1. DEGENERACIES
Author: Lahiru
1

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

8. DEGENERATE BOUNDARY
8
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.
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