2.4 Face Commands

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

Symbol	Command	Description
	Form Face	Creates a face from existing edges or vertices
	Create Face	Creates a face in one of three primitive shapes
	Boolean Operations	Unites, intersects, or subtracts faces
	Connect Faces Disconnect Faces	Connects real and virtual faces; disconnects faces shared between entities
	Modify Face Color Modify Face Label	Changes a face color; changes a face label
	Move/Copy Faces Align Faces	Moves and/or copies faces: aligns faces and connected geometry
	Split Face Merge Faces Collapse Face (Virtual) Simplify Faces	Splits faces about a face or vertices; merges faces; collapses a face; simplifies faces by removing dangling edges
	Smooth/Heal Real Faces Convert Faces (Nonreal to Real)	Smoothes and heals real face geometry; converts non-real faces to real faces
	Summarize Faces Check Faces Query Faces Total Entities	Displays face summary information; checks validity of topology and geometry; opens a face query list; displays entity totals
	Delete Faces	Deletes real or virtual faces

2.4.1 Form Face

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

Symbol	Operation	Description
	Create Face from Wireframe	Creates a face from existing edges
	Create Parallelogram Face	Creates a parallelogram face from three existing vertices
	Create Polygon Face	Creates a polygonal face from a set of three or more existing vertices
	Create Circular Face from Vertices	Creates a planar, circular face defined by a set of three vertices
	Create Elliptical Face from Vertices	Creates a planar, elliptical face defined by a set of vertices and angles
	Create Skin Surface Face	Creates a skin surface defined by a set of existing edges
	Create Net Surface Face	Creates a net-surface face from a specified set of edges
	Create Face from Vertex Rows	Creates a face from specified rows of existing vertices
	Create Offset Face	Creates a face by offsetting a source face
	Sweep Edges	Creates a face by sweeping an existing edge in a direction defined by an edge or vector
	Revolve Edges	Creates a face by revolving an existing edge about an axis

Create Face from Wireframe

The Create Face from Wireframe operation (face create wireframe command) creates a face from a set of existing edges. The operation requires spec­ification of the following parameters:

• Edges that define the face boundary (wireframe)
• Face type—real or virtual
• Options specific to the face type

Specifying the Wireframe Edges

As an example of edge specification for the Create Face from Wireframe opera­tion, consider the four coplanar edges shown in Figure 2-59(a), each of which is connected to its neigh­boring edges and all of which lie in the x-y plane. If you specify all four edges for the Create Face from Wireframe operation, GAMBIT creates the planar face shown in Figure 2-59(b).

Figure 2-59: Wireframe edges and created face

NOTE: The sequence in which the edges are specified for the Create Face from Wireframe operation does not affect the outcome of the operation.

Specifying the Face Type

Creating a Real Face

• Standard covering
• Advanced covering
• Least-squares fit

GAMBIT provides three options for specifying entities to be used for the advanced covering techniques:

• Initial Face
• Guide Edges
• Guide Vertices

NOTE (1): The Initial Face, Guide Edges, and/or Guide Vertices entities can be real or non-real. If you specify a non-real entity, GAMBIT creates and uses a real copy of the specified entity for the advanced covering operation and deletes the real copy when the operation is complete.

NOTE (2): The following sections describe the effects of each option when used independently, but the options can be combined for any Create Face from Wireframe operation to help define the shape of the created face.

Specifying an Initial Face

The Initial Face option allows you to specify an existing face the surface of which is used to define the surface of the created face. The effect of the option depends, in part, on whether the wireframe edge loop lies on the surface of the Initial Face. Specifically:

• If the wireframe edge loop lies on the surface of the Initial Face, GAMBIT attempts to use the surface of the Initial Face to define the surface of the new face.
• If the wireframe edge loop does not lie on the surface of the Initial Face, GAMBIT uses the Initial Face as a projection surface to help define the shape of the new face.

Figure 2-60: Cylindrical tube with saddle-shaped hole

Figure 2-61 illustrates the effect of specifying an Initial Face when using the saddle-shaped edge as the wireframe loop for a Create Face from Wireframe operation. Specifically:

• If you do not specify an Initial Face, GAMBIT fills the saddle-shaped hole with the face shown in Figure 2-61(a)—the surface of which deviates signifi­cantly from the cylindrical surface surrounding the hole.
• If you do specify the tube face as the Initial Face, GAMBIT fills the hole with the face shown in Figure 2-61(b)—the surface of which is defined by the surface of the cylindrical face.

Figure 2-61: Effect of Initial Face option on tube with saddle-shaped hole

The Initial Face option can be used to repair holes in irregular surfaces as well as smooth surfaces such as that shown in Figure 2-60, above. As an example of the effect of the Initial Face option on irregular surfaces, consider the geometry shown in Figure 2-62(a). The geometry consists of a ribbed face with a hole that represents the intersection of its surface with a circular cylinder perpen­dicular to the general orientation of the face.

If you specify the hole boundary edge as the wireframe loop and the ribbed face itself as the Initial Face, GAMBIT fills the hole with the face shown in Figure 2-62(b). In this case, the surface of the created face follows the ribbed contours of the Initial Face. (NOTE: You can use the GAMBIT Merge Faces command to merge the faces shown in Figure 2-62(b) into a single real face with a continuous ribbed surface.)

Figure 2-62: Effect of Initial Face option on face with a ribbed surface

As noted above, if the wireframe edge loop does not lie on the surface of the Initial Face, GAMBIT uses the Initial Face as a projection surface to help define the shape of the created face. Consequently, the Initial Face option can be used to control the shape of a face the boundary edges of which would otherwise define invalid geometry. As an example of this application, con­sider the geometry shown in Figure 2-63(a). The geometry consists of a six-edge inner wireframe loop surrounded by a coaxial cylindrical face that is split at its top by a single straight edge (see NOTE, below).

Figure 2-63: Use of Initial Face as a projection surface

In this case, the effect of the Initial Face specification is as follows.

• If you do not specify the outer cylindrical face as the Initial Face, GAMBIT either fails to create a face from the wireframe loop or creates a face that fails geometry checks and can cause problems in subsequent GAMBIT operations.
• If you do specify the outer cylindrical face as the Initial Face, GAMBIT creates the inner face shown in Figure 2-63(b)—which constitutes valid geometry and can be safely used in subsequent GAMBIT operations.

Specifying Guide Edges

The Guide Edges option allows you to control the shape of the created face by specifying edges through which the surface of the face must be fitted. As an example of the effect of the Guide Edges option, consider the geometries shown in Figure 2-64. The basic wireframe edge loop for both geometries consists of six straight, con­nected edges, three of which (a-b-c) lie in the z-x plane, and three of which (d-e-f) lie in the y-z plane (see Figure 2-64(a)). The geometry shown in Figure 2-64(b) includes a set of three guide edges.

Figure 2-64: Basic wireframe edge loop and guide edges

Figure 2-65 illustrates the effect of specifying Guide Edges when using the six-edge wireframe for a Create Face from Wireframe operation. Specifically:

• If you specify the wireframe edge loop shown in Figure 2-64(a) and do not specify guide edges, GAMBIT creates the face shown in Figure 2-65(a)—the surface of which exhibits severe curvature.
• If you specify the Guide Edges option using the three guide edges shown in Figure 2-64(b), GAMBIT creates the face shown in Figure 2-65(b)—the surface of which approximates a flat, rectangular sheet with a right-angle bend.

Figure 2-65: Effect of guide edges on face surface shape

Specifying Guide Vertices

The Guide Vertices option allows you to control the shape of the created face by specifying vertices through which the surface of the face must be fitted. As an example of the effect of the Guide Vertices option, consider the geometries shown in Figure 2-66. The basic wireframe edge loop for both geometries consists of a single, saddle-shaped edge (see Figure 2-66(a)). The geometry shown in Figure 2-66(b) includes a guide vertex that can be used to control the shape of the surface for the created face.

Figure 2-66: Basic wireframe edge loop and guide vertex

Figure 2-67 illustrates the effect of specifying the guide vertex when using the saddle-shaped wireframe edge loop shown in Figure 2-66. Specifically:

• If you do not specify the guide vertex, GAMBIT creates the face shown in Figure 2-67(a), the surface of which exhibits saddle-shaped curvature.
• If you specify the guide vertex shown in Figure 2-66(b), GAMBIT creates the face shown in Figure 2-67(b). In this case, the guide vertex is positioned such that the created face represents a section of a cylindrical surface, such as that shown in Figure 2-61(b), above.

Figure 2-67: Effect of guide vertex on face surface shape

Specifying the Tolerance Value

The advanced-covering techniques used by the Create Face from Wireframe operation employ tolerance values to determine how closely the surface of any created face matches the wireframe edge loop that defines its boundaries. In general, the smaller the tolerance value, the more closely the surface matches the edge loop at its boundaries.

To construct a face the surface of which closely matches the edges that define its bound­aries, GAMBIT must sometimes distort the surface in its interior regions. Consequently, the tolerance values can greatly affect the shape of the created face. As an example of this effect, consider the wireframe edge loop shown in Figure 2-68. The loop consists of eight straight edges four of which (a-b-c-d) lie in the z-x plane and the other four of which (e-f-g-h) lie in a plane angled slightly from the z-x plane.

Figure 2-68: Non-planar wireframe edge loop

Figure 2-69 illustrates the general effect of tolerance value on the shape of the created face for this geometry. (NOTE: The geometries shown in Figure 2-69 are meshed to accentuate their surface shapes.) The effects shown in Figure 2-69 can be summarized as follows.

• If you specify a Tolerance value of 0.05, GAMBIT creates the face shown in Figure 2-69(a), the middle surface of which is strongly curved.
• If you specify a Tolerance value of 0.5, GAMBIT creates the face shown in Figure 2-69(b), the middle surface of which is more closely aligned with the z-x and angled planes associated with the wireframe edges.

Figure 2-69: Effect of Tolerance value on face surface shape

NOTE (1): Faces created using large tolerance values can sometimes present problems in subsequent GAMBIT operations—such as Boolean and meshing operations.

NOTE (2): The advanced covering algorithms that GAMBIT uses to create faces such as those shown in Figure 2-69, above, cannot produce surfaces possessing "G1" discontinuities; therefore, neither face possesses a crease along its bend.

GAMBIT provides two Tolerance options for Type:Real wireframe face creation operations:

• Auto
• Manual

Creating a Virtual Face

• If you do not specify a host face or volume, GAMBIT creates an orphan face the shape of which is defined only by means of its boundary edges.
• If you specify a host face or volume, GAMBIT creates a parasite face and employs the existing geometry (shape) of the host entity to define the shape of the virtual face.

If you specify a host face, you can specify the visibility of the host face by means of the Hide host option on the Create Face from Wireframe form. If you select the Hide host option, GAMBIT renders the host face invisible for all operations, including display operations executed by means of the Specify Display Attributes command (see Chapter 3 of the GAMBIT User’s Guide). To render the host face visible again, you must delete the hosted virtual face.

Specifying the Tolerance Value

If you specify a host face for the creation of a virtual face, GAMBIT allows you to specify a Tolerance value. The Tolerance value constitutes the maximum allowable distance between the face-boundary (wireframe) edges and the surface of the host face.

Using the Create Face from Wireframe Form

To open the Create Face from Wireframe form (see below), click the Create Face from Wireframe command button on the Geometry/Face subpad.

The Create Face from Wireframe form includes the following specifications.

Edges	specifies the edges to be used in creating the face.
Type:	specifies the type of face to be created: Real Virtual For descriptions of the options available for each face type, see "Specifying the Face Type," above.

The specifications available in the lower section of the Create Face from Wireframe form vary according to Type option as follows.

Real Face Specifications

When you select the Type:Real option, the lower portion of the Create Face from Wireframe form appears as shown above and includes the following specifica­tions.

Initial Face	specifies an existing face the surface of which is used to help define the surface of the created face.
Guide Edges	specifies existing edges through which the surface of the created face is fitted.
Guide Vertices	specifies existing vertices through which the surface of the created face is fitted.
Tolerance	specifies the tolerance values used when creating the face. GAMBIT provides two Tolerance options: Auto—automatically assigns individual tolerance values to edges during face creation Manual—specifies an overall tolerance value to be applied to all edges during face creation
Label	(Real and Virtual face types) specifies a label for the new face. (See Section 2.1.1.)

Virtual Face Specifications

For this option, the lower portion of the Create Face from Wireframe form appears as shown below and includes the following specifications.

Host	specifies that the virtual face is to be attached to a host face or volume.
Face Volume	specifies whether the host entity is a face or a volume.
Face Volume	specifies the entity to be used as a host.
Hide host	renders the host entity invisible.
Tolerance	specifies the maximum allowable distance between the wireframe edges and the host face (default = 10-5).

Create Parallelogram Face

The Create Parallelogram Face operation (face create plane command) creates a four-sided face in the shape of a parallelogram.

To create a face by means of the Create Parallelogram Face operation, you must specify three existing vertices that define the face. If all three vertices are real vertices, GAMBIT creates a real face; otherwise, GAMBIT creates a virtual face. The vertices are designated as Origin, Base, and Incline and define the face shape as shown in Figure 2-70.

