Degeneracy in 3D modelling
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| What is "Degeneracy"? |
What is "Degeneracy"?
According to Oxford Learner's Dictionary "Degeneracy" means "The process of becoming worse or less acceptable in quality or condition".
In geometries, this word is used for shapes that lose their characteristics or that are not generated correctly. Degeneracies can arise due to issues in geometry (parametric) or topology.
eg:
- Small edge length - which has a finite length and is smaller than the coincidence of two points (In Open CASCADE this value is equal to 1e-7, which equals to Precision::Confusion())
- Zero edge length
- The point at the tip of a shape
What is the difference between topology and geometry?
Let me explain that briefly.
Most of the CAD models are described using the B-Rep method, which described shapes using limits, and boundaries. A B-Rep method is composed using two parts.
- Topology - Describes how elements are bounded and connected
- Geometry - Describes how the shapes of each element.
Degeneracies formed during modelling
When parametric space is incompatible with the real world of the geometric model, degeneracy is created. Degeneration can happen not only for edges but also for curves and faces.
eg:
The apex of the cone (single point) is represented by an edge in parametric representation forms a degenerated edge.
Important: Degeneracy is not this kind is not harmful in and of itself. These shapes can be used in Boolean operations, and mesh.
Degeneracies that happen after a Boolean operation will cause problems and at that time, we need to be aware of its existence.
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| Degenerate symbol |
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| Different ways of generating degeneracies |
Degenerate boundary
The degenerate boundary is an incomplete or zero-area loop or an incomplete or zero-volume shell. These are commonly referred to as topological degeneracy.
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| Potential degenerate loop |
Here you can see how degenerate loops and degenerate shells can be formed. There will be other ways of generating degeneracies but here are the most common types.
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| Degenerate loops vs Degenerate shell |
Some corrective actions when Boolean operations are failed.
- Try to use primitives whenever possible to create solid models.
- Try to avoid geometries with degeneracies if the degeneracy lies on a potential intersection curve. (See Degeneracies formed during modelling)
- Try to avoid performing Boolean operations on entities that are tangent to each other.
- If the Boolean operation included more than two input shapes, break that into a series of operations with fewer inputs.
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| Break Boolean operations into multiple steps |
Summary
- Degeneracies can arise due to geometry (parametric) or topology issues.
- Degeneration can happen not only for edges but also for curves and faces.
- Degeneracy is not this kind harmful in and of itself.
- Degeneracy due to Boolean operations needs to be handled.
- Degenerated edges can be identified using the "Degenerated" flag.
Reference
- Ansys Modeling And Meshing Guide.pdf