Boundary representations

ProcGen generates a scaled 3D model of the test specimen geometry, in the form of a faceted boundary representation. This model is made available for use by other software tasks in the system. The STEP file format (the ISO standard for product data exchange) was chosen to provide future compatibility with CAD models produced externally. In particular part 204 (faceted b-rep) of this standard is used. 

The most common boundary representation is periodic boundary conditions which assumes that the system consists of a periodic array (or a crystal ) of identical systems [1], Another common method, developed for the simulation of biomacromolecules, is the stochastic boundary approach, in which the influences of the atoms outside the boundary are replaced by a simple boundary force [78, 79, 80], Warshel uses a Langevin dipoles model in which the solvent is explicitly replaced by a grid of polarizable dipoles. The energy is calculated in a similar way to the polarization energy in a molecular mechanics force field (see above) [15]. 

I.2.2. Solid Modeling A very important class of 3D modelers is generated by the volume systems. The appropriate internal computer representation is broken down into either boundary representation models (B-reps) or Constructive Solid Models (CSGs). The representation depends on the basic volume modeling principles and the deciding differences between the 3D CAD system classes. 

Existing solid modelling methods are reviewed in order to know whether or not they satisfy the requirements previously discussed. Among several solid modelling methods [Chiyokura, 1985, for description], the Boundary Representation(BR) model, the Spatial Occupancy Enumeration(SOE) model and the Constructive Solid Geometry(CSG) model are selected for the review. 

The boundary representation (BREP) model, another model of CAD, defines each object by its surface. Usually the surface is divided in patches of possibly different kind, e.g., a piece of a plane, a sphere, or more complex surface. The union of all patches should wrap the whole volumetric object with no gap. This property is also denoted as waterproof . 

On the right of Figure 2-4, the shape of a part is visualized. Any point and curve can be computed in the model coordinate system using the mathematical description of the shape. The shape in this example is covered by flat surfaces it does not contain any curved surfaces or curves on its boundary. Lines and flat surfaces constitute a complete closed boundary of the body. The shape model is based on the principle of boundary representation with surfaces covering the shape and lines at the intersection of surfaces. 

The analysis of the effect of the change of a geometric entity on other geometric entities needs information about the geometric entities adjoining it. In other words, the model must include information about connecting curves and surfaces. This information is carried by topological entities of the boundary representation. 

The boundary representation must allow all necessary geometric operations during construction, modification, and application of the model such as intersection by curves and surfaces, and modification of continuity conditions. 

Additional information is necessary for mapping surface-curve-surface connections. Boundary representation applies the traditional mathematical method of topology for this purpose. 

Another misunderstanding involves application of constructive solid geometry (CSG). In early solid modeling, CSG was a leading model representation now it has been replaced by boundary representation. CSG is still important as one of the model construction methods for solids, but CSG modeling procedures generate boundary representation. 

The shape of a mechanical part can be divided into a well-defined set of solid primitives. A purposeful sequence of combination operations with the primitives can be applied to form the shape of the part. Constructive solid geometry (CSG) is based on this recognition. CSG was the traditional way of solid modeling. The construction method is also applied in advanced part modeling. While the traditional method applied CSG data structure, present modeling methods generate boundary representation. This difference often causes misunderstanding around CSG. 

Surface modeling produces boundary representations of surfaces with or without a history of model construction. The development and modification of complex curves and surfaces needs information about how existing curve and surface entities... 

Surface models are modified by building them into the boundary representation of one or more solids. When a solid part model changes, surfaces associated with the part are changed accordingly. 

A typical solid sweep is shown in Figure 8-4. A flange is created as a sweep feature along the inside boundary curve of a curved surface, in a boundary representation of a solid. 

Chuang, S. H. F., and Henderson, M. K. Using Subgraph Isomorphisms to Recognize and Decompose Boundary Representation Features, Journal of Mechanical Design, vol. 116 (1994) pp. 793-800. 

Boundary Representation (BREP) BREP provides the highest level of representation precision. Data generated with BREP is compressed by using different algorithms and stored without loss. In its present specification (9.5), only two BREP types are allowed the conventional JT-BREP representation and XT-BRED based on the Parasolid boundary representation. The XT-BREP will be favored in the further implementation of JT based software. 

Plastics with their inherent complex geometries are typically better suited to boundary representation models. Also functions such as finite element modeling or numerical control tool paths require explicit surface definitions which are only available with boundary representations. With constructive solid geometry systems, surface information must be evaluated before it is user accessible. Wireframe models again may be used as the base and are easily transferred to a boundary representation system. Conversely a boundary representation model may be readily converted to a wireframe. Many current commercial systems combine the features of both constructive solid geometry and boundary representation. A project consisting of simple machineable shapes may be done faster in a constructive solid geometry mode while a sculptured surface model would be more easily created in a boundary representation mode. The separate models can... 

Two principal representations are supported, namely Boundary Representation (B-rep) and Constructive Solid Geometry (CSG). 

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