The TRIRADIUS in a fingerprint: how it develops, it's characteristics + a definition!

Figure 134 is a tented arch. The ridge marked "A—A" in the sketch enters on one side of the impression and flows to the other with an acute rise in the center. Ridge C strikes into A at point B and should not be considered as a bifurcating ridge. The ridges marked "D—D" would form a tented arch if the rest of the pattern were absent.

Patti wrote:Here is a different example regarding bifurcations and angles.

see fig. 134 below.



They are telling us not to call the angle at B where C meets A as a bifurcation.

Figure 134 is a tented arch. The ridge marked "A—A" in the sketch enters on one side of the impression and flows to the other with an acute rise in the center. Ridge C strikes into A at point B and should not be considered as a bifurcating ridge. The ridges marked "D—D" would form a tented arch if the rest of the pattern were absent.

Disregarding all but A, B & C in Fig. 134, we are looking at a configuration that you have described as a probably 'well fed' bifurcation.

Martijn (admin) wrote:

Patti wrote:Here is a different example regarding bifurcations and angles.

see fig. 134 below.



They are telling us not to call the angle at B where C meets A as a bifurcation.

Figure 134 is a tented arch. The ridge marked "A—A" in the sketch enters on one side of the impression and flows to the other with an acute rise in the center. Ridge C strikes into A at point B and should not be considered as a bifurcating ridge. The ridges marked "D—D" would form a tented arch if the rest of the pattern were absent.

Disregarding all but A, B & C in Fig. 134, we are looking at a configuration that you have described as a probably 'well fed' bifurcation.

Patti, I am wondering: regarding what aspect of our discussion are your presenting this example?


PS. At point B we clearly see a continuing ridge (A-A) + an abutting ridge (C)... so there can be no doubt that all: point B can not be described as 'bifurcation'... because at point B the ridge A-A does not change it's direction.

Patti wrote:My point if it seems lost, is that a bifurcation is not a triradius.

It is used as an FBI "delta" (same as Penrose Triradial Point etal) only when it is 'open to the core'.

Patti, the issue 'open to the core' really only relates to a situation when "... there is a choice between two or more possible deltas".

So your requirement (relating to the word only) can not be used as a general requirement for any bifurction to become a 'delta' (basically, that requirement will typically only to serve a requirement when there are multiple bifurcations that could serve as the location for the delta).


I already mentioned that the concept of a 'triradius' has become completely irrelevant in the F.B.I. system, and for example figure 139 & 292 present clear examples where a 'triradius' is described as... a bifurcation:

EXAMPLE 139:


"Once studied, however, the pattern presents no real difficulty. There are no ridges intervening between the delta, which is formed by a bifurcation, and the core."

(Because the angles between the 3 radiants from the delta are all larger than 90 degrees!)


EXAMPLE 292:


"Whenever the ridge traced bifurcates, the rule for tracing requires that the lower limb or branch proceeding from the bifurcation be followed. This is illustrated in 292."


...So, in the F.B.I. system any point that truely meets all requirements to be described in the scientific approach as a 'triradius'... can in the F.B.I. approach be described as a 'bifurcation'.

Because otherwise, that would for sure mean that the F.B.I. has failed to describe the most common manifestation form of a 'delta' (= the 'triradius' in the scientific approach)... and I think it would basically be quite silly to make such a claim.

Patti wrote:You are mistaken about fig. 292. It is speaking of encountering bifurcations when tracing the type lines. They are saying here to move away from the pattern when tracing and you reach a bifurcation.

It is not describing the fbi focal point delta as a bifurcation.

Martijn (admin) wrote:

Patti wrote:My point if it seems lost, is that a bifurcation is not a triradius.

It is used as an FBI "delta" (same as Penrose Triradial Point etal) only when it is 'open to the core'.

Patti, the issue 'open to the core' really only relates to a situation when "... there is a choice between two or more possible deltas".

So your requirement (relating to the word only) can not be used as a general requirement for any bifurction to become a 'delta' (basically, that requirement will typically only to serve a requirement when there are multiple bifurcations that could serve as the location for the delta).