Figure 2-70: Create Parallelogram Face vertex definitions

The edges formed in the creation of the face are defined such that their senses are from the Origin vertex to the Base vertex and from the Incline vertex to the Origin vertex. If you reverse the specifications regarding which vertices constitute the Base and Incline vertices, respectively, the shape of the resulting face does not change, but GAMBIT reverses the sense of each of its boundary edges.

Using the Create Parallelogram Face Form

To open the Create Parallelogram Face form (see below), click the Create Parallelogram Face command button on the Geometry/Face subpad.

The Create Parallelogram Face form includes the following specifications.

Vertices:
Origin	specifies the vertex that constitutes a common endpoint for both the base edge and one of the inclined edges of the parallelogram.
Base	specifies the vertex that constitutes the other endpoint of the base edge of the parallelogram.
Incline	specifies the vertex that constitutes the other endpoint of one of the inclined edges of the parallelogram.
Label	specifies a label for the new face. (See Section 2.1.1.)

Create Polygon Face

The Create Polygon Face operation (face create polygon command) creates a planar, polygonal face defined by a set of three or more existing vertices. (NOTE: If you specify a set of five or more vertices, all vertices in the set must be coplanar.)

To create a face by means of the Create Polygon Face operation, you must specify a set of at least three vertices. If all of the specified vertices are real vertices, GAMBIT creates a real face; otherwise, GAMBIT creates a virtual face.

To create the polygonal face, GAMBIT first creates a closed loop of edges that join the specified vertices then creates a face bounded by the closed loop. The order in which the vertices are specified on the Create Polygon Face form determines the order in which the bounding edges are created— which, in turn, affects the shape of the created face. As an example of this effect, consider the set of six vertices shown in Figure 2-71(a).

Figure 2-71: Effect of vertex specification sequence

Figure 2-71(b) and Figure 2-71(c) show two example faces created using the vertex specification sequences listed in the following table.

Using the Create Polygon Face Form

To open the Create Polygon Face form (see below), click the Create Polygon Face command button on the Geometry/Face subpad.

The Create Polygon Face form includes the following specifications.

Vertices	specifies the vertices that define the bounding region of the polygonal face.
Label	specifies a label for the new face. (See Section 2.1.1.)

Create Circular Face from Vertices

The Create Circular Face from Vertices operation (face create circle command) creates a planar face in the shape of a full circle the dimensions of which are defined by three vertices.

The Create Circular Face from Vertices form provides two methods for creating a face in the shape of a full circle. Both methods require specification of three existing vertices to define the size and location of the circle. The methods are defined as follows (see Figure 2-72):

• Method 1 (Figure 2-72(a)) requires specification of one vertex that defines the center of the circle and two vertices that define the circular edge that bounds the face. The two vertices that lie on the circular boundary edge must be located equidistant from the vertex that defines the center of the circle.
• Method 2 (Figure 2-72(b)) specifies three vertices that define the circular edge that bounds the face. The three vertices must not be collinear.

Figure 2-72: Create Circular Face from Vertices vertex specifications

For either method, if the vertices that lie on the circular boundary edge are real vertices, GAMBIT creates a real face; otherwise, GAMBIT creates a virtual face.

Using the Create Circular Face from Vertices Form

To open the Create Circular Face from Vertices form (see below), click the Create Circular Face from Vertices command button on the Geometry/ Face subpad.

The Create Circular Face from Vertices form includes the following specifications.

Method:

contains two radio buttons that allow you to specify the method by which the circular face is created. For either method, you must specify three vertices. The two methods differ in their treatment of the vertices as follows: Method 1—One vertex defines the center of the circle and the other two vertices define the cir­cular edge that bounds the face. Method 2—All three vertices define the circular edge that bounds the face.

The center section of the Create Circular Face from Vertices form varies according to the method selected to construct the bounding circle. The specifications available on the center section of the form are as follows.

Method 1

Vertices:
Center	specifies the vertex that defines the center of the circle.
End-Points	specifies the vertices that define the circular boundary edge.
Label	specifies a label for the new face. (See Section 2.1.1.)

Method 2

When you specify Method 2 for the creation of a circular face, the middle section of the Create Circular Face from Vertices form appears as shown below.

Vertices

specifies the three vertices that define the circular boundary edge.

Create Elliptical Face from Vertices

The Create Elliptical Face from Vertices operation (face create ellipse command) creates a face that represents a section of a full ellipse. The operation requires specification of the following parame­ters (see Figure 2-73):

• Center, Major, and On Edge vertices
• Start Angle and Stop Angle values

Figure 2-73: Create Elliptical Face from Vertices vertex specifications

The Center, Major, and On Edge vertices define the size and shape of the ellipse. (NOTE: The three vertices must not be collinear.) The Start Angle and Stop Angle define the radial section of the ellipse that defines the shape of the created face. If the Major vertex is a real vertex, GAMBIT creates a real face; otherwise, GAMBIT creates a virtual face.

Using the Create Elliptical Face from Vertices Form

To open the Create Elliptical Face from Vertices form (see below), click the Create Elliptical Face from Vertices command button on the Geometry/ Face subpad.

The Create Elliptical Face from Vertices form includes the following specifications.

Center	specifies the vertex that defines the center of the ellipse.
Major	specifies the vertex that defines the major axis of the ellipse.
On Edge	specifies a vertex that lies on the edge of the full ellipse.
Start Angle	specifies the start angle for the radial section that defines the face. (NOTE: The zero-angle reference vector points from the Center vertex to the Major vertex.)
End Angle	specifies the end angle for the radial section that defines the face. (NOTE: The zero-angle reference vector points from the Center vertex to the Major vertex.)
Label	specifies a label for the new face. (See Section 2.1.1.)

Create Skin Surface Face

The Create Skin Surface Face operation (face create skin command) creates a surface consisting of one or more faces from a set of "ribs" that define the shape of the surface. You can also specify one or two independent vertices that further define the shape of the created surface.

Specifying Ribs for a Skin-Surface Face

To create a surface by means of the Create Skin Surface Face command, you must specify two or more "ribs" that define its shape. Each rib can consist of either a single edge or a chain of connected edges. The types of ribs speci­fied determine the geometry of the created surface as follows:

• If each rib in the set consists of a single edge, GAMBIT creates a single face.
• If one or more ribs in the set consists of an edge chain (a set of con­nected edges), GAMBIT creates a surface composed of two or more connected faces.

Specifying Rib Sets That Include Only Single Edges

As a simple example of rib specification for the Create Skin Surface Face operation, consider the five ribs (A, B, C, D, and E) shown in Figure 2-74(a). Each rib consists of a single edge (1, 2, 3, 4, and 5, respectively). If you spec­ify all five ribs in the correct order (see below) as the rib set for a Create Skin Surface Face operation, GAMBIT creates the face shown in Figure 2-74(b). (NOTE: The created faces shown in the following figures include mesh displays to accentuate their contours.)

Figure 2-74: Create Skin Surface Face operation—five-edge rib set

In this case, GAMBIT creates a single four-sided face. Two of the four edges that bound the face constitute the first and last ribs specified in the rib set—that is, edges 1 and 5. The other two boundary edges (6 and 7) represent cont­inuous curves fit through the endpoint vertices of the specified ribs.

NOTE (1): The order in which you specify ribs determines the shape of the created face. For example, to create the face shown in Figure 2-74(b), you must specify the edges in the order (1, 2, 3, 4, 5) or (5, 4, 3, 2, 1), rather than (1, 4, 2, 3, 5) or (3, 2, 5, 1, 4). If you specify the edges out of order in this case, GAMBIT fails to create the face, because doing so would create self-intersecting (invalid) geometry.

NOTE (2): GAMBIT ignores edge sense when creating a face by means of the Create Skin Surface Face operation. For example, the final shape of the face shown in Figure 2-74(b) is independent of the senses of the edges that define its surface.

Specifying Rib Sets That Include Edge Chains

As noted above, GAMBIT allows you to specify rib sets that include any combination of single edges and edge chains. To include edge chains in the rib set, you must select the Connected edges option on the Create Skin Surface Face form.

As an example of specifying rib sets that include edge chains, consider the set of five ribs (A - E) shown in Figure 2-75(a). This rib set consists of five ribs, one of which (A) is a single edge (1), and the other four of which consist of edge chains ([B:2,3], [C:4,5], [D:6,7,8], and [E:9,10]). If you correctly specify all of the ribs in this set (see below) and select the Connected edges option, GAMBIT creates the surface shown in Figure 2-75(b).

Figure 2-75: Create Skin Surface Face operation—rib set with edge chains

In this case, GAMBIT creates a four-sided surface consisting of six connected faces. The widths of the created faces are determined by the locations of the internal (non-endpoint) vertices in each of the ribs. Specifically, the total number of created faces is equal to (n + 1), where n is the number of internal vertices in the rib set. In this example, the rib set includes five internal vertices; therefore, the surface consists of six faces.

To create a skin surface using a rib set that contains edge chains, you must specify the edges in correct order. The correct specification of edges for a rib set that includes edge chains can be thought of as a two-step process:

1. Specify at least one edge in each rib from one side of the surface to the other.
2. Specify all other connected edges to be included in the definition of the surface in any order.

• 1, 2, 4, 6, 9, 3, 5, 7, 8, 10
• 1, 2, 4, 6, 9, 10, 5, 8, 3, 7
• 1, 2, 3, 4, 6, 10, 5, 7, 8, 9
• 9, 7, 5, 3, 1, 2, 4, 8, 6, 10
• 10, 7, 4, 3, 1, 9, 2, 8, 5, 6

Specifying Start and End Vertices

In addition to specifying rib sets for the Create Skin Surface Face opera­tion, GAMBIT allows you to specify one or two independent vertices (Start and End) that further define the shape of the created surface. The Start and End vertices should be located in proximity to the first and last ribs, respec­tively, in the specified rib set.

As an example of the effect of the independent vertices on the shape of the created surface, consider the rib set shown in Figure 2-76(a). This configura­tion is identical to that shown in Figure 2-74(a), above, but includes an inde­pendent vertex located in proximity to rib E (edge 5). If you specify the rib-set edges in the order (1, 2, 3, 4, 5) and specify the vertex as an End vertex, GAMBIT creates the surface shown in Figure 2-76(b).

Figure 2-76: Create Skin Surface Face operation—effect of End vertex

NOTE: As noted above, the Start and End vertices must be located in prox­imity to the first and last specified ribs, respectively. If the ribs in this example are specified in the order (5, 4, 3, 2, 1), rather than (1, 2, 3, 4, 5), the independent vertex shown in Figure 2-76(a) must be specified as a Start vertex, rather than an End vertex.

Using the Create Skin Surface Face Form

To open the Create Skin Surface Face form (see below), click the Create Skin Surface Face command button on the Geometry/Face subpad.

The Create Skin Surface Face form includes the following specifications.

Edges	specifies the edges that define the shape of the created surface.
Connected edges	specifies that ribs consisting of chains of connected edges are to be used defining the created surface.
Start Vertex	specifies an independent vertex in proximity of the first speci­fied rib (see "Specifying Start and End Vertices," above).
End Vertex	specifies an independent vertex in proximity of the last speci­fied rib (see "Specifying Start and End Vertices," above).
Label	specifies a label for one of the new faces (see Section 2.1.1).

Create Net Surface Face

The Create Net Surface Face operation (face create net command) creates a four-sided face from two sets of logically parallel edges that define the boundaries and shape of its surface.

Specifying Edges for a Net-Surface Face

To create a face by means of the Create Net Surface Face option, you must specify two or more sets of existing edges that define the shape of the face. Each set must include at least two edges. The surface of the created face constitutes an interpolation through all of the edges specified for the face.

As an example of edge specification for the Create Net Surface Face operation, consider the edges shown in Figure 2-77(a). The figure consists of nine edges, four of which (designated by the letter u) are logically perpendicular to the other five (designated by the letter v).

Figure 2-77: Create Net Surface Face edge specifications

If you use all four edges in the u direction and all five edges in the v direction to create a net-surface face, GAMBIT creates a face such as that shown in Figure 2-77(b).

If you specify edges in either direction the lengths of which exceed the boundary defined by the first or last edges specified in the other direction, GAMBIT truncates the created face. As an example of such truncation, consider the edges shown in Figure 2-77(a), above. If you specify edges 2, 3, and 4 in the u direction and edges 2, 3, 4, and 5 in the v direction, GAMBIT creates the net-surface face shown in Figure 2-77(c). Note that the final form of the net-surface face approximates the intersection of skin-surface faces created by means of edges 2, 3, and 4 in the u direction and edges 2, 3, 4, and 5 in the v direction.

NOTE: To create a face by means of the Create Net Surface Face operation, you must specify the edges monotonically in each direction with respect to their relative positions in defining the face. For example, to create the face shown in Figure 2-77(b), you must specify the u-direction edges in the order (1, 2, 3, 4) or (4, 3, 2, 1) and the v-direction edges in the order (1, 2, 3, 4, 5) or (5, 4, 3, 2, 1).

Specifying the Tolerance Value

Using the Create Net Surface Face Form

To open the Create Net Surface Face form (see below), click the Create Net Surface Face command button on the Geometry/Face subpad.

The Create Net Surface Face form includes the following specifications.

