Comparison between CSG and B-rep in 3D Modeling

 

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3D models in computers are classified based on geometric characteristics. They can be divided into three types: box models, surface models, and solid models. If an object is classified by the method of representation, the entity model can be divided into three categories: Decomposition representation, constructive solid geometry, and boundary representation.
 
Common decomposition methods include: quadtree, octotree, multi-tree, BSP Tree, and so on.
Main Methods for constructing representation: scanning representation, constructing ry representation, feature and parameterized representation.
A typical representation of a boundary is a wing-edge structure.
 
In the CSG modeling method, an object is represented as a Boolean operation result of a series of simple basic objects (such as cubes, cylinders, and CONES). The data structure is a tree structure. The leaf is the base ontology or transformation matrix. The node is an operation. The top node corresponds to the object to be modeled. A Brep object is represented as many surfaces (such as patches, triangles, and splines) bond to form a closed space area.

Brep advantages:
1. There are a lot of information about the surface, edge, point and their relationship.
2. It is conducive to generating and drawing line charts and projection charts, and to calculating geometric characteristics. It is easy to link with two-dimensional drawing software and be associated with the same surface modeling software.

Brep limitations:
Because its core information is a plane, the ability to describe a geometric object as a whole is relatively poor, so it cannot provide information about the entity generation process, it is also impossible to record the raw data of the elements that constitute the basic element of the ry. At the same time, the amount of information required to describe the object is large, and the expressions of the boundary expressions are not unique.
 
CSG advantages:
The method is concise, fast to generate, easy to process, and has no redundant information. It also records in detail the original feature parameters that constitute an object, you can even modify the surerx parameters or surerx parameters to re-splice them if necessary. The data structure is relatively simple, the data volume is small, the modification is easier, and can be easily converted into a boundary (Brep) representation.
 
CSG limitations:
Because the information is simple, such a data structure cannot store the final details of an object, such as the boundary and vertex information. Because CSG represents the type of receptor and the restriction on the type of body operation, CSG has great limitations on the coverage of the form and local operations on the form (for example, it is not easy to implement. It is also long to display the result form represented by CSG.

Which method is used? Depending on different perspectives, they both have advantages and disadvantages. You can consider the following points:
1. Reality-whether the model needs to approximate the actual material density, thickness, and volume, or whether the actual surface details need to be displayed
2. Precision-what kind of precision level is needed
 
The hybrid mode (hybird model) is based on Brep and CSG. In the same system, the two are combined to represent entities. The CSG method is used as the external model of the system, and the B-rep method is used as the internal model. the CSG method is suitable for user interfaces and is transformed into a B-rep data model within the computer. It is equivalent to expanding the data structure of the boundary method on the CSG tree node. The hybrid mode is a logical extension based on CSG, and plays a leading role in the CSG structure. The existence of B-rep reduces the mathematical computing workload in the intermediate link, it can completely express the geometric and topological information of objects and facilitate product model construction.
 
There is also a spatial division representation, which uses a quad-tree or eight-Cross data structure to represent a 2D/3D model.

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To determine if the B-Rep model of the handle was actually smaller than models created using the CSG method, a sample handle was created using both of these methods. the CSG method produced a model that used 50% more disk space than the B-rep method handle.
It was also more difficult to construct, and required more constraint equations and variables. Clearly, the B-rep method was indeed the best choice for this model.

Next, a similar study was conducted for the connector model. again, the same model was created using CSG and B-rep methods. the CSG method did have to use a profile and circular sweep to construct the countersink on the bottom of the connector. for this
Set of models, the CSG method had a 10% smaller file size, and was easier to construct. this is most likely due to the complex profile that had to be created for the B-rep method. by constructing this part as a series of co-axial cylinders that all start
The same point, but have different heights and diameters, the process was significantly simpler than the original design. the original design for the CSG model used cylinders stacked on top of each other, and the inside part of the connector was not hollow.
The describe to create a hollow center in the connector complicated the B-rep method significantly, but simplified the CSG method. due to this change, the connector model wowould probably have been better created using the CSG method from this test.

The third family was simply a profile, so those parts cocould not be made with CSG methods. for the fourth family, the main body of the part was again constructed with B-rep and a combination of B-rep and CSG methods. again, the method that used CSG proved
To be a better choice. a csg box primitive of the proper size was inserted. then, a B-rep rotate face operation was completed MED on two of the faces. the pure B-rep method required that the cplane first be changed from the default top cplane TO THE RIGHT cplane.
The profile had to be inserted in two parts and then unioned. the profile was extruded, And the cplane changed back to the top cplane. this required six commands, and multiple attempts before the profile cocould be constructed correctly. the B-rep method also
Resultedin a 10% larger disk file.

 

 

 

Currently, the commonly used Feature Representation Methods are as follows:

(1) B-rep-Based Method: in B-rep method, a feature is defined as a set of surfaces (surface sets) that are correlated with each other of parts ). These features are also called "surface features ". The B-Rep model is based on graphs. All geometric/topological information is explicitly expressed in the top vertex graph of the plane. Therefore, the B-Rep model is often called a value assignment model. B-rep indicates that the feature method is favored by many researchers because it can obtain sufficient information and it is a graph-based representation method (many feature recognition systems are graph-based ). B-rep models can be associated with attribute values (such as surface roughness and material), dimensions, and tolerances, the disadvantage of the B-rep method is that it has no direct relationship with feature ontology and volume features, and it is difficult to perform feature operations (such as deleting features.

(2) CSG-Based Method: CSG-based feature expression defines features as volume elements, and volume elements construct parts through Boolean operations. The CSG representation method is simple, effective, easy to edit, and operates on the body elements. It also provides meaningful connections between the CSG and the feature body elements, and a binary tree can be used to construct a feature model. For feature extraction, the main problem of the CSG model is its uniqueness and lack of explicit expression of lower-layer configuration elements. However, assigning values to the CSG model and exporting its corresponding boundary representation can overcome these problems.

(3) the method based on the mixed CSG/B-Rep: because both CSG and B-Rep have their own advantages and disadvantages, a hybrid representation method based on the advantages of both is generated. Nnaji and Liu developed a process planning system that extracts CSG-based information (B-rep information is exported from the CSG model ). Reconstructs the CSG tree and B-rep information to make it another CSG tree that represents features in a hybrid form. Roy and Liu proposed a hybrid CSG/B-rep method to represent features, dimensions, and tolerances. The hierarchical structure of features provides multi-level representation of object component relationships, and maintains a boundary representation for each level of detail. Gossard et al. proposed a method to explicitly represent dimensional tolerances and geometric features in geometric modeling, this method combines CSG and B-rep representation into a graph structure called a shape graph.