# Degeneracies in 3D modeling.pdf

Mechanical and Software Engineer at Turbogen Consultancy
Nov. 14, 2022
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### Degeneracies in 3D modeling.pdf

• 2. OVERVIEW Progress • What is degeneration? • Degeneracies formed during modelling • Degenerate boundary • Identify degenerated shapes 2
• 3. WHAT IS DEGENERACY? ● According to Oxford Learner’s Dictionaries “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 ○ Small edge length – which has a finite length and is smaller than the coincidence of two points (Precision::Confusion() ~ 1e-7). ○ Zero edge length ○ Point at the tip of a shape 3
• 4. • 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. Ex: The apex of the cone (single point) is represented by an edge in parametric representation. -> this forms degenerated edge 4
• 5. • DEGENERACIES FORMED DURING MODELLING 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. 5
• 6. • DEGENERACIES FORMED DURING MODELLING 6
• 7. • DEGENERATE BOUNDARY ● Degenerate boundary is an incomplete or zero-area loop, or an incomplete or zero-volume shell. ● These are commonly referred as topological degeneracy. 7
• 9. • IDENTIFY DEGENERATED SHAPES ● You can use the following function to identify degenerated edges. Degenerated edges do not have a 3D curve. It has only a 2D curve and usually, that is a line segment. In 3D space, one vertex will represent that edge. The vertex belongs to the start and ends of the edge. Those edges have “Degenerated” flag. 9 Source: How to recognize that some surface point is degenerated? - Forum Open Cascade Technology
• 10. • 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. (Slide 6) ● 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. 10
• 11. • SUMMARY ● Degeneracies can arise due to issues in geometry (parametric) or topology. ● Degeneration can happen not only for edges but also for curves, and faces. ● Degeneracy is not this kind is not harmful in and of itself. ● Degeneracy due to Boolean operations needs to be handled. ● Degenerated edges can be identified using the “Degenerated” flag. 11
• 12. • REFERENCE ● Book ○ ANSYS Modeling and Meshing Guide Ansys Modeling And Meshing Guide.pdf ● Web site ○ How to recognize that some surface point is degenerated? - Forum Open Cascade Technology ○ Degenerated edges removal will change the shape - Forum Open Cascade Technology ○ https://www.simscale.com/docs/simwiki/preprocessing/cad- topology/#:~:text=Topology%3A%20Describes%20how%20elements%20are,the%20shape%20of%20each%20element 12