U Dir. Edges	specifies the edges that define the surface of the face with respect to the u direction (see Figure 2-77(a)).
V Dir. Edges	specifies the edges that define the surface of the face with respect to the v direction (see Figure 2-77(a)).
Tolerance	specifies the maximum allowable distance between any of the edges and the surface of the resulting face (default = 10-3).
Label	specifies a label for the new face. (See Section 2.1.1.)

Create Face from Vertex Rows

The Create Face from Vertex Rows operation (face create vertices command) creates a four-sided face from a series of vertex rows that define the surface of the face. The operation requires specification of the following input parameters:

• A sequence of vertices that define the face
• The number of rows of vertices to be used in defining the face
• The method used to fit curves through the vertices that define the face

Specifying the Vertex Sequence

When you specify vertices for the Create Face from Vertex Rows operation, you must select the vertices in an ordered sequence that represents the position of each vertex in a sequential series of rows. That is, you must specify all the vertices that constitute the first row, then all the vertices that constitute the second row, and so on.

The first and last rows of vertices specified define edges that comprise two of the four sides of the face. The other two sides of the face consist of continuous curves fit through two sets of vertices defined as follows:

• The first vertex specified in each row
• The last vertex specified in each row

Figure 2-78: Create Face from Vertex Rows specifications—4 rows

Specifying the Number of Vertex Rows

When you create a face by means of the Create Face from Vertex Rows operation, you must specify the number of rows represented by the specified vertices. The total number of vertices must represent an integer multiple of the number of vertex rows. For example, if you specify a total of 12 vertices, you must specify either 2, 3, 4, or 6 vertex rows. The number of vertices in each row is equal to the total number of vertices divided by the number of rows.

It is possible to create a face of a given shape using two different specifications for the number of rows. For example, the face shown in Figure 2-79 represents a face created from the same set of vertices employed to create the face in Figure 2-78. The face differs from the face in Figure 2-78 in that it is created by specifying three rows of four vertices each rather than four rows of three vertices each.

Figure 2-79: Create Face from Vertex Rows specifications—3 rows

Although the shapes of the two faces are identical to each other, they differ in two respects:

• The sequence in which the vertices are specified
• The numbering of the edges created in the creation of the face

Specifying the Curve Fit Method

GAMBIT allows you to specify one of two methods by which curves are fit through the vertex rows to define the face. The two methods are as follows.

• Interpolate
• Approximate

Using the Create Face from Vertex Rows Form

To open the Create Face from Vertex Rows form (see below), click the Create Face from Vertex Rows command button on the Geometry/Face subpad.

The Create Face from Vertex Rows form includes the following specifications.

Vertices	specifies the vertices to be used in the creation of the face.
No. of Rows	specifies the total number of vertex rows. (NOTE: The total number of vertices specified must be equal to an integer multiple of the number of vertex rows.)
Method:
Interpolate	specifies that the face passes through all vertices.
Approximate	specifies that the face passes near to the internal vertices to within the specified Tolerance value.
Tolerance	specifies the maximum allowable distance between the face and any of the internal vertices.
Label	specifies a label for the new face. (See Section 2.1.1.)

Create Offset Face

The Create Offset Face operation (face create offset command) creates a face by offsetting the surface of specified (source) face by a specified distance. The operation requires specification of the following parameters:

• Source Face
• Offset Distance
• Reverse option

Figure 2-80: Create Offset Face operation

Specifying the Reverse Option

The Reverse option reverses the direction of the offset operation with respect to the outward-pointing normal of the source face. If the source face is non-planar, the Reverse option can affect the size of the offset face as well as its position (see Figure 2-81).

Figure 2-81: Create Offset Face operation—Effect of Reverse option

Using the Create Offset Face Form

To open the Create Offset Face form (see below), click the Create Offset Face command button on the Geometry/Face subpad.

The Create Offset Face form includes the following specifications.

Face	specifies the source face to be offset.
Distance	specifies the distance by which the new face is to be offset from the source face.
Reverse	reverses the offset direction.
Label	specifies a label for the new face. (See Section 2.1.1.)

Sweep Edges

The Sweep Edges operation (face create translate and face create rotate commands) creates faces by sweeping one or more edges along a specified path. If you sweep a non-real edge to create a face, GAMBIT creates a virtual face.

The Sweep Edges command requires the following input parameters.

• Profile
• Path
• With mesh option (meshed edges only)
• Type

Specifying the Sweep Profile

To create a face by sweeping an edge, you must specify a set of one or more edges that constitutes the sweep profile. The edges can be straight or curved, real or non-real, and they may or may not be connected to each other. The validity of any edge as a profile component depends on the sweep type. In general, however, GAMBIT does not allow you to specify profile edges that are parallel to the sweep path.

Specifying the Sweep Path

• Edge
• Vector

If you specify a vector to define the sweep path, GAMBIT defines the path as a straight line possessing the magnitude and direction of the vector. The vector is defined by means of the Vector Definition form (see "Using the Vector Definition Form" in Section 2.1.4).

Specifying the With mesh Option

If both the path and profile are defined by meshed edges, GAMBIT uses the mesh-node spacing on the path edge to determine the mesh-element spacing along the sides of the created face. Otherwise, GAMBIT uses the default face meshing parameters to compute the mesh-element spacing.

As an example of the effect of the With mesh option, consider the meshed path and profile edges shown in Figure 2-82(a). The profile consists of a single straight edge aligned with the x axis, and the path is a circular arc edge aligned with the y-z plane. If you perform a simple rigid sweep operation using these edges and select the With mesh option, GAMBIT sweeps the profile along the path to create the meshed face shown in Figure 2-82(b). In this case, the face mesh density is determined by the mesh node spacing on both the profile and path edges.

Figure 2-82: Effect of With mesh option on edge-sweep operations

Specifying the Sweep Type

GAMBIT provides two general types of sweep operations:

• Rigid
• Perpendicular

Performing a Rigid Sweep

When you perform a rigid sweep operation, GAMBIT sweeps the profile along the specified path while maintaining the orienta­tion of the profile with respect to the global coordinate system. The shape and orientation of the created face depend on two factors:

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

The following examples demonstrate the effects of the shapes and orienta­tions of the profile and path on the final form of a face created by means of a simple rigid sweep operation.

Rigid Sweep—Profile Perpendicular to the Path

Figure 2-83 illustrates a rigid sweep operation in which the path and profile are defined by straight edges oriented perpendicular to each other. The profile (edge a) is aligned with the x coordinate axis, and the path lies in the y-z coordinate plane.

Figure 2-83: Rigid sweep—straight, perpendicular profile and path

In this case, the sweep operation creates a planar rectangular face. Two opposing boundary edges (b and d) of the created face are parallel to, and equivalent in length to, the path. The other two opposing boundary edges consist of the original profile edge (a) and its opposing duplicate edge (c).

Rigid Sweep—Profile Not Perpendicular to the Path

The profile edges for a rigid sweep operation can be located anywhere in the model domain as long as they are not parallel to the path. For example, Figure 2-84 shows a rigid sweep operation similar to that shown in Figure 2-83 but in which the profile consists of a curved, circular arc edge that lies in the z-x plane.

Figure 2-84: Rigid sweep—profile not perpendicular to the path

As in the previous example, the boundary edges of the created face consist of the original profile edge (a), its opposing duplicate (c), and two opposing edges (b and d) that are parallel to, and equivalent in length to, the path.

Rigid Sweep—Curved Path

The path used for a rigid sweep opera­tion can be straight or curved. To employ a straight path, you can define the path by means of either a straight edge or a vector. To employ a curved path, you must define the path by means of a curved edge.

Figure 2-85 shows a rigid sweep operation similar to that shown in Figure 2-84, above, but for which the path consists of a circular arc edge that lies in the y-z plane.

Figure 2-85: Rigid sweep—curved profile, curved path

As in the previous two examples, the created face is bounded by the original profile edge (a), its opposing duplicate (c), and two opposing edges (b and d) that possess the shape and orientation of the path. In this case, however, the path-shaped edges are curved.

Performing a Perpendicular Sweep

Perpendicular and rigid sweep opera­tions differ from each other with respect to the orientation that GAMBIT maintains for the profile as it is swept along the path. The basic difference can be stated as follows.

• For rigid sweep operations, GAMBIT maintains the orientation of the profile with respect to the global coordinate system.
• For perpendicular sweep operations, GAMBIT maintains the orienta­tion of the profile with respect to the path.

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

In this case, the profile edge is perpendicular to the path at its starting point; therefore, GAMBIT maintains the perpendicularity throughout the sweep operation.

The Effect of Path Position

The shape of the created face depends, in part, on the relative positions of the profile and path. Specifically, the effect can be summarized as follows.

• If the path edge starts at a point on the profile edge, GAMBIT retains the global position of the path when performing the sweep operation.
• If the path edge does not start at a point on the profile edge, GAMBIT (by default) moves the starting point of the path to the midpoint of the profile when performing the sweep operation. (NOTE: You can alter this default behavior by means of the GEOMETRY.VOLUME.SWEEP_PATH_ALIGNMENT default variable (see below).)

If the path edge starts at a point on the profile edge, GAMBIT retains the global position of the path when performing the sweep operation. As an example of this behavior, consider the perpendicular sweep operation illustrated in Figure 2-87. In this case, the profile consists of a straight edge (with endpoint vertices a and b) that lies in the x-y coordinate plane (see Figure 2-87(a)). The path is defined by a circular arc edge (representing one quarter of a full circle) that lies in the y-z plane and starts at a point on the profile edge (vertex a).(NOTE: The cubic volume shown in Figure 2-87 is included for spatial reference only.)

Figure 2-87: Perpendicular sweep—path starting on profile at vertex a

In this case, GAMBIT maintains the original orientation of the profile to the path, resulting in the face shown in Figure 2-87(b).

For sweep operations in which the path starts at a point on the profile, the relative positions of the profile and path strongly affect the shape of the created face. For example, Figure 2-88(a) shows a path and profile the shapes of which are identical to those shown in Figure 2-87, above, but for which the path starts on the profile at vertex b rather than vertex a. Again, GAMBIT maintains the orientation of the profile with respect to the path when sweeping the edge (see Figure 2-88(b)).

Figure 2-88: Perpendicular sweep—path starting on profile at vertex b

Path Not Connected to Profile

If the path edge does not start at a point on the profile edge, GAMBIT (by default) moves the sweep path to the midpoint of the profile edge when sweeping the face. (NOTE: GAMBIT does not actually move or duplicate the sweep path edge during the sweep operation. It merely reproduces the shape of the path edge and locates the sweep-path starting point at the midpoint of the edge.)

As an example of this behavior, consider the path and profile shown in Figure 2-89(a). The path and profile are identical in shape and orientation to those shown in the previous two examples; however, the path does not start on the profile. In this case, GAMBIT moves the path to the midpoint of the profile edge when performing the sweep operation, thereby creating the face shown in Figure 2-89(b). (NOTE: The path is shown in this figure for illustrative purposes only. As noted above, GAMBIT does not actually move or duplicate the path edge when creating the face.)

Figure 2-89: Perpendicular sweep—path not starting on profile

The Effect of Sweep Default Variables

The shape of any face created by means of the edge-sweep operation is determined, in part, by the values associated with two GAMBIT default variables:

• GEOMETRY.VOLUME.SWEEP_PATH_ALIGNMENT
• GEOMETRY.VOLUME.SWEEP_METHOD

Sweep Path Alignment Default

As noted above, if the path does not start at a point on the profile, GAMBIT (by default) moves the path to the midpoint of the edge when performing the sweep operation. You can change this default behavior by modifying the value of the SWEEP_PATH_ALIGNMENT default variable, the allowable values of which are 0 and 1. The default-variable values affect the perpendicular edge-sweep operation for separated path/profile configura­tions in the following ways.

• 0—Moves the path to the nearest point on the profile
• 1—(Default) Moves the sweep path to the midpoint of the profile (as shown in Figure 2-89, above)

Sweep Method Default

The SWEEP_METHOD default variable allows you to control the shape of the created face at the end of the sweep path. Specifically, when you set the default variable equal to 2, GAMBIT constructs the face such that one end represents the truncation of the sweep operation by a plane perpendicular to the path at its endpoint.

As an example of the effect of the SWEEP_METHOD default variable, consider the two faces shown in Figure 2-90. Both faces are created by sweeping the path/profile combination indicated in Figure 2-90(a), where the path and profile lie in the x-y and y-z planes, respectively. In both cases, GAMBIT (by default) moves the path to the midpoint of the profile edge before performing the sweep operation. (NOTE: The sweep paths shown in Figure 2-90 are included for illustrative purposes only; GAMBIT does not actually move or duplicate the specified path when sweeping the edge.) In this case, the operations differ only with respect to the value of the SWEEP_METHOD default variable as specified at the time of their creation.

Figure 2-90: Effect of SWEEP_METHOD default variable

When the SWEEP_METHOD default variable is specified as 0 or 1, GAMBIT maintains the original profile orientation throughout the sweep operation and creates the face shown in Figure 2-90(a). When the SWEEP_METHOD default variable is specified as 2, GAMBIT creates a face that represents the truncation of the sweep operation by a plane perpendicular to the path at its endpoint Figure 2-90(b).

