Geometry Topology Definition

 

 

 

 

 

GTS allows its users to create highly complex geometric data for an accurate FE analysis model with any dimensions or shapes, by providing advanced geometric functions.

A geometry model is fundamentally formed by the interlocking relationship of various geometric entities. The geometric entities in GTS are listed in the following table.
 

Compound

Group of independent entities

Shape

General term used for defining an independent entity

Solid

Part of 3-D space bound by a shell
Property: Volume

Surface

Shell

A group of Faces connected by boundary edges

Face

Part of a plane or a surface bounded by a closed wire
Ex: Plane Surface, Cylinder, Sphere  
Property: Area

Curve

Wire

A sequence of Edges connected by their Vertices
Ex: Rectangle, Polyline

Edge

A shape corresponding to a curve and bound by a Vertex at each extremity
Ex: Straight Line, Circle, Ellipse, Arc, etc
Property: Length

Vertex

A zero-dimensional shape corresponding to a point in Geometry
Property: Coordinate

Selection Filter enables selection of desired shapes by its geometrical type.  (refer to Selection Filter)

 

<Geometry Shape Definition and Topology>
 

  • The boundary of a Face consists of one Wire and the boundary of a Solid consists of one Shell.

  • The user may interchange freely between closed Wire and Face or between closed Shell and Solid because they are subject to share the same Sub-Shapes.

  • Extruding an Edge creates a Face. Extruding a Wire creates a Shell. This Shell shares the same Sub-Shapes with a group of Faces which is generated by the extrusion of the original Sub-Edges of the Wire.
    Extrude, Revolve, Loft, Sweep and Turning on Solid options will transform the shape into a Solid.
     



<Compound>
 

Compound is generally used to sort shapes easily (Ex: grouping hundreds of Curves imported from AutoCAD .dxf file into a single Compound). The above example is a Compound of 8 Shapes (5 Vertices, 1 Wire, 1 Face and 1 Solid). Once the shapes are grouped into a Compound, they do not exist as independent Shapes any longer. The Compound becomes the highest level independent shape. However, since their geometrical type remains unchanged, they still can be utilized in general modeling operations.

 



<A Shell extruded from a Wire in the above Compound>
 

The following examples will help to more comprehensively understand the topology.

Highest Level Shape

One Face

Sub-Shape

Wire

One (Face Boundary)
Group of Edges(E1~E5)

Edge

Five (E1~E5)

Vertex

Five (V1~V5)

Highest Level Shape

One Face

Sub-Shape

Wire

Two (Inner/Outer Boundary)
= E1 and E2

Edge

Two (E1, E2)

Vertex

Two (V1, V2)

No matter how many edges exist, a boundary of a Face will be always regarded as a Wire.
In a closed Edge, such as a Circle, the starting and ending Vertices are identical.

Highest Level Shape

One Shell

Sub-Shape

Face

Two (F1, F2)

Wire

Two (Boundary of each face)

Edge

Seven (E1~E7)
Faces share E4

Vertex

Six

When the user sews two neighboring Faces into a Shell, one or more Edge(s) will be shared between Faces. In the diagram, two independent Faces have a total of 8 edges, but the combined Shape, a Shell, has only 7 edges. Unlike an Edge, Wires are not shared by Faces within a Shell.

Highest Level Shape

One Solid

Sub-Shape

Shell

One (Solid's Boundary)

Face

Six

Wire

Six (Boundary of each face)

Edge

Twelve

Vertex

Eight

 

GTS provides both the Top-down Modeling and Bottom-up Modeling methods.
 

  • Top-down Modeling Method

In this method, the user creates the highest level Shape, and its Sub-Shapes are formed automatically. The user does not need a lot of effort to model each Sub-Shape. This method is often exercised for a simply shaped model or for a preliminary design process.
<Ex> If a cube is created with the primitive box feature of GTS, all Sub-Shapes of this solid, such as Faces, Wires and Edges are automatically generated.

  • Bottom-up Modeling Method

The user will start to model from the lowest level entities first. With these independently generated Sub-Shapes, the final shape is assembled together. The operation may take more time than the Top-down Modeling Method. However,  by using this method, the user can generate a very complex shape which cannot be accomplished by the other method. In most of the geometry modeling practices, the Bottom-up Modeling Method is used.
<Ex> A surface model of terrain is extremely difficult to model directly at once. Therefore, Vertices and Edges, which express the Face, will be created first, and the Face will be generated by using those Vertices and Edges.
It is not always necessary to follow each step from the lowest level shape to the complete model in the Bottom-up Modeling Method. Some procedures can be eliminated if necessary.

GTS provides both Top-down Modeling and Bottom-up Modeling methods.  Therefore, the user can choose either method, or a combination of both, depending on beneficial characteristics of the particular model.

 


<Example of Combining the Two Modeling Methods>