs a cylindrical volume the base and top of which differ only in size. To define the size and shape of the base and top, you must specify three radii-Radius 1, Radius 2, and Radius 3.

Radius 1 and Radius 2 are the axes of the ellipse that constitutes the base of the frustum. Radius 3 specifies the size of the top of the frustum relative to Radius 1.

Figure 2-101 shows a frustum with an elliptical base defined by Radius 1 (minor axis) and Radius 2 (major axis). The top of the frustum is identical in shape and orientation to the base, but the lengths of its axes differ from those of the base by the ratio of Radius 3:Radius 1.

Figure 2-101: Frustum radii specifications

Using the Create Real Frustum Form

To open the Create Real Frustum form (see below), click the Create Real Frustum command button on the Geometry/Volume subpad.

The Create Real Frustum form includes the following specifications.

Create Real Sphere

The Create Real Sphere command allows you to create a volume in the shape of a sphere.

To create a sphere by means of the Create Real Sphere form, you must specify the radius of the sphere and the coordinate system the origin of which constitutes the center of the sphere.

Using the Create Real Sphere Form

To open the Create Real Sphere form (see below), click the Create Real Sphere command button on the Geometry/Volume subpad.

The Create Real Sphere form includes the following specifications.

Create Real Torus

The Create Real Torus command allows you to create a volume in the shape of a torus.

To create a torus by means of the Create Real Torus command, you must specify the following parameters:

• The circumferential radius
• The radius of the torus tube
• The reference coordinate system
• The coordinate axis that constitutes the axis of the torus

Specifying the Radii of the Torus

To define the dimensions of a torus, you must specify two radii (see Figure 2-102). The circumferential radius (Radius 1) defines the size of the circle that constitutes the center of the torus tube. The tube radius (Radius 2) defines the size of the tube itself.

Figure 2-102: Torus radius specifications

Specifying the Axis of the Torus

To orient the torus in the model domain, you must specify the coordinate axis that constitutes the central axis of the torus. The axis options include x axis, y axis, and z axis.

Using the Create Real Torus Form

To open the Create Real Torus form (see below), click the Create Real Torus command button on the Geometry/Volume subpad.

The Create Real Torus form includes the following specifications.