Figure 2-91 illustrates the truncation associated with the value of 2 for the SWEEP_METHOD default variable. Specifically, the figure shows the general orientation of a theoretical plane that truncates the sweep operation to produce the face shown in Figure 2-90(b), above. (NOTE: For comparison, Figure 2-91 includes an overlay of the face created for SWEEP_METHOD default variable values of 0 or 1.)

Figure 2-91: General truncation operation

The SWEEP_PATH_ALIGNMENT and SWEEP_METHOD default variables interact for edge-sweep operations in that the position of the path affects the location and orientation of the truncation plane. For example, if you specify the profile and path indicated in Figure 2-90(a), above, but do not allow the sweep path to move (SWEEP_PATH_ALIGNMENT = 0), GAMBIT locates the truncation plane as shown in Figure 2-92(a) and creates the face shown in Figure 2-92(b).

Figure 2-92: Truncation for non-moved path

Perpendicular Sweep Options

Perpendicular sweep operations can be modified such that the surface of the created face deviates from the sweep path by a specified angle. GAMBIT provides two such options:

• Draft
• Twist

Draft Option

When you specify the Draft option for a perpendicular sweep operation, you can also specify an angle by which the swept surface of the created face deviates from the path. The effect of the draft angle depends strongly on the shapes and orientations of the profile and path relative to each other and is difficult to generalize. Figure 2-93 illustrates the effect of the draft angle for two simple path/profile combinations similar to those shown in Figure 2-83 and Figure 2-86, above.

Figure 2-93: Effect of draft angle on swept face

In Figure 2-93(a), the path and profile consist, respectively, of a circular arc edge aligned with the y-z plane and a straight edge aligned with the y coordinate axis. In this case, the draft angle determines the angle by which the created face deviates from the y-z plane. In Figure 2-93(b), the profile edge is aligned with the x coordinate axis. In this case, the draft angle specification affects the size and shape of the arc represented by the profile of the created face.

NOTE: The projections of the three faces shown in Figure 2-93(a) onto the y-z coordinate plane are identical to each other.

Figure 2-94 shows the effect of draft angle for a path/profile configuration consisting of a circular arc edge profile aligned with the z-x plane and a path defined by a straight edge aligned with the y axis. In this case, the draft angle specification determines the shape of the partial conical cylinder face created by the sweep operation.

Figure 2-94: Effect of draft angle circular arc edge profile

Twist Option

When you specify the Twist option for a perpendicular sweep operation, GAMBIT revolves the profile through a specified angle as it sweeps the profile along the length of the path. The profile and path can be either straight or curved, but curved paths sometimes require an additional restriction with respect to the orientation between the profile and path (see below).

Using a Straight Path

Figure 2-95 illustrates the effect of the perpendicular twist sweep operation for a configuration that involves a straight sweep path. In this case, the profile is defined by a straight edge aligned with the x axis, the path is defined by a straight edge that lies in the y-z plane, and the twist angle is 360°. (NOTE: In this example, the path has not been moved to the midpoint of the profile edge.)

Figure 2-95: Perpendicular Twist sweep operation—straight path

Using a Curved Path

In certain cases, GAMBIT allows you to perform twist sweep operations using a curved path. Figure 2-96 illustrates the effect of the twist sweep operation for a configuration that involves a curved path. In this case, the path is defined by a circular arc edge aligned with the y-z plane, the profile consists of a straight edge aligned with the x axis, and the twist angle is specified as 360°.

Figure 2-96: Perpendicular Twist sweep operation—curved path

Effect of Sweep Path Alignment Default

As noted above, the shape of any face created by means of a perpendicular sweep operation is determined in part by the alignment of the sweep path to the profile-which, in turn, is determined by the value of the SWEEP_PATH_ALIGNMENT default variable. Specifically, the default variable value affects the perpendicular edge-sweep operation for separated path/profile configura­tions in the following ways.

• 0—Moves the path to the nearest point on the profile
• 1—(Default) Moves the sweep path to the midpoint of the profile (as shown in Figure 2-96, above)

Using the Sweep Edges Form

To open the Sweep Edges form (see below), click the Sweep Edges command button on the Geometry/Face subpad.

The Sweep Edges form includes the following specifications.

Edges	specifies one or more edges that constitute the sweep profile. (NOTE: GAMBIT creates a new face for each specified edge.)
Path:
Edge	specifies that the path is described by the length, shape, orientation, and sense of an existing edge.
Edge	specifies the edge to be used as the sweep path.
Reverse	reverses the direction of the path relative to the sense of the specified edge.
Vector	specifies that the path is described by a vector. When you select the Vector option, GAMBIT displays a pushbutton titled Define. When you click the Define pushbutton, GAMBIT opens the Vector Definition form, which allows you to specify parameters that define the path vector. For instructions on using the Vector Definition form, see "Using the Vector Definition Form" in Section 2.1.4.
With mesh	(Meshed profile edges only) projects the profile edge mesh when sweeping the edge, thereby creating a meshed face.
Type:
Rigid	specifies a rigid sweep operation.
Perpendicular	specifies a perpendicular sweep operation
Option:
Draft	specifies the draft perpendicular sweep method.
Twist	specifies the twist perpendicular sweep method.
Angle	specifies the draft angle or twist angle.
Label	specifies a label for the new face. (See Section 2.1.1.)

Revolve Edges

The Revolve Edges operation (face create revolve command) creates faces by revolving existing edges about a specified axis. The operation requires specification of the following parameters:

• One or more profile Edges to be revolved
• The Axis of revolution
• The Angle through which the edges are revolved
• With mesh option (meshed edges only)

Figure 2-97: Revolve Edges operation

Specifying Profile Edges

To create faces by means of the Revolve Edges form, you must spec­ify one or more "profile" edges to be revolved about the axis of rotation. GAMBIT creates a separate face corresponding to each profile edge. The speci­fied edges can be straight or curved, real or non-real, and they do not have to be coplanar with the axis of rotation.

NOTE (1): If you specify a profile edge that intersects the axis of revolution, GAMBIT does not execute the Revolve Edges operation, because doing so would create self-intersecting (invalid) geometry.

NOTE (2): If you revolve a non-real edge to create a face, GAMBIT first creates a real copy of the non-real edge, then revolves the real copy to create the face.

Specifying the Axis and Angle of Rotation

To specify the axis of revolution, 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 revolution for the Revolve Edges operation are identical to those described in "Rotating an Entity" in Section 2.1.4.

Specifying the With mesh Option

When you revolve a meshed profile edge, GAMBIT allows you to project the edge mesh onto the created face, thereby creating a meshed face. To project the mesh of a profile edge when revolving the edge, select the With mesh option on the Revolve Edges form.

As an example of the effect of the With mesh option, consider the configura­tion shown in Figure 2-98(a). If you revolve the meshed profile edge as shown and select the With mesh option, GAMBIT creates the meshed face shown in Figure 2-98(b).

Figure 2-98: Revolve Edges operation—With mesh option

In this case, the mesh on the projected edge (d) of the created face is identical to that of the pro­file edge (a). GAMBIT uses the current default face-meshing parameters to compute the mesh interval spacing along the edges of the face that are created by revolv­ing the edge endpoint vertices (edges b and c).

If you specify a meshed profile edge one endpoint vertex of which is coinci­dent with the axis of revolution (and select the With mesh option), GAMBIT creates a three-sided face that includes triangular mesh elements in the region adjacent to the coincident endpoint (see Figure 2-99).

Figure 2-99: Revolve Edges operation—coincident profile endpoint

Using the Revolve Edges Form

To open the Revolve Edges form (see below), click the Revolve Edges command button on the Geometry/Face subpad.

The Revolve Edges form includes the following specifications.

Edges	specifies one or more profile edges to be revolved.
Angle	specifies the angle through which the profile edges are revolved.
Axis:	includes two components: A Define command button that allows you to define the axis around which the edge is to be revolved The coordinates of the start and end points for a vector defining the rotational axis
With mesh	(Meshed profile edges only) projects the edge mesh when revolving the edge, thereby creating a meshed face.
Label	specifies a label for one of the new faces (see Section 2.1.1).

2.4.2 Create Face

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

Symbol	Operation	Description
	Create Real Rectangular Face	Creates a real face in the shape of a rectangle
	Create Real Circular Face	Creates a real face in the shape of a circle
	Create Real Elliptical Face	Creates a real face in the shape of an ellipse

Create Real Rectangular Face

The Create Real Rectangular Face operation (face create rectangle command) creates a real, planar face in the shape of a rectangle aligned with one of the coordinate planes of a specified coordinate system. The operation requires specification of the following input parameters:

• Width
• Height
• Coordinate Sys.
• Direction

Using the Create Real Rectangular Face Form

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

The Create Real Rectangular Face form includes the following specifications.

Width	specifies the width of the rectangular face. (NOTE: For faces created in the x-y, y-z, and z-x planes, the Width dimension is aligned with x, y, and z directions, respectively.)
Height	specifies the height of the rectangular face. (NOTE: For faces created in the x-y, y-z, and z-x planes, the Height dimension is aligned with y, z, and x directions, respectively.)
Coordinate Sys.	specifies the reference coordinate system for the face creation operation (default = currently active coordinate system).
Direction
+X +Y +X -Y -X +Y -X -Y XY Centered +Y +Z +Y -Z -Y +Z -Y -Z YZ Centered +Z +X +Z -X -Z +X -Z -X ZX Centered	specifies the face orientation plane relative to the reference coordinate system and the region of the orientation plane in which the face is created.
Label	specifies a label for the new face. (See Section 2.1.1.)

Create Real Circular Face

The Create Real Circular Face operation (face create circle command) creates a real, planar face in the shape of a circle aligned with one of the coordinate planes of a specified coordinate system. The operation requires specification of the following input para­meters:

• Radius
• Coordinate Sys.
• Plane

Using the Create Real Circular Face Form

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

The Create Real Circular Face form includes the following specifications.

Radius	specifies the radius of the circular face.
Coordinate Sys.	specifies the reference coordinate system for the face creation operation (default = currently active coordinate system).
Plane
XY YZ ZX	specifies the face orientation plane relative to the reference coordinate system.
Label	specifies a label for the new face. (See Section 2.1.1.)

Create Real Elliptical Face

The Create Real Elliptical Face operation (face create ellipse command) creates a real, planar face in the shape of a circle aligned with one of the coordinate planes of a specified coordinate system. The operation requires specification of the following input para­meters:

• Radius 1
• Radius 2
• Coordinate Sys.
• Plane

The Coordinate Sys. parameter specifies the reference coordinate system for the face creation operation. The Plane parameter specifies the orientation of the face relative to the reference coordinate system. (NOTE: The created face is always centered at the origin of the reference coordinate system.)

Using the Create Real Elliptical Face Form

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

The Create Real Elliptical Face form includes the following specifications.

Radius 1	specifies the length of the major or minor axis of the ellipse.
Radius 2	specifies the length of the minor or major axis of the ellipse.
Coordinate Sys.	specifies the reference coordinate system for the face creation operation (default = currently active coordinate system).
Plane
XY YZ ZX	specifies the orientation plane for the face relative to the reference coordinate system.
Label	specifies a label for the new face. (See Section 2.1.1.)

2.4.3 Boolean Operations

The Boolean Operations command button allows you to perform the following operations.

Symbol	Operation	Description
	Unite Faces	Unites two or more faces into a single face
	Subtract Real Faces	Subtracts the intersecting region(s) between two or more real faces
	Intersect Real Faces	Creates a face representing the intersection of two or more real faces

Overview

Each of the commands listed above allows you to perform a Boolean operation involving two or more faces. The specified faces do not have to be planar, but they must be coincident in the intersecting region between them. (NOTE: For the lone exception to this rule, see "Unite Faces," below.)

Figure 2-100 illustrates the general results of each of the Boolean face operations on a coplanar circle and square.

Figure 2-100: Boolean face operations

NOTE (1): Geometry that fails GAMBIT geometry checks ("bad" geometry) can sometimes cause Boolean operations to fail. By default, if a Boolean operation fails due to bad geometry, GAMBIT aborts the operation. It is possible, however, to specify that instead of aborting the procedure, GAMBIT automatically attempts to smooth and/or heal the geometry and retries the Boolean operation. This specification is made by means of the GEOMETRY.VOLUME.BOOLEAN_METHOD default variable. Specifically, if you set the GEOMETRY.VOLUME.BOOLEAN_METHOD default variable to 2, GAMBIT performs the automatic smooth/heal-retry operation.

NOTE (2): If you set the GEOMETRY.VOLUME.BOOLEAN_METHOD default variable to 3, GAMBIT attempts to preserve existing vertex and edge labels when performing a face Boolean operation.

Retaining the Specified Faces

Each Boolean operation form includes at least one Retain option. When you perform a Boolean operation involving a set of specified faces, GAMBIT replaces the specified faces with a single face that constitutes the result of the operation. If you select the Retain option, GAMBIT retains the original faces when it performs the Boolean operation.