I already mentioned that the concept of a 'triradius' has become completely irrelevant in the F.B.I. system, and for example figure 139 & 292 present clear examples where a 'triradius' is described as... a bifurcation:

EXAMPLE 139:


"Once studied, however, the pattern presents no real difficulty. There are no ridges intervening between the delta, which is formed by a bifurcation, and the core."

(Because the angles between the 3 radiants from the delta are all larger than 90 degrees!)


EXAMPLE 292:


"Whenever the ridge traced bifurcates, the rule for tracing requires that the lower limb or branch proceeding from the bifurcation be followed. This is illustrated in 292."


...So, in the F.B.I. system any point that truely meets all requirements to be described in the scientific approach as a 'triradius'... can in the F.B.I. approach be described as a 'bifurcation'.

Because otherwise, that would for sure mean that the F.B.I. has failed to describe the most common manifestation form of a 'delta' (= the 'triradius' in the scientific approach)... and I think it would basically be quite silly to make such a claim.

Martijn (admin) wrote:

Patti wrote:You are mistaken about fig. 292. It is speaking of encountering bifurcations when tracing the type lines. They are saying here to move away from the pattern when tracing and you reach a bifurcation.

It is not describing the fbi focal point delta as a bifurcation.

Patti, the comment that I have quoted can only relate to the upper radiant of the right 'triradius'... which does make the bifurcation (at the upper left side of the 'whorling ridges').

So, that right 'delta' is here clearly described as a 'bifurcation'... while it also have all necessary elements to be called a 'triradius' (in the scientific perspective).

Patti wrote:

Martijn (admin) wrote:

Patti wrote:You are mistaken about fig. 292. It is speaking of encountering bifurcations when tracing the type lines. They are saying here to move away from the pattern when tracing and you reach a bifurcation.

It is not describing the fbi focal point delta as a bifurcation.

Patti, the comment that I have quoted can only relate to the upper radiant of the right 'triradius'... which does make the bifurcation (at the upper left side of the 'whorling ridges').

So, that right 'delta' is here clearly described as a 'bifurcation'... while it also have all necessary elements to be called a 'triradius' (in the scientific perspective).

"Whenever the traced ridge traced bifurcates".

It's not saying the bifurcated ridge is traced.

<edit> and it's not saying the delta is a bifurcation - although I'm sure they would, because they are interchanging the angled formation of the triangular triradius with the term bifurcation.

Patti wrote:

In fig. 139 you are looking at 3 ridges meeting at the center type of triradius. A Star triradius as I would describe it.

The FBI focal point delta is exactly the same location as Penrose etal. i.e. the middle of 3 ridges meeting at the center.

Martijn (admin) wrote:

Patti wrote:

In fig. 139 you are looking at 3 ridges meeting at the center type of triradius. A Star triradius as I would describe it.

The FBI focal point delta is exactly the same location as Penrose etal. i.e. the middle of 3 ridges meeting at the center.

Patti, does your comment implicate that you now finally recognize as well my point?

(My point is: that in the F.B.I. approach the concept of a 'bifurcation' relates to a rather wide range of manifestation shapes - including examples which can very well be described in the scientific approach as a 'triradius')

Martijn (admin) wrote:

... Now, maybe this is illustrated by the fact that Danuta Loesch introduced in 1983 another (more specified) definition for the triradius (quoted from 'Quantitative Dermatoglyphics', page 7):

"The triradius is formed when three fields of parallel lines meet and its centre has three radiant lines which lie approximately 120 degrees to one another (in practice, however, singularities in the lines of greatest curvature on a surface may produce unsymmetrical triradii so that the angles between the radiants may not be equal)."



Voila... ...!!!! In Loesch's definition we see a characteristic that can directly be associated with a typical characteristic of how a 'fork'/'splitting' has always been defined - except of course... (1) while in a true 'fork'/'splitting' the two diverging ridges continue parallel... (3) and in a true 'triradius' the diverging ridges continue in a different direction (2) but in a true 'bifurcation' the diverging ridges continue in a different direction... making an angle between 90 and 120 degrees.


And after saying this... I hope it makes sense that next to the words 'triradius' and 'triradial point'... the F.B.I. is also not using the words 'fork' and 'splitting'!!!

Which implicates that the F.B.I. really is using the word 'bifurcation' as an ALTERNATIVE NAME for a group of words, including: the 'triradius', the 'fork' and the 'splitting'!

