Virtual Topology Operators for Meshing 拓扑重定义与操作
1. Introduction
问题的由来
However, attempts at direct analysis of models obtained from CAD geometry sources have unveiled numerous obstacles preventing true automation of the analysis process. As a result models generated by CAD systems are often unsuitable for analysis needs, requiring multiple editing and adjustment before the meshing can proceed. The difficulty increases when the design and analysis are done in different software systems, as often is the case.
In view of the advances in mesh generation automation, integration of CAD and analysis is quickly becoming a major focus in providing a fully automated model analysis.
局限性
One common approach to provide the necessary geometric editing is through direct geometric adjustments, i.e. the underlying definitions of surfaces and edges are modified accomplish the required changes. This requires the use of sophisticated surface definitions, is expensive, approximates the true geometry, and usually destructively replaces the old geometry with new definitions. Such techniques require extensive user interaction and while dealing with most of the editing problems, lack generality. Using just topological modifications for detail suppression was suggested by Armstrong, but was not extended further to other editing operations.
拓扑重定义与操作
The virtual topology provides a alternative model representation along with a set of operators to perform the editing operations commonly required for the meshing pre-processing. The operators are applied only on the topological structure or connectivity of the model. This significantly simplifies the modeling process as geometric description are maintained, the original model can be easily restored.
An additional benefit of virtual topology arises from its direct use during meshing. The virtual structure often allows easy geometric modification (e.g. sliding a virtual edge on face), making it very flexible or "rubberized" to the user. Since the mesh "owned by" the virtual structure, it must follow the topology movement. Moving virtual entities then allows whole sections of the mesh to be dynamically adjusted, providing direct control of the final mesh.
2. CAD and Analysis Integration Problems
2.4 Pre-Processing Requirements
3. Virtual Topology Definition
The B-Rep describes the topology and the geometry of a solid boundary. It uses vertices, edges faces and volumes as the basic topological entities. The B-Rep provides a full description of the topological connectivity between the entities, such as which edges bound a face, which faces form an envelope of volume, and so on. The connectivity information of a solid can be viewed as a hierarchical structure with a volume at the top and vertices at the bottom and with links between each higher dimension entity and lower dimension entities that bound it. When referring to entities in the hierarchy above the current entity, the term "upper topology" is commonly used. Entities below the entity in the hierarchy are referred to as it's "lower topology".
拓扑变，几何不变
Each topological entity has a full geometric description such as a curve for an edge and a surface for a face. The geometric description is usually encapsulated as a separate entity.
The virtual topology enhancement of the B-Rep uncouples the topology and geometry. While in the standard B-Rep each entity has a mathematical (geometric) description attached, in the enhanced B-Rep an entity can have a virtual description instead. Thus two types of topological entities are defined, based on the geometry description attached.
- Real, containing as the description the exact, mathematical definition of the entity geometry (curve, surface, etc...)
- Virtual, referencing topological entities from which the entity geometric description is to be derived and the type of relationship with those entities as descripbed below.
The entities on which the virtual topological entity relies are defined as hosts of the entity. A virtual entity provides all the geometric properties of a real entity by accessing the hosts' data. An entity that relies on another entity is called a guest of that entity.
几何与拓扑的分离，外放方式未讲明白
The seperation of topology and geometry allows a common simplified interface for both real and virtual topological entities. The user is not exposed to the type of virtual entity and the guest/host relationship is hidden to simplify user interactions.
4. Virtual Topology Operators
All the operators are applied only on the model topology, leaving the geometry unchanged as opposed to standard CAD or solid modeling systems.
5. Use of Virtual Topology for Modeling
As described in the introduction, models acquired from CAD sources are usually not suitable to be used "as is" by the existing range of mesh generation tools. Hence a pre-processing phase usually exists where the models is edited to make it meshable. The editing usually includes completion and correction of the model. Once a model is well defined it is usuaslly simplified and when necessary decomposed into several parts.
5.1 Geometry Completion and Correction
5.2 Geometry Simplication
5.3 Geometry Decomposition
5.4 Mesh Adustment
参考书籍
- Sheffer A. VIRTUAL TOPOLOGY OPERATORS FOR MESHINGJ.International Journal of Computational Geometry & Applications, 2012.