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. 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. 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. Degenerate boundary is an incomplete or zero-area loop, or an incomplete or zero-volume shell.

1. DEGENERACIES
Author: Lahiru
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2. OVERVIEW
Progress
• What is degeneration?
• Degeneracies formed during modelling
• Degenerate boundary
• Identify degenerated shapes
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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
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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
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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.
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6. • DEGENERACIES FORMED DURING
MODELLING
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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.
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8. DEGENERATE BOUNDARY
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Degenerate loop Degenerate shell

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.
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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.
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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.
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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
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