Unite Faces

The Unite Faces operation (face unite command) unites two or more faces to create a single face. GAMBIT provides two types of face-unite operations:

• Real
• Virtual

Performing a Real Face-Unite Operation

As noted above, the Real option on the Unite Faces form allows you to unite real faces that overlap each other to create a single real face. When you unite real, overlapping faces using the Real option, GAMBIT creates one real face that represents the union of the overlapping faces. If you specify a set of faces to be united that includes two or more subsets of faces that overlap each other but do not overlap the faces of any other subset, GAMBIT creates a separate real face for each subset.

Specifying the Tolerance Value

GAMBIT allows you to specify the maximum allowable distance (tolerance) between faces to be united. The operation includes two tolerance options:

• Auto
• Manual

Performing a Virtual Face-Unite Operation

The Virtual option on the Unite Faces form allows you to unite real or virtual faces to create a virtual face. The faces to be united can either be separated by a gap or overlap each other.

Uniting Faces Separated by a Gap

As an example of using the Virtual option to unite faces separated by a gap, consider the two square, planar faces shown in Figure 2-101(a). The two faces are coplanar but are separated by a small gap and are slightly offset from each other. If you unite the two faces using the Virtual option on the Unite Faces form, GAMBIT creates the virtual face (v_face.3) shown in Figure 2-101(b). (NOTE: The shape of the created face depends, in part, on the specification of the critical points that define its outer boundary (see "Specifying Critical Points," below).)

Figure 2-101: Union of two square, planar faces separated by a gap

Specifying the Tolerance Value

When you perform a face-unite operation such as that shown in Figure 2-101, you must specify a Tolerance value. The Tolerance value must be greater than the width of the smallest gap between the face boundary edges. If the gap between the adjacent boundary edges of the faces to be united is greater than the specified Tolerance, GAMBIT does not perform the face-unite operation.

NOTE: GAMBIT allows you to unite faces that are separated from each other by very large gaps, but such faces can create problems during meshing operations. As an example of the effect of such gaps on meshing, consider the configuration shown in Figure 2-102(a). The configuration consists of two planar faces, one square face and one circular face, separated by a large vertical gap. Figure 2-102: Effect of large gaps on meshing You can use the Virtual option on the Unite Faces form to create the virtual face (v_face.3) shown in Figure 2-102(b), but if you mesh the face using a simple pave-meshing scheme, GAMBIT creates large, distorted mesh elements in the region that represents the original gap. As a general rule, you should avoid using the GAMBIT virtual face-unite operation to unite faces that are separated by large gaps. In addition, when meshing a face created by uniting two faces separated by a gap, you should specify a mesh interval length greater than the width of the original gap. Failure to do so can result in very poor mesh quality and, in some cases, complete malfunction of the face-mesh operation.

Uniting Overlapping Faces

In addition to uniting faces separated by gaps, the Virtual option on the Unite Faces form allows you to unite faces that overlap. The virtual face-unite operation for overlapping faces is similar to the real face-unite operation (see "Performing a Real Face-Unite Operation," above) but differs in two respects:

• The virtual face-unite operation allows you to unite overlapping real or virtual faces.
• You must define the shape of the created face by specifying critical points.

Specifying Critical Points

When you perform a virtual face-unite operation, you must specify a set of critical points that are used to define the outer boundary of the created face. The critical points lie on the boundary edges of the faces to be united. (NOTE: To specify a critical point, click (highlight) the Boundary pick-list field on the Unite Faces form and select (in the graphics window) the face-boundary edge on which the critical point is to be located. GAMBIT allows you to drag the critical point to any location on the selected boundary edge.)

If you specify critical points at vertices that lie on the boundary edges of the faces to be united and at points of intersection between the boundary edges, GAMBIT creates a new face the shape of which represents the complete union of the original faces. If you specify critical points that do not lie on face-boundary vertices and points of intersection, GAMBIT creates a face that does not necessarily represent the complete union of the original faces.

As an example of the effect of critical-point locations on the shape of the created face, consider the two overlapping, coplanar faces shown in Figure 2-103.

Figure 2-103: Square and circular coplanar faces

If you perform a virtual face-unite operation on these overlapping faces and specify the six critical points (a, b, c, d, e, and f) shown in Figure 2-104(a), GAMBIT creates the virtual face shown in Figure 2-104(b).

Figure 2-104: Effect of critical points—vertices and points of intersection

In this case, each critical point is located either at a vertex that lies on the boundary edge of one of the faces to be united (a, b, c, and e) or at a point of intersection between the boundary edges of the faces (d and f). As a result, the created face possesses a shape representing the complete union of the original faces.

As noted above, if you specify critical points that do not lie either at boundary-edge vertices or at points of intersection, GAMBIT creates a face that does not represent the complete union of the original faces. For example, if you specify the critical points shown in Figure 2-105(a), GAMBIT creates the face shown in Figure 2-105(b).

Figure 2-105: Effect of critical points—non-vertex and intersection locations

To create the face shown in Figure 2-105(b), GAMBIT constructs edges between the specified critical points. If two or more consecutive critical points lie on a given edge, GAMBIT retains the shape of the edge between the points. For example, GAMBIT retains the shape of the arc edges between critical points e and f and between points g, h, and i. GAMBIT also retains the shape of the straight edge segment between points j and a. For all other edge segments, GAMBIT constructs straight edges between consecutive critical points.

When you perform a virtual face-unite operation, you must use caution when determining the sequence in which the critical points are specified. Due to the manner in which GAMBIT constructs faces for the virtual face-unite operation, it is possible to create a face that constitutes invalid geometry. As an example of the effect of specification sequence, consider the virtual face-unite operation represented by Figure 2-106.

Figure 2-106: Virtual face-unite operation—effect of critical-point sequence

If you specify the critical points as shown in Figure 2-106(a), GAMBIT creates the face shown in Figure 2-106(b)—which is self-intersecting and, therefore, represents invalid geometry.

Using the Unite Faces Form

To open the Unite Faces form (see below), click the Unite Facescommand button on the Geometry/Face subpad.

The Unite Faces form includes the following specifications.

Faces	specifies the set of faces to be united.
Retain	specifies that all original specified faces are retained.
Type	specifies the type of face-unite operation to be performed. The two available face-unite operations are: Real Virtual

The options and specifications available on the Unite Faces form vary accord­ing to whether you select the Real or Virtual face-unite option as follows.

Real Option

If you select the Real option on the Unite Faces form, GAMBIT displays the form as shown above. To perform the face-unite operation, simply specify the Faces to be united, select or unselect the Retain option, and click Apply. (NOTE: The Real option applies only when all faces to be united are real.)

Tolerance

specifies the the maximum allowable distance between the faces to be united. Auto—Specifies that GAMBIT computes the tolerance value Manual—Allows you to specify a tolerance value (default = 10-6)

Virtual Option

If you select the Virtual option on the Unite Faces form, GAMBIT displays the following specifications on the form.

Boundary	specifies the face(s) the boundary edges of which host the critical points that define the shape of the new face (see "Specifying Critical Points," above).
Tolerance	specifies the maximum allowable gap between adjacent faces to be united (default = 10-5).
U Value	specifies the u-value location of the current critical point with respect to the current Boundary face.
V Value	specifies the v-value location of the current critical point with respect to the current Boundary face.
Coordinate Sys.	specifies the coordinate system with respect to which the current critical-point coordinates are specified.
Type
Cartesian Cylindrical Spherical	specifies the type of coordinate parameters to be used in defining the current critical point.
Global | Local	specifies the location of the current critical point with respect to either the Global or Local system.

Subtract Real Faces

The Subtract Real Faces operation (face subtract command) performs a Boolean sub­trac­tion involving two or more real faces. The command requires two specifi­cations:

• Target face
• Tool face set

The Effect of Intersecting Faces

Figure 2-107: Square planar face and cylindrical face

The results of the subtraction operation for this configuration depend on which face is specified as the target face. Figure 2-108(a) and (b) show the results of the subtraction operation when either the square planar face or cylindrical face, respectively, is specified as the target face.

Figure 2-108: Subtraction results for square planar and cylindrical target faces

Figure 2-109 shows the effect of the subtraction operation for two partially intersecting square planar faces. In this case, the subtraction operation creates a dangling edge on the target face.

Figure 2-109: Effect of partially intersecting faces

Specifying the Tolerance Value

GAMBIT allows you to specify the maximum allowable distance (tolerance) between faces to be subtracted. The operation includes two tolerance options:

• Auto
• Manual

Using the Subtract Real Faces Form

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

The Subtract Real Faces form includes the following specifications.

Face	specifies the target face from which overlapping regions are to be subtracted.
Retain	specifies that the target face is retained.
Subtract
Faces	specifies one or more faces that constitute the subtraction tool face set.
Retain	specifies that all subtraction-tool faces are retained.
Tolerance	specifies the the maximum allowable distance between the faces to be subtracted. Auto—Specifies that GAMBIT computes the tolerance value Manual—Allows you to specify a tolerance value (default = 10-6)

Intersect Real Faces

The Intersect Real Faces operation (face intersect command) performs a Boolean intersection of two or more real faces.

Specifying the Tolerance Value

GAMBIT allows you to specify the maximum allowable distance (tolerance) between faces to be intersected. The operation includes two tolerance options:

• Auto
• Manual

Using the Intersect Real Faces Form

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

The Intersect Real Faces form includes the following specifications.

Faces	specifies two or more faces for the intersection operation.
Retain	specifies that all original specified faces are retained.
Tolerance	specifies the the maximum allowable distance between the faces to be subtracted. Auto—Specifies that GAMBIT computes the tolerance value Manual—Allows you to specify a tolerance value (default = 10-6)

2.4.4 Connect/Disconnect Faces

The Connect/Disconnect Faces command button allows you to perform two operations.

Symbol	Operation	Description
	Connect Faces	Connects coincident real faces or creates virtual faces that represent the connection of one or more existing faces
	Disconnect About Real Face	Disconnects volumes that share a common real face

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

NOTE: The Specify Color Mode command button on the Graphics/Windows Control toolpad allows you to display model colors based on entity connectivity rather than topology. For a description of the use of the Specify Color Mode command button, see the GAMBIT User's Guide, Section 3.4.2.

Connect Faces

The Connect Faces operation (face connect command) connects sets of two or more faces. When you connect a set of faces, GAMBIT replaces the faces in the set with a single face.

NOTE (1): If you connect two or more meshed faces, and the meshes on each face are topologically identical to each other, GAMBIT preserves the meshes when connecting the faces.

NOTE (2): If any of the faces to be connected are mesh-linked to other faces in the model, GAMBIT preserves the mesh link(s) and assigns it/them to the single face that results from the connect operation.

The operation requires specification of the following parameters:

• Two or more faces to be connected
• The connection type

Specifying the Faces to Be Connected

The faces to be connected can be real or virtual, but they are subject to certain restrictions imposed by the connection type (see below).

Specifying the Connection Type

There are four types of face connection operations:

• Real
• Virtual (Forced)
• Virtual (Tolerance)
• Real and Virtual (Tolerance)

Specifying a Real Connection

The Real option allows you to connect coincident real faces—that is, two or more real faces the edges of which are coincident. When you connect real faces and specify the Real option, GAMBIT deletes all but one of the specified faces and connects the remaining real face to any and all volumes of which the deleted faces were a part.

Specifying a Virtual (Forced) Connection

The Virtual (Forced) option allows you to connect real and/or virtual faces, regardless of their proximity to each other. When you connect faces and specify the Virtual (Forced) option, GAMBIT replaces the specified faces with a virtual face. If a specified face constitutes part of a volume, GAMBIT overlays the volume with a virtual volume and forms the virtual volume according to the shape and position of the new virtual face.

Specifying a Virtual (Tolerance) Connection

The Virtual (Tolerance) option allows you connect real and/or virtual faces the edges of which are near to each other to within a specified tol­erance value. GAMBIT provides two ways to express the tol­erance value:

• Tolerance
• Shortest Edge%

Specifying the T-Junctions Option

If you select the Virtual (Tolerance) option, you can also select the T-Junctions option. The T-Junctions option specifies whether or not GAMBIT is allowed to split edges and form T-junctions when connecting the face boundary edges. Some face-connect operations will not succeed unless the T-Junctions option is selected.

As an example of the effect of the T-Junctions option on a face-connect opera­tion, consider the two circular, parallel, planar faces (A and B) shown in Figure 2-110(a). Each face possesses a circular boundary split into three arc edges that are connected to each other at three vertices (a-b-c for face A and d-e-f for face B). Only two of the six vertices (a and d) form a companion pair—that is, are located directly opposite each other.

Figure 2-110: Effect of T-Junctions option on two circular faces

If you attempt to connect faces A and B without specifying the T-Junctions option, GAMBIT fails to perform the connect operation due to a lack of correspondence between the vertex locations for the two face boundary edges. If you specify the T-Junctions option when attempting to connect the faces, GAMBIT creates a new face (C) the edges of which are split at locations (b', c', e', and f') that correspond to the vertices on the boundary edges of the original faces (see Figure 2-110(b)).

Figure 2-111 illustrates the effect of the T-Junctions option for a geometric con­figuration consisting of two rectangular brick volumes the abutting faces (A and B) of which differ in orientation in the y-z plane (see Figure 2-111(a)).