Patti wrote:

Martijn (admin) wrote:

Patti wrote:

In fig. 139 you are looking at 3 ridges meeting at the center type of triradius. A Star triradius as I would describe it.

The FBI focal point delta is exactly the same location as Penrose etal. i.e. the middle of 3 ridges meeting at the center.

Patti, does your comment implicate that you now finally recognize as well my point?

(My point is: that in the F.B.I. approach the concept of a 'bifurcation' relates to a rather wide range of manifestation shapes - including examples which can very well be described in the scientific approach as a 'triradius')

(1) If you agree that the FBI interchanges a splitting bifurcation at times with one of the angles of the Penrose's F or G examples, then 'yes' I agree that the FBI has a multiple use of the term 'bifurcation'.

(2) I think this isn't helpful on their part, but only is an issue to those of us who mix the FBI's rules with the scientific communities' methods.

(3) I would imagine Cummins & Midlo would add a paragraph relating to that misuse of a term if they were alive today.

(4) Using a bifurcation as the all-purpose fbi delta point does not always get the same results when using the scientific method. Both methods should always have the same results, or one of the methods is being incorrectly applied.

Patti... ; sounds to me that you made at least some progress in recognizing that the F.B.I. really has only one single 'label' available that could be used for describing a 'triradius': the word 'bifurcation'.

By the way, the implication of this point is that the F.B.I. has basically implicitely declared the word 'triradius' as ... outdated and completely irrelevant.


And this is also confirmed by internet statistics - a few weeks ago I did some research on internet statistics in the 'Google Scholar', and I found that since the 1980's the word 'delta' became gradually much more popular in scientific publications related to fingerprints. And in the past few years the word triradius is only still quite often used in the perspective of the palmar triradii (especially regarding the 'axial triadius').


Now regarding your points 1-3:

Ad 1) Sounds find with me.

Ad 2) Sure.

Ad 3) I think that Cummins & Midlo would actually have embraced the F.B.I. perspective, because it is really much more detailed. There is nothing 'misleading' (quoted from you words Patti) about the F.B.I.'s system. And the F.B.I. also does not 'misuse' (also quoted from your words) the word bifurcation.... especially since earlier today I have also identified how Loesch has started to describe explicitely that the idea of a perfect 'triradius' is basically only an imaginary concept - because in practice ridges do not develop straight, they always have a small 'curve' resulting in smaller or larger 'asymmetrical' shapes.

Ad 4) Well, all I can say is that in all 'complex' fingerprint examples that we have discussed so far I was able to find the same result (in terms of 'pattern type' & ridge count) with both methods - and after our lengthy discussions so far, Lynn was able to confirm my assessment for the Disney print and the two fingerprint examples from Kiwihands' hands.

Patti wrote:...

Loesch is not adding anything different in her description than has already been presented.

Well, Loesch basically only refers to the work of Penrose.

But I am not sure about what Penrose has said about how ridges in a 'triradius' manifest IN PRACTICE.

However, Loes does mention that in the work of C.A.B. Smith (1979) a 'cusp' was introduced as a third element next to the basic elements 'triradius' and 'loop'.


(Notice: the illustration below does not relate to fingerprint... but I think it does serve well as an example of how a 'cusp' can manifest with different shapes.)



I recognize how Smith's idea of a 'cusp' could very well also relate to how a 'triradius' typically manifests in practice - because due to the nature of how how fingerprints develop (in terms of 'forces' acting pressure in the skin)... I can visualize that when studying the details of any triradius in practice, it will very likely nearly alwas display a characteristic that is typically also seen in a 'cusp'.

So, regarding Loesch's comment about how a 'triradius' typically manifests in practice with an 'asymmetric' shape... I would not be surprized if that notification can not be traced back to passages in the work of Penrose.


And finally for the F.B.I. perspective: I can easily relate Smith's 'cusp' with what the F.B.I. calls a 'meeting of two ridges' (see page 9)

Martijn (admin) wrote:

Patti wrote:

Martijn (admin) wrote:

Patti wrote:

In fig. 139 you are looking at 3 ridges meeting at the center type of triradius. A Star triradius as I would describe it.

The FBI focal point delta is exactly the same location as Penrose etal. i.e. the middle of 3 ridges meeting at the center.

