﻿ Boundary Representation

# Boundary Representation

Boundary Representation on German bounding surface model, (b- rep or brep ) is a representation of the form of a surface or solid model, are described in the objects by their bounding surfaces. The term is a contraction of the words boundary for boundary, edge and representation for presentation together.

• 2.1 Example

## Application

### Visualization

Boundary representation models are preferably used in the visualization of 3D computer graphics and CAD programs, their application because they are algorithmically processed quickly.

### Solid modeling

With the boundary representation model can also describe solid models. Since in this case a body is represented only by its bounding surfaces, it is called an indirect modeling (as opposed to direct modeling with constructive solid geometry, is constructed in the bodies with ). The user or an intelligent testing algorithm must ensure that there is a closed shell case.

## Object creation

The definition of instances can be connected to a node - edge-faces - graph ( vef - graph, Eng. Vertex, edge, face) take place. Here, the geometry is determined by the coordinates of the points. The topology, that is the relationship between the points which describe the edges and surfaces. Edge to reference it on points and areas on edges.

### Example

By way of example a vef - graph is constructed for a tetrahedron. The storage of information is done using a relational database model. The description of the object can be done in many ways. Here the following three lists are defined for this purpose:

• The node list contains the coordinates of the points,
• The edge list that references for each edge two points, and
• The area list, which has a closed sequence of edges for each face.

In order to achieve uniqueness is laying the Direction of the edge sequence with the definition, is the area eg the left of it, firmly. It is in the 2D possible to describe with opposite direction of rotation holes. In 3D thus determined by the right-hand rule, the surface normal, which in turn can be used to define the "front ". Note that not the sequence of the points, but the edge is evaluated.

If you want to describe a volume model, a fourth table is still necessary that enumerates all enclosing surfaces. The user must - as mentioned above - ensure that the patches completely define the volume and that no gaps. The entry in the column " orientation " specifies whether the normal vector of the first given in the list of the boundary surfaces face away from the volume or the volume shows inside. As in 2D for surfaces can be modeled as holes.

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