Figure 2-111: Effect of T-Junctions option on abutting rectangular bricks

If you attempt to connect faces A and B without specifying the T-Junctions option, GAMBIT fails to perform the connect operation due to a lack of correspondence between the geometries of the two faces. If you specify the T-Junctions option when attempting to connect the faces, GAMBIT splits both faces bidirectionally and connects the volumes by means of a new face (C) (see Figure 2-111(b)).

Specifying a Real and Virtual (Tolerance) Connection

When you specify the Real and Virtual (Tolerance) option, GAMBIT performs the following two operations in sequence:

1. Real connect operations for faces that are coincident to within the global tolerance value
2. Virtual (Tolerance) connect operations for unconnected, specified faces that are near to each other to within the user-specified tolerance

Using the Connect Faces Form

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

The Connect Faces form includes the following specifications.

Faces	specifies the faces to be connected.
All Pick	All specifies all faces in the model. Pick specifies faces selected by means of the Faces list box.
Real	specifies that the face that results from the connection of faces is a real face. (NOTE: To obtain a real face from the connection of two or more real faces, the specified faces must be coincident.)
Virtual (Forced)	specifies the following characteristics for the face that results from connection of faces: The face is a virtual face The face is created irrespective of the distance between the specified faces
Virtual (Tolerance)	specifies the following characteristics for the face that results from connection of faces: The face is a virtual face The specified faces are connected only if the distance between them is less than a specified tolerance (see below)
Real and Virtual (Tolerance)	specifies the following sequence of operations: Real connect operations where possible Virtual (Tolerance) connect operations for the remaining specified, unconnected faces
Tolerance	specifies the maximum allowable distance (absolute units) between faces to be connected.
Shortest Edge %	specifies the maximum allowable distance (percent of shortest edge in the model) between faces to be connected.
Highlight shortest edge	highlights the shortest edge that exists in the current model.
T-Junctions	allows the formation of T-junctions when creating a virtual face to replace the original, unconnected faces.

Disconnect About Real Face

The Disconnect About Real Face operation (face disconnect command) disconnects sets of faces and/or volumes that share a common real face.

When you disconnect faces, GAMBIT creates a new face for all but one of the entities to which the specified face is connected. For example, if the specified face is shared by three volumes, GAMBIT creates two new faces that are coincident with the specified face and connects them to two of the three volumes. The original face is connected to the remaining volume.

Specifying the Edge and Vertex Options

GAMBIT provides the following three options with respect to the treatment of endpoint vertices for the disconnected edges:

• Face + Edges/Vertices
• Face Only
• Face + Selected Edges

Using the Disconnect About Real Face Form

To open the Disconnect About Real Face form (see below), click the Disconnect command button on the Geometry/Face subpad.

The Disconnect About Real Face form includes the following specifications.

Face	specifies the face to be disconnected.
Face + Edges/ Vertices	specifies that all edges and vertices that are components of the face are to be disconnected.
Face Only	specifies that only the face is to be disconnected and that any new faces created in the disconnection process share the edges and vertices of the specified face.
Face + Selected Edges	specifies that one or more user-specified edges are to be disconnected along with the face. Any edges not specified are shared between the specified face and any new faces created in the disconnection process.
Edge	specifies the edges to be disconnected in conjunction with the specified face.

2.4.5 Modify Face Color/Label

The Modify Face Color/Label command button allows you to perform two operations.

Symbol	Operation	Description
	Modify Face Color	Changes the color of the geometry and/or mesh associated with one or more faces as displayed in the graphics window
	Modify Face Label	Changes a face label

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

Modify Face Color

The Modify Face Color operation (face modify command) changes the displayed color of the geometry and/or mesh and/or shading associated with one or more faces.

Using the Modify Face Color Form

To open the Modify Face Color form (see below), click the Modify Color command button on the Geometry/Face subpad.

The Modify Face Color form includes the following specifications.

Faces	specifies one or more faces for which the color is to be changed.
Color:
Geometry	specifies modifying the color of the face(s).
Mesh	specifies modifying the color of the mesh associated with the face(s).
Shade	specifies modifying the color of the shading associated with the face(s).

For specific instructions on setting colors, see "Using the Set Color Form" in Section 2.2.4.

Modify Face Label

The Modify Face Label operation (face modify command) changes the label associated with any face.

Using the Modify Face Label Form

To open the Modify Face Label form (see below), click the Modify Label command button on the Geometry/Face subpad.

The Modify Face Label form includes the following specifications.

Face	specifies the face to be modified.
Label	specifies a new label for the face. (See Section 2.1.1.)

2.4.6 Move/Copy/Align Faces

The Move/Copy/Align Faces command button allows you to perform two operations.

Symbol	Description	Operation
	Move/Copy Faces	Moves and copies faces
	Align Faces	Aligns faces and connected geometry with existing topological entities

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

Move/Copy Faces

The Move/Copy Faces operation (face copy, face move, face cmove, face reflect, face creflect, face scale, and face cscale com­mands) repositions and/or reorients one or more faces or creates copies of faces. For a general description of the procedures and specifications required to move and/or copy entities, see "Moving an Entity" and "Copying an Entity," respectively, in Section 2.1.4.

Using the Move/Copy Faces Form

To open the Move/Copy Faces form (see below), click the Move/Copy command button on the Geometry/Face subpad.

For a complete description of the specifications available on the Move/Copy Faces form, see "Using Move/Copy Forms" in Section 2.1.4.

Align Faces

The Align Faces operation (face align command) repositions a set of one or more faces with respect to a set of translation, rotation, and plane-alignment vertices. (For a general description of the procedure and specifications required to align an entity, see "Aligning an Entity," in Section 2.1.4, above.)

Using the Align Faces Form

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

For a complete description of the specifications available on the Align Faces form, see "Using Align Forms" in Section 2.1.4.

2.4.7 Split/Merge/Collapse/Simplify Faces

The Split/Merge/Collapse/Simplify Faces command button allows you to perform the following operations.

Symbol	Operation	Description
	Split Face	Splits an existing face into a set of one or more real or virtual faces
	Merge Faces	Merges two or more existing faces into a real or virtual face
	Collapse Face (Virtual)	Collapses two or more real or virtual faces into a virtual edge or vertex.
	Simplify Faces	Simplifies face geometry by removing dangling edges

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

Split Face

The Split Face operation (face split command) splits an existing face into one or more real or virtual faces. The operation requires specification of the fol­lowing parameters:

• Target face
• Split type

NOTE (1): Geometry that fails GAMBIT geometry checks ("bad" geometry) can sometimes cause split operations to fail. By default, if a split operation fails due to bad geometry, GAMBIT aborts the operation. For split operations that involve only two entities, however, it is possible to specify that instead of aborting the procedure, GAMBIT auto­matically attempts to smooth and/or heal the geometry and retries the split operation. This specification is made by means of the GEOMETRY.VOLUME.BOOLEAN_METHOD default variable. Specifically, if you set the GEOMETRY.VOLUME.BOOLEAN_METHOD default variable to 2, GAMBIT performs the automatic smooth/heal-retry operation.

NOTE (2): If you set the GEOMETRY.VOLUME.BOOLEAN_METHOD default variable to 3, GAMBIT attempts to preserve existing vertex and edge labels when performing a face split operation.

Specifying the Target Face

NOTE: If you split a face that serves as a source or attachment entity for a size function, and one of the faces resulting from the split operation retains the label of the original face, GAMBIT preserves the size function and assigns it to the face that retains the original label.

Specifying the Split Type

GAMBIT provides the following types of face-split operations:

• Faces
• Face (Virtual)
• Edges
• Vertices
• Locations

Performing a Faces Split-type Operation

The Faces split operation allows you to split a real or virtual target face using a set of one or more real or virtual split-tool faces. (NOTE: The Faces split operation cannot be used to split a target face that is mesh-linked to other faces in the model.)

Effects of Intersection and Overlap

The results of the split operation depend, in part, on whether faces in the split-tool face set intersect or partially overlap the target face. Specifically:

• If a split-tool face intersects the target face, GAMBIT either splits the target face into two or more faces or creates a dangling edge on the target face.
• If a split-tool face partially overlaps the target face, GAMBIT splits the target face along the boundary edges of the split-tool face.

For geometric configurations in which the target and split-tool faces intersect but do not overlap, the general rules governing the results of the split opera­tion are as follows.

• If a split-tool face fully intersects the face to be split, GAMBIT fully splits the target face (see Figure 2-112(a)).
• If the split-tool face partially intersects the face to be split, GAMBIT creates one or more dangling edges on the target face (see Figure 2-112(b)).

Figure 2-112: Intersecting target and split-tool faces

Overlapping Target and Split-Tool Faces

If a split-tool face partially overlaps the target face, GAMBIT splits the target face along the boundaries of the split-tool face. As an example of this behavior, consider the set of faces shown in Figure 2-113(a). In this case, the target face is a square, planar face, and the split-tool face set consists of one square face and one circular face, both of which lie in the same plane as the target face. If you specify this set of faces for a Faces split operation, GAMBIT splits the target face to create the configuration shown in Figure 2-113(b).

Figure 2-113: Overlapping target and split-tool faces

The behavior described above applies to both planar and non-planar faces. For example, if you specify the curved faces shown in Figure 2-114(a) for a Faces split operation, GAMBIT splits the target face as shown in Figure 2-114(b).

Figure 2-114: Overlapping target and split-tool faces—non-planar surfaces

Specifying the Tolerance Value

GAMBIT allows you to specify the maximum allowable distance (tolerance) between the target face and split-tool face(s) for any Faces split operation. The operation includes two tolerance options:

• Auto
• Manual

Specifying the Resulting Geometry Options

The Faces split operation includes three options that determine the geometry condi­tions resulting from the operation:

• Retain—Specifies that the split-tool face(s) are retained upon completion of the split operation
• Bidirectional
—Specifies that the tool and target faces split each other during the split operation
• Connected
—Specifies that the faces resulting from the split operation are connected along their common edge(s)

Performing a Face (Virtual) Split-type Operation

NOTE: Although the Face (Virtual) option always appears on the Split with option button, the Face (Virtual) split functionality is disabled by default. To enable the Face (Virtual) functionality, set the GEOMETRY.FACE.VIRTUAL_FACE_FACE_SPLIT default variable to 1.

The Face (Virtual) split operation allows you to split a real or non-real target face using a virtual split-tool face. (NOTE: The Face (Virtual) split operation cannot be used to split a target face that is mesh-linked to other faces in the model.)

Specifying the Tolerance Value

GAMBIT allows you to specify the maximum allowable distance (tolerance) between the target face and split-tool face(s) for any Face (Virtual) split operation. The operation includes two tolerance options:

• Auto
• Manual

Specifying the Resulting Geometry Options

The Face (Virtual) split operation includes two options that determine the geo­metry condi­tions resulting from the operation:

• Retain—Specifies that the split-tool face(s) are retained upon comple­tion of the split operation
• Bidirectional—Specifies that the tool and target faces split each other during the split operation

Performing an Edges Split-type Operation

The Edges split operation allows you to split a real or non-real target face using a set of one or more real or non-real edges. The split-tool edge set can consist of either a single edge or a chain of connected edges.

Splitting Mesh-linked Faces

If you use an Edges split operation to split a target face that is mesh-linked to other faces in the model, GAMBIT attempts to split the mesh-linked faces along with the target face. The success of the split operation requires the following conditions.

• Each mesh-linked face must be associated with a set of edges that corresponds topologically to the edge set used to split the target face.
• Each edge in the split-tool edge set must be mesh-linked to its corre­sponding edge(s) on the mesh-linked face(s).

Figure 2-115: Edges split operation—mesh-linking conditions

Specifying a Tolerance Value

GAMBIT allows you to specify the maximum allowable distance between the edges in the split-tool edge set and the surface of the target face. The Edges split operation includes two tolerance options:

• Auto
• Manual

Performing a Vertices Split-type Operation

The Vertices split operation allows you to split a real or non-real target face using a split-tool consisting of two or more real and/or non-real vertices. The split-tool vertex set must consist of two or more vertices each of which is located on the surface of the face. If the first and last vertices specified for the split-tool vertex set are located on or connected to the boundary of the target face, GAMBIT fully splits the target face; otherwise, the split operation results in the creation of dangling edges.

Figure 2-116 illustrates the Vertices face split operation for a circular target face and split-tool vertex set consisting of four vertices (see Figure 2-116(a)). In this case, the first and last vertices specified for the split-tool vertex set (a and d) are located on the target face boundary, and the other two vertices (b and c) are located interior to the target face. For these specifi­ca­tions, the Vertices split operation produces the set of faces shown in Figure 2-116(b).

Figure 2-116: Vertices split operation

NOTE (1): Self-intersecting edge loops are not allowed in the Vertices split operation, but GAMBIT does not pre-check the set of specified vertices to ensure that it will not result in an attempt to create self-inter­secting loop. It is the user's responsibility to ensure that the vertex location and sequence speci­fied for the operation does not constitute a self-intersecting loop.

NOTE (2): To split the target face, GAMBIT first creates a set of virtual edges between the split-tool vertices. The proximity of the virtual edges to the surface of the original face depends on the number of facets used to define each edge. You can control the number of facets used by means of the GEOMETRY.EDGE.VIRTUAL_NUM_FACETS default variable. If the target face possesses a complex surface, it is sometimes necessary to increase the value of this default variable in order to produce a splitting edge that follows the contours of the original face.

