On Limitations of the Witness Configuration Method for Geometric Constraint Solving in CAD Modeling

[Mark Szlazak]

On Limitations of the Witness Configuration Method for Geometric Constraint Solving in CAD Modeling

This paper presents discussions on the limitations of the witness configuration method. These limitations have rarely been reported in previous studies. The witness configuration method is a very recent approach for geometric constraint solving, which is of critical importance for modern computer-aided design systems. The witness configuration method may be the most promising method to solve satisfactorily the challenges of geometric constraint solving. This method, in the current form, is however found to be limited for the three essential tasks in the geometric constraint solving domain. Examples are given to validate this work’s statements on these limitations.

https://arxiv.org/pdf/1904.00526.pdf

[Mark Szlazak]

Follow up paper by same group:

Variational B-rep Model Analysis for Direct Modeling using Geometric Perturbation


The very recent CAD paradigm of direct modeling gives rise to the need of processing 3D geometric constraint systems defined on boundary representation (B-rep) models. The major issue of processing such variational B-rep models (in the STEP format) is that free motions of a well-constrained model involve more than just rigid-body motions. The fundamental difficulty lies in having a systematic description of what pattern these free motions follow. This paper proposes a geometric perturbation method to study these free motions. This method is a generalization of the witness method, allowing it to directly deal with variational B-rep models represented with the standard STEP scheme. This generalization is essentially achieved by using a direct, geometric representation of the free motions, and then expressing the free motions in terms of composites of several basis motions. To demonstrate the effectiveness of the proposed method, a series of comparisons and case studies are presented.

https://www.researchgate.net/publicatio ... rturbation

[vocx]

This paper presents discussions on ...

I don't mind you posting papers and all that about geometrical constraints. I just have simple questions. Do you personally understand the mathematics involved in it? Are you working on solvers so this can be implemented in FreeCAD? Or do you just want to draw attention to this knowledge so that somebody (the core developers?) takes a look at it, so that they implement it?

I can almost guarantee that 95% of the people in this forum haven't worked at all with geometrical solvers or optimization. So although I think it's interesting, I wonder why you keep posting these mathematics filled papers.

[Mark Szlazak]

This paper presents discussions on ...

I don't mind you posting papers and all that about geometrical constraints. I just have simple questions. Do you personally understand the mathematics involved in it? Are you working on solvers so this can be implemented in FreeCAD? Or do you just want to draw attention to this knowledge so that somebody (the core developers?) takes a look at it, so that they implement it?

I can almost guarantee that 95% of the people in this forum haven't worked at all with geometrical solvers or optimization. So although I think it's interesting, I wonder why you keep posting these mathematics filled papers.

Yes.

[vocx]

Yes.

C'mon, man, I'm asking nicely. No need to be a ****************** with that answer.

[Mark Szlazak]

Yes.

C'mon, man, I'm asking nicely. No need to be a ******* **** moderator edit with that answer.

Now I understand your background and don’t bother asking me questions again.

[kisolre]

C'mon, man, I'm asking nicely. No need to be a ************* ***** with that answer.

https://github.com/FreeCAD/FreeCAD/blob ... CONDUCT.md

[jmaustpc]

Follow up paper by same group:

You are very welcome to have made these posts, they are obviously appropriate for this forum.

The FreeCAD program, project and forums are complex and very often intellectually challenging by their very nature. Many of us are here for the intellectual stimulation, brain exercise!

We are all at different intelligence levels and types, with wide variations in areas and depths of knowledge and experience. We are inclusive of all peoples of all levels/types of intelligence, experience and knowledge. We welcome the most inexperienced newbies all the way up to the most informed/experienced intelligent brainiacs!

However we would never suggest something as ridiculous, unhelpful and inappropriate as dumbing down FreeCAD or all the discussions around it, just to make it suitable for the most inexperience newbie.

I don't mind you posting papers and all that about geometrical constraints. I just have simple questions. Do you personally understand the mathematics involved in it? Are you working on solvers so this can be implemented in FreeCAD? Or do you just want to draw attention to this knowledge so that somebody (the core developers?) takes a look at it, so that they implement it?

I can almost guarantee that 95% of the people in this forum haven't worked at all with geometrical solvers or optimization. So although I think it's interesting, I wonder why you keep posting these mathematics filled papers.

You are not a moderator etc. here, so please refrain from trying to act as though you are. You are, like everyone, free to report a post or ask a moderator about one privately but leave the moderating to those of us who are moderators/administrators.

No need to be a ****************** with that answer.

obviously that post was inappropriate, offensive, unneccassary and unacceptable. You have been banned for few days, hopefully after this period you will behave politely and appropriately.

You have been moderated, this matter is now finalised, we will not tolerate this topic being hijacked by any further discussions regarding your having been moderated.

[chrisb]

https://arxiv.org/pdf/1904.00526.pdf

I'm not sure if this document is helpful, but finally Abdullah should decide that. From my point of view the FreeCAD solver is a brilliant piece of software, with the only medium severe drawback, that it becomes rather slow if there are too many constraints. The authors of the paper state

... last one is secondary since the efficiency issue, if we do not solve it, will be solved by time, a result of the exponential growth in computing power or advances of quantum computing techniques.

I haven't seen any exponential growth in conventional computing power and I'm afraid that the average FreeCAD user lacks the budget for several generations of quantum computers.

Nevertheless, I liked the definitions, especially the distinction between "consistently overconstraint" and "well constraint". All of these definitions can be applied to FreeCAD as well:

As already noted, a given GCS can be expressed as a system of algebraic equations, denoted as F(X)=0 where X represents the parameters of the participating geometric entities. Through examining the solution (S) of this system, notions of under-, well-, and over-constraint can be formally defined as follows, which is the base of the discussion in this work.

• Definition 1. Let F(X)=0 be the constraint equations of a GCS, and S the solution space. The GCS is consistently constrained if S≠∅, and inconsistently constrained otherwise.
• Definition 2. Let F(X)=0 represent a consistently constrained GCS, and S the solution space. The GCS is under-constrained if the cardinality |S| is infinite.
• Definition 3. Let F(X)=0 represent a consistently constrained GCS, and S the solution space. The GCS is consistently over-constrained if there exists a subset of the GCS such that the corresponding reduced equations have the same solution space as S.
• Definition 4. A GCS is over-constrained if it is inconsistently constrained or consistently over-constrained.
• Definition 5. A GCS is well-constrained if it is neither under-constrained nor over-constrained.
• Definition 5. A GCS is rigid if it is consistently constrained and not under-constrained.