Avoid singularities?



Is there a reason to avoid singularities with stacked control points?

As I am writing a training module I was wondering what reasons there may be in order to give proper advice.

Happy to hear from you.


(Menno Deij - van Rijswijk) #2

Hi Gerard!

As far as I understand, the surface normal may not be defined at the singularity, which could lead to problems when doing e.g. milling (CNC) if the normal is used to orient the mill head. This is why we create “sharp” corners by placing control points very close, but not exactly on top of
each other, when drawing for milling purposes.


Hi Menno,

That is one very good reason!



(Menno Deij - van Rijswijk) #4

Another reason to avoid them is that they bunch the control lines together When meshing for e.g. CFD this give very small triangles which grid generation does not like. Create a mesh on a cone and look at the cone tip: very small triangles.


Ah yes, I can imagine that this is another good reason to avoid singularities.

Thanks again Menno.

(Brian James) #6

Hi Gerard,

I don’t know the Math backing up why things can go wrong at singularities but I often teach my students to avoid these by trimming them off and using blends or tucking them into a model prior to a Boolean. My favorite way of describing it is “singularities are like the poles of the Earth, you don’t want to live there.”


Haha, that’s a good explanation

(Pascal Golay) #8

Hi Gerard- if the entire edge, and not just some points of the edge, are compressed to a single point, i.e. a ‘true’ singularity, then this is perfectly legitimate to do as far as I know.

One reason to avoid them, in some cases, is that it can be very difficult to match surfaces cleanly around singularities such as you get when sweeping (sweep2) to a point on converging rails. Surfaces like this often have very very high curvature approaching the point, as the cross section becomes more and more compressed. This is not specific to singularities - that is, the sweep or whatever need not some to a point, but shows up often there. At any rate, matching for curvature to surfaces like this can be pretty hard to do- I try to make a trimmed surface with more rectangular UV structure if possible.

What is good to avoid is making adjacent (untrimmed) edges of a surface tangent to one another where there is normally a hard corner of some kind (4 sided surface). There, U and V are parallel and the surface normal is undefined and things tend to go haywire with offsetting and related operations like filleting.



The rule you have to follow to get a smooth rounded tip on a surface that’s been lofted or swept to a point is a constant source of irritation on any non-trivial shape.


Thanks Pascal

Do you mean like the attached example?

corner.3dm(200.4 KB)

Nearly any ship or yacht hull will have this kind of ‘corner’ somewhere in the bow area. As you might notice, the offset behaves indeed strange at the ‘corner’.


Yep that is completely true.

(Vicente Soler) #12

Another good reason to avoid singularities is spaghettification.


LOL ! :smiley:


Haha, yes from another perspective that is another very good reason.