Splitting Mesh-linked Faces

If you use a Vertices split operation to split a target face that is mesh-linked to other faces in the model, GAMBIT attempts to split the mesh-linked faces along with the target face. In this case, the split-tool vertex set must consist of only two vertices both of which are connected to the boundary of the target face.

Figure 2-117 illustrates this requirement for a simple face split operation involving two mesh-linked circular faces. In this case, the boundary of each face consists of two circular arc edges, but the edges are of different lengths for each face. If the vertices are mesh-linked to each other as shown in Figure 2-117(a), GAMBIT splits the faces as shown in Figure 2-117(b).

Figure 2-117: Vertices split operation—mesh-linked faces

Specifying a Tolerance Value

GAMBIT allows you to specify the maximum allowable distance between split-tool vertices and the surface of the target face. Specifically, the Vertices split operation includes two tolerance options:

• Auto
• Manual

Specifying the Shaped edge Option

If the first and last vertices specified for the Vertices split tool are located on the boundary of the target face, you can control the shape of the resulting face-face boundary by means of the Shaped edge option. The Shaped edge option specifies that face-face boundary resulting from the split operation bisects the interior angles of the ori­ginal face boundaries at its end­points (Figure 2-118).

Figure 2-118: Effect of Shaped edge option

Performing a Locations Split-type Operation

To execute the Locations split operation, you must specify a set of two or more points that define the split tool. For a virtual split operation, the first and last points specified must be located on the boundary of the target face. You can specify any split-tool point by clicking on the face bound­ary and dragging the point to its split location.

NOTE (1): Self-intersecting edge loops are not allowed in the Locations split operation.

NOTE (2): For a virtual split operation, the edge loop created from the spec­ified points is not allowed to cross any existing edges on the face.

Splitting Mesh-linked Faces

If you use a Locations split operation to split a target face that is mesh-linked to other faces in the model, GAMBIT attempts to split the mesh-linked faces along with the target face. In this case, the split-tool point set must consist of only two points both of which are located on the boundary of the target face.

Specifying the Resulting Geometry Options

The Locations split operation includes three options that determine the geo­me­try type and the shape of the face-face boundary resulting from the operation:

• Virtual
• Merge resulting edges
• Shaped edge

If you use the Locations split operation to split a real face, GAMBIT attempts to generate real geometry from the operation and produces virtual geometry only if the attempt is unsuccess­ful. The Virtual option specifies that the split operation produces only virtual geometry.

Specifying the Merge resulting edges Option

As noted above, when splitting the target face, GAMBIT creates a chain of edges between the points that constitute the split tool. If you specify a split tool consisting of three or more points and select the Merge resulting edges option, GAMBIT attempts to merge adjacent edges in the chain when per­forming the split operation. GAMBIT merges the edges only if the angle between them at their shared vertex is greater than the current edge-merge minimum angle (default = 135°). You can change the edge-merge minimum angle value by mod­ifying the GEOMETRY.EDGE.VIRTUAL_MERGE_MIN_ANGLE default variable on the Edit Defaults form.

Specifying the Shaped edge Option

The Shaped edge option specifies that the face-face boundary resulting from the split operation bisects the interior angles of the ori­ginal face boundaries at its endpoints (see Figure 2-118, above).

Using the Split Face Form

To open the Split Face form (see below), click the Split command button on the Geometry/Face subpad.

The specifications on the Split Face form are as follows.

Face	specifies the face to be split.
Split with
Faces Face (Virtual) Edges Vertices Locations	specifies the split type.

The specifications available on the lower section of the Split Face form depend on the specified Split with option as follows.

Faces Split-type Option

When you specify the Faces option, the lower section of the Split Face form appears as shown above and includes the following specifications.

Faces	specifies one or more real or virtual faces that constitute the split tool.
Tolerance	specifies the the maximum allowable distance between the target face and split-tool face(s). Auto—Specifies that GAMBIT computes the tolerance value Manual—Allows you to specify a tolerance value (default = 10-5)
Retain	retains the split-tool face(s) at the conclusion of the operation.
Bidirectional	splits the target and tool faces with each other during the split operation.
Connected	connects faces resulting from the split operation.

Face (Virtual) Split-type Option

When you specify the Face (Virtual) option, the lower section of the Split Face form appears as shown below and includes the following specifications.

Face	specifies the face that constitutes the split tool.
Retain	retains the split-tool face at the conclusion of the operation.
Bidirectional	splits the target and tool faces with each other during the split operation.

Edges Split-type Option

When you specify the Edges option, the lower section of the Split Face form appears as shown below and includes the following specifications.

Edges	specifies the real or non-real edges that constitute the split tool.
Tolerance	specifies that the split operation is performed if the split-tool edges are located in proximity to the face to within the tolerance value. Auto—Specifies that GAMBIT computes the tolerance value Manual—Allows you to specify a tolerance value (default = 10-5)

Vertices Split-type Option

When you specify the Vertices option, the lower section of the Split Face form appears as shown below and includes the following specifications.

Vertices	specifies the vertices that constitute the split tool.
Tolerance	specifies that the split operation is performed if the split-tool vertices are located in proximity to the face to within the specified tolerance value. Auto—Specifies that GAMBIT computes the tolerance value Manual—Allows you to specify a tolerance value (default = 10-5)
Shaped edge	shapes the edge resulting from the split operation so that it bisects the interior angles of the face boundaries at its endpoints.

Locations Split-type Option

When you specify the Locations option, the lower section of the Split Face form appears as shown below and includes the following specifications.

Locations	specifies the points that constitute the split tool.
U Value	specifies the u-value location of the current split-tool point with respect to the target-face boundary.
V Value	specifies the v-value location of the current split-tool point with respect to the target-face boundary.
Coordinate Sys.	specifies the coordinate system with respect to which the current coordinates are specified.
Type	specifies the type of coordinate parameters to be used in defining the point.
Cartesian Cylindrical Spherical	specifies the type of coordinate parameters to be used in defining the point.
Global | Local	specifies the location of the point with respect to either the Global or Local system.
Virtual	creates virtual geometry from the split operation.
Merge resulting edges	attempts to merge the edges resulting from the split operation.
Shaped edge	shapes the edge resulting from the split operation so that it bisects the interior angles of the face boundaries at its endpoints.

Merge Faces

The Merge Faces operation (face merge command) merges two or more real and/or non-real faces into a single real or virtual face. (NOTE: If you merge faces that possess identical boundary-zone type specifications, GAMBIT retains the specification and assigns it to the face that results from the merge operation. If the faces differ with respect to their boundary-zone specifica­tions, GAMBIT does not assign a specification to the resulting face.)

The Merge Faces operation requires specification of the following parameters:

• Faces to be merged
• Merge type
• Merge edges option

Specifying the Faces to Be Merged

GAMBIT applies the following rules with respect to the set of faces to be merged.

• Each face in the set must be connected by means of a common edge to at least one other face in the set.
• None of the common edges between faces may be connected to faces that are not in the set of faces to be merged.

Specifying the Merge Type

When you merge faces, you must specify the merge type. GAMBIT provides two types of face-merge operations:

• Real and Virtual (Forced)
• Virtual (Tolerance)

Real and Virtual (Forced) Option

NOTE: By default, GAMBIT does not allow you to merge faces oriented such that they form "sharp" angles with each other as defined by the face normals along their common edges. Specifically, GAMBIT does not merge faces the normals of which differ by less than 90° or greater than 270°. You can override this restriction by setting the GEOMETRY.FACE.SHARP_ANGLE_MERGE default variable to 1.

Virtual (Tolerance) Option

Specifying the Merge edges Option

When you specify the Merge edges option, GAMBIT merges the edges that result from the face-merge operation. As an example of the effect of the Merge edges option, consider the two square, coplanar faces shown in Figure 2-119, which are connected by means of edge.1.

• If you do not specify the Merge edges option when merging the square, coplanar faces, GAMBIT creates a four-sided face bounded by six edges (see Figure 2-120(a)).
• If you specify the Merge edges option, GAMBIT merges the pairs of edges that constitute the upper and lower sides of the four-sided face, thereby creating a face bounded by only four edges (see Figure 2-120(b)).

Figure 2-119: Face merge—effect of Merge edges option, original faces

Figure 2-120: Face merge—effect of Merge edges option, merged faces

Using the Merge Faces Form

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

The Merge Faces form includes the following specifications.

Faces	specifies the set of faces to be merged.
All Pick	(Virtual (Tolerance) option only) All specifies all faces in the model. Pick specifies faces selected by means of the Faces list box.
Type:
Real and Virtual (Forced)	specifies that the faces in the set are to be merged to create either real or virtual faces (see "Real and Virtual (Forced) Option," above).
Virtual (Tolerance)	specifies that the faces in the set are to be merged only if their distances and orientations with respect to neighbor­ing faces meet specified Min. Angle criterion.
Min. Angle	specifies the minimum allowable angle between neighboring faces to be merged for the Virtual (Tolerance) option.
Merge edges	merges edges that result from the face-merge operation.

Collapse Face (Virtual)

The Collapse Face (Virtual) operation (face collapse command) collapses a real or non-real face between two or more neighboring real and/or non-real faces.

When you collapse a face, GAMBIT performs the following operations:

1. Split the face into two or more faces of approximately equal size.
2. Merge the resulting faces with their specified neighboring faces.

The following sections illustrate the results of the face collapse operation for three different situations involving planar faces.

Three Coplanar Faces in a Line

Figure 2-121: Face collapse—3 coplanar faces arranged in a line

Three Coplanar Faces at an Angle

Figure 2-122: Face collapse—3 coplanar faces arranged at an angle

Four Non-coplanar Faces

In Figure 2-123, a triangular face is surrounded by three faces that are arranged at right angles with respect to each other. The face-collapse operation replaces face.4 with a virtual vertex (v_vertex.12), and overlays three virtual faces that share the vertex.

Figure 2-123: Face collapse—4 non-coplanar faces

Face Collapse Specifications

To collapse a face by means of the Collapse Face (Virtual) form, you must specify the following parameters:

• The face to be collapsed
• The neighboring faces between which the face is to be collapsed

• You cannot collapse a face that constitutes part of a volume. For example, GAMBIT does not allow you to collapse one end of a prism.
• Each of the specified neighboring faces must be connected to the face to be collapsed by means of a common edge.

Using the Collapse Face (Virtual) Form

To open the Collapse Face (Virtual) form (see below), click the Collapse command button on the Geometry/Face subpad.

The Collapse Face (Virtual) form includes the following specifications.

Face	specifies the face to be collapsed.
Between
Faces	specifies the neighboring faces that define the collapse operation.

Simplify Faces

The Simplify Faces operation (face simplify command) removes (deletes) dangling edges from faces. Dangling edges are edges that are included in the list of edges that define a face but which do not constitute necessary parts of the closed edge loop that circumscribes the face. They most often result from face-split operations in which the split-tool face only partially intersects the target face (see "Split Face," above).

Figure 2-124 shows two different types of dangling edges, both of which can be removed by means of the Simplify Faces command. In Figure 2-124(a), the dangling edge is connected to the boundary-edge loop of its associated face. In Figure 2-124(b), the dangling edge exists apart from and is not connected to the boundary even though it is included in the list of edges associated with the face.

Figure 2-124: Faces that include dangling edges

Using the Simplify Faces Form

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

The Simplify Faces form includes the following specification.

Faces

specifies one or more faces for which dangling edges are to be deleted.

2.4.8 Smooth/Heal/Convert Faces

The Smooth/Heal/Convert Faces command button allows you to perform the following operations.

Symbol	Operation	Description
	Smooth/Heal Real Faces	Smoothes and heals real face geometry
	Convert Faces (Nonreal to Real)	Converts non-real faces to real faces

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

Smooth/Heal Real Faces

The Smooth/Heal Real Faces operation (face smooth geometry and face heal commands) repairs geometry and topology prob­lems that sometimes occur in sets of real faces.

Overview

GAMBIT real geometry operations employ ACIS modeling techniques. ACIS modeling algorithms require a high degree of precision and accuracy in the geometric data that describe the model. Such precision and accuracy manifests in the form of tight distance tolerances and completeness of connectivity informa­tion.

In most cases, model geometry data generated from within GAMBIT auto­mati­cally meet the stringent integrity standards required by the ACIS modeler. However, a few GAMBIT operations can sometimes produce geometry that fails to meet the ACIS standards. In addition, geometry imported to GAMBIT from outside sources might not meet such standards due to any of the follow­ing factors:

• Inherent numerical limitations in the system used to generate the geometry
• Limitations of data transfer through neutral file formats
• Differences in tolerance settings between the model-generating pro­gram and GAMBIT

• Smooth faces
• Heal geometry

Specifying the Smooth faces Option

The Smooth faces option allows you to automatically "smooth" faces and edges to repair conditions that might cause problems for the ACIS modeler. It includes the following options:

• Replace bad geometry
• Reduce complexity

In addition to these two options, GAMBIT allows you to specify a Tolerance option. The Tolerance option determines the maximum allowable distance that the spline control points can be moved during the smooth operation.

NOTE (1): When you select the Smooth faces option, GAMBIT automatically smoothes the edges associated with the specified faces (see "Smooth Real Edges," in Section 2.3.6.)

NOTE (2): The face-smooth operation should be performed as soon as possible after the specified faces are created or imported. Doing so reduces the chances of the migration of any discontinuities into other geometry and simplifies the task of smoothing.

NOTE (3): The face-smooth operation should involve as many faces at one time as possible, because the smoothing algorithm takes advantage of fact that one geometrical entity can support multiple topological entities.

Replace bad geometry Option

When you select the Replace bad geometry option, GAMBIT detects any bad geometry (including geometry with G1 and C1 discontinuities) and attempts to repair the geometry.

Reduce complexity Option

When you select the Reduce complexity option, GAMBIT attempts to reduce the number of control points in the spline definitions of the underlying surfaces and curves.

Specifying the Tolerance Option

When you select the Replace bad geometry or Reduce complexity option, you can also specify a Tolerance option. The Tolerance option determines the maximum allowable distance that the spline control points can be moved.

GAMBIT provides two Tolerance options:

• Auto
• Manual

Specifying the Heal geometry Option

The Heal geometry option attempts to detect and repair geometry and topology problems that involve the specified face entities. The healing operation is a three-step process that involves simplifying geometry, stitching together loose faces (if necessary), and recomputing geometry to repair geometry and topology problems. The steps are associated with the following Heal geometry suboptions:

• Simplify geometry
• Stitch faces
• Repair geometry

NOTE: The GAMBIT Heal geometry operations are not guaranteed to correct all geometry and topology problems in a given model. In general, both operations should be used with caution, because they are not robust and sometimes produce peculiar model geometry.

Simplify geometry Option

The Simplify geometry option allows you to specify whether or not GAMBIT employs geometry simplification when healing faces. If you select the Simplify geometry option, you can also specify the Tolerance option. The Tolerance option determines whether or not spline surfaces can be approximated by analytic surfaces. If the Tolerance is too loose, approximate analytic fits to spline geometry may be obtained. In such cases, the gaps between surfaces may increase, and healing in subsequent steps may be more difficult or may fail.

GAMBIT provides two Simplify geometry:Tolerance options:

• Auto
• Manual

Stitch faces Option

The Stitch faces option allows you to specify whether or not GAMBIT stitches faces during the healing operation. If you select the Stitch faces option, you can also specify a Tolerance option. The Tolerance option determines the maximum gap size for which GAMBIT performs stitching.

GAMBIT provides two Stitch faces:Tolerance options:

• Auto
• Manual

Repair geometry Option

When you specify the Repair geometry option, GAMBIT attempts to repair the model geometry by recomputing and/or extending surface and curve defini­tions so that the model "fits together" properly. The Make tolerant option (which is always on) creates tolerant geometry, where necessary, to ensure valid topology. (For more information regarding the Make tolerant option, see "Import­ing ACIS Files" in Section 4.1.9 of the GAMBIT User’s Guide.)

In addition to creating tolerant geometry, the Make tolerant option causes GAMBIT to automatically detect and remove short edges and sliver faces during the healing operation. (NOTE: A "sliver" face is defined as a face with multiple boundary edges that possesses a region narrower than a specified distance.)

You can control the short-edge and sliver-face detection and removal operations by means of two default variables:

• GEOMETRY.TOLERANCE.HEAL_REMOVE_SHORT_EDGE
• GEOMETRY.TOLERANCE.HEAL_REMOVE_SLIVER_FACE

NOTE: It is inadvisable to use the Repair geometry option on the first attempt at healing the geometry. The operation is computationally intensive and can sometimes produce bad geometry.

Repairing Gaps Between Faces

One of the primary purposes of the Heal geometry operation is to repair gaps between adjacent faces. If you perform the Heal geometry operation on a set of unconnected faces the bounding edges of which are located near to each other (see Figure 2-125(a)), GAMBIT stitches the faces together and connects their adjacent boundary edges (see Figure 2-125(b)).

Figure 2-125: Heal geometry operation on faces with boundary edge gaps

If the set of connected faces resulting from the Heal geometry operation represents a closed three-dimensional region, GAMBIT creates a volume bounded by the set of faces (see Figure 2-126).

Figure 2-126: Heal geometry operation—volume creation

Using the Smooth/Heal Real Faces Form

To open the Smooth/Heal Real Faces form (see below), click the Smooth/Heal command button on the Geometry/Face subpad.

The specification on the Smooth/Heal Real Faces form is as follows.

Faces	specifies the faces for which GAMBIT attempts the repair opera­tions.
All Pick	All specifies all faces in the model. Pick specifies faces selected by means of the Faces list box.
Smooth faces	attempts to smooth the specified faces.
Replace bad geometry	attempts to reconstruct the specified faces to replace bad geometry.
Reduce complexity	attempts to reduce the number of control points for the underlying surfaces and curves.
Tolerance	specifies the maximum distance by which a control point can be moved. Auto—Specifies that GAMBIT computes the tolerance based on the size(s) of the specified entities Manual—Allows you to specify a tolerance value (default = 10-3)
Heal geometry	attempts to heal the specified faces.
Simplify geometry	attempts to simplify geometry during the healing operation.
Tolerance	specifies a simplification tolerance value. Auto—Specifies that GAMBIT computes the tolerance Manual—Allows you to specify a tolerance value (default = 10-4)
Stitch faces	attempts to stitch faces during the healing operation.
Tolerance	specifies the maximum tolerance value for the stitching operation. Auto—Specifies that GAMBIT computes the tolerance based on an internal algorithm Manual—Allows you to specify a tolerance value (default = 10-3)
Repair geometry	attempts to repair the model geometry by redefining surfaces and curves so that the model "fits together" properly.
Make tolerant	(always on) creates tolerant geometry, where necessary, to ensure valid topology.

Convert Faces (Nonreal to Real)

The Convert Faces (Nonreal to Real) operation (face convert command) converts converts non-real faces to real faces. The operation preserves the topology and any existing mesh(es) associated with the converted face(s) and converts all non-real edges and vertices associated with the face(s) to real edges and vertices.

GAMBIT can use any of three techniques to convert a non-real face:

• Underlying real host
• Deformable modeling
• Net-surface-based

NOTE (1): The algorithm that determines the technique to be used is internal to GAMBIT and is not user-specified.

NOTE (2): The DM technique can be used to convert a face with multiple edge loops as long as the face possesses a single peripheral edge loop.

NOTE (3): The net-surface-based technique cannot be used to convert faces with multiple edge loops.

NOTE (4): If the net-surface-based technique is used to convert a face, it is generally advisable to pre-mesh the face with a mapped mesh rather than using the automatically generated mesh.

NOTE (5): Hidden entities that serve as hosts for virtual entities may become visible when their guests are converted to real geometry.

NOTE (6): When using the DM technique, the convert-to-real operation is restricted to non-real faces that are "simply plane projectable"—that is, faces that can be readily projected onto a plane. Non-real faces that are flat or nearly flat can be converted with­out problem; however, the operation generally fails for non-real faces that are highly curved, such as a 3/4-cylinder or half-torus.

The general methodology sequence that GAMBIT uses when attempting to convert a non-real face can be summarized as follows.

For example, to convert a virtual face that does not have a single, real host and that is neither meshed nor conformally faceted, GAMBIT attempts to generate a triangle mesh for use with the DM technique. If the triangle meshing operation fails, GAMBIT attempts to generate conformal facets for the face. If the DM attempt fails, GAMBIT attempts to generate a mapped mesh and convert the face using the net-surface-based technique.

NOTE (1): The GEOMETRY.FACE.NUM_SAMPLING_POINTS default variable can be used to limit the number of points used by the DM algorithm regardless of the number of mesh nodes or faceting points on the face to be converted.

NOTE (2): The GEOMETRY.FACE.CONFORMAL_FACETS default variable must be set to 1 for GAMBIT to attempt to generate conformal facets.

Using the Convert Faces (Nonreal to Real) Form

To open the Convert Faces (Nonreal to Real) form (see below), click the Convert command button on the Geometry/Face subpad.

The Convert Faces (Nonreal to Real) form includes the following specifications.

Faces	specifies the non-real faces that are to be converted to real faces.
All Pick	All specifies all faces in the model. Pick specifies faces selected by means of the Faces list box.

2.4.9 Summarize/Check/Query Faces and Total Entities

The Summarize/Check/Query Faces and Total Entities command button allows you to perform the following operations.

Symbol	Operation	Description
	Summarize Faces	Displays face summary information in the Transcript window
	Check Faces	Checks the topological and geometrical validity of model faces
	Query Faces	Opens the face query list
	Total Entities	Displays in the Transcript window the total number of entities of one or more specified types

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

Summarize Faces

The Summarize Faces operation (face summarize command) displays face summary information in the Transcript window.

Using the Summarize Faces Form

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

The Summarize Faces form includes the following specifications.

Faces	specifies the faces for which information is to be summarized in the Transcript window.
All Pick	All specifies all faces in the model. Pick specifies faces selected by means of the Faces list box.

Check Faces

The Check Faces operation (face check command) assesses the topological and/or geometrical validity of faces in the model and summarizes the results in the Transcript window.

When you execute the Check Faces command, GAMBIT checks the model to determine its validity with respect to either or both of the following types of characteristics:

• Topology
• Geometry

Topology Check

Topological validity is an assessment of the underlying organization of the model-for example, the correct associations between a face entity and the edges that comprise its boundaries or between entities that are associated with each other by virtue of a virtual-geometry, guest-host relationship.

For a given face, the Check Faces topology check operation examines the model to ensure that it meets the following criteria:

• Lower-topology edges are in separate loops.
• Lower-topology edges are visible and correctly reference the face.
• Sense information (in the form of co-edges) exists for all edges.
• Upper-topology volumes correctly reference the face.
• Upper-topology volumes maintain correct sense information for the face (in the form of co-faces).
• Virtual guest entities correctly reference the face as a host.

Geometry Check

Geometrical validity is an assessment of the model with respect to proximity and shape characteristics-such as the distances between connected edges and/or the mathematical continuity of model curves and surfaces. The Check Faces geometry check criteria are as follows:

• All real faces correctly reference the ACIS model.
• No real faces exhibit problems related to continuity, self-intersection, bad closure, degeneracies, or singularities.
• Any virtual-face hosts are of the correct type. For example, a virtual face formed by connecting or merging two faces must reference only the two faces as hosts. Similarly, a virtual face defined on a volume must not be hosted by a face, and a virtual face formed by splitting a face must be hosted by the face that is split. (NOTE: The face geometry check operation also checks the validity of host geometry.)

Using the Check Faces Form

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

The Check Faces form includes the following specifications.

Faces	specifies the faces to be included in the checking operations.
All Pick	All specifies all faces in the model. Pick specifies faces selected by means of the Faces list box.
Check Topology	specifies a topology check on the selected faces.
Check Geometry	specifies a geomtery check on the selected faces.

Query Faces

The Query Faces operation (no corresponding command-line command) allows you to identify the locations and/or labels of individual faces or subsets of faces in the model. Its use is similar to that of the Query Vertices command (see "Query Vertices" in Section 2.2.7, above).

Using the Query Faces Form

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

For a general description of the Query Faces form, see "Using the Query Vertices Form" in Section 2.2.7, above.

Total Entities

The Total Entities operation (list totals command) displays in the Transcript window the total number of geometry and/or mesh entities that currently exist in the model. For example, if you select only the Geometry entities option on the Total Entities form and click Apply, GAMBIT displays in the Transcript window the total numbers of vertices, edges, faces, volumes, groups, and coordinate systems that currently exist in the model.

Using the Total Entities Form

For a description of the options available on the Total Entities form, see "Total Entities," in Section 2.2.7.

2.4.10 Delete Faces

The Delete Faces operation (face delete command) deletes one or more faces from the model. The operation is subject to the following restrictions:

• GAMBIT does not allow you to delete faces that constitute parts of a volume.
• If you delete a virtual face that constitutes the connection of two or more real or virtual faces, GAMBIT restores those faces to the model when it deletes the specified face.

Retaining Face Edges

By default, when you delete a face, GAMBIT deletes the edges that constitute parts of the face as well as their endpoint vertices. To retain the edges and vertices when the face is deleted, unselect the Lower Geometry option at the bottom of the Delete Faces form. When you delete a face and retain its edges, the edges remained connected to each other by means of their common endpoint vertices.

Retaining and Deleting Associated Vertices

When you delete a face with associated vertices created by means of the Create Vertex on Face command, GAMBIT retains or deletes the vertices depending on whether they are real or virtual entities, respectively. For example, if you delete a face that is associated with one real vertex and one virtual vertex—both of which were created by means of the Create Vertex on Face command—GAMBIT retains the real vertex and deletes the virtual vertex. (The virtual vertex cannot exist without the host face.)

Deleting Virtual Faces

If you delete a virtual face, GAMBIT deletes all lower topology and virtual hierarchy that is associated with the face and is not associated with any other entities in the model.

Using the Delete Faces Form

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

The Delete Faces form includes the following specifications.

Faces	specifies one or more faces to be deleted.
All Pick	All specifies all faces in the model. Pick specifies faces selected by means of the Faces list box.
Lower Geometry	deletes all lower-geometry edges and vertices associated with the faces.

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