Patti, does your comment implicate that you now finally recognize as well my point?

(My point is: that in the F.B.I. approach the concept of a 'bifurcation' relates to a rather wide range of manifestation shapes - including examples which can very well be described in the scientific approach as a 'triradius')

(1) If you agree that the FBI interchanges a splitting bifurcation at times with one of the angles of the Penrose's F or G examples, then 'yes' I agree that the FBI has a multiple use of the term 'bifurcation'.

(2) I think this isn't helpful on their part, but only is an issue to those of us who mix the FBI's rules with the scientific communities' methods.

(3) I would imagine Cummins & Midlo would add a paragraph relating to that misuse of a term if they were alive today.

(4) Using a bifurcation as the all-purpose fbi delta point does not always get the same results when using the scientific method. Both methods should always have the same results, or one of the methods is being incorrectly applied.

Patti... ; sounds to me that you made at least some progress in recognizing that the F.B.I. really has only one single 'label' available that could be used for describing a 'triradius': the word 'bifurcation'.

Martijn (admin) wrote:

Patti wrote:

Martijn (admin) wrote:

Patti wrote:

In fig. 139 you are looking at 3 ridges meeting at the center type of triradius. A Star triradius as I would describe it.

The FBI focal point delta is exactly the same location as Penrose etal. i.e. the middle of 3 ridges meeting at the center.

Patti, does your comment implicate that you now finally recognize as well my point?

(My point is: that in the F.B.I. approach the concept of a 'bifurcation' relates to a rather wide range of manifestation shapes - including examples which can very well be described in the scientific approach as a 'triradius')

(1) If you agree that the FBI interchanges a splitting bifurcation at times with one of the angles of the Penrose's F or G examples, then 'yes' I agree that the FBI has a multiple use of the term 'bifurcation'.

(2) I think this isn't helpful on their part, but only is an issue to those of us who mix the FBI's rules with the scientific communities' methods.

(3) I would imagine Cummins & Midlo would add a paragraph relating to that misuse of a term if they were alive today.

(4) Using a bifurcation as the all-purpose fbi delta point does not always get the same results when using the scientific method. Both methods should always have the same results, or one of the methods is being incorrectly applied.

Patti... ; sounds to me that you made at least some progress in recognizing that the F.B.I. really has only one single 'label' available that could be used for describing a 'triradius': the word 'bifurcation'.

By the way, the implication of this point is that the F.B.I. has basically implicitely declared the word 'triradius' as ... outdated and completely irrelevant.


And this is also confirmed by internet statistics - a few weeks ago I did some research on internet statistics in the 'Google Scholar', and I found that since the 1980's the word 'delta' became gradually much more popular in scientific publications related to fingerprints. And in the past few years the word triradius is only still quite often used in the perspective of the palmar triradii (especially regarding the 'axial triadius').


Now regarding your points 1-3:

Ad 1) Sounds find with me.

Ad 2) Sure.

Ad 3) I think that Cummins & Midlo would actually have embraced the F.B.I. perspective, because it is really much more detailed. There is nothing 'misleading' (quoted from you words Patti) about the F.B.I.'s system. And the F.B.I. also does not 'misuse' (also quoted from your words) the word bifurcation.... especially since earlier today I have also identified how Loesch has started to describe explicitely that the idea of a perfect 'triradius' is basically only an imaginary concept - because in practice ridges do not develop straight, they always have a small 'curve' resulting in smaller or larger 'asymmetrical' shapes.

Ad 4) Well, all I can say is that in all 'complex' fingerprint examples that we have discussed so far I was able to find the same result (in terms of 'pattern type' & ridge count) with both methods - and after our lengthy discussions so far, Lynn was able to confirm my assessment for the Disney print and the two fingerprint examples from Kiwihands' hands.

Martijn (admin) wrote:

Patti wrote:...

Loesch is not adding anything different in her description than has already been presented.

Well, Loesch basically only refers to the work of Penrose.

But I am not sure about what Penrose has said about how ridges in a 'triradius' manifest IN PRACTICE.

However, Loes does mention that in the work of C.A.B. Smith (1979) a 'cusp' was introduced as a third element next to the basic elements 'triradius' and 'loop'.


(Notice: the illustration below does not relate to fingerprint... but I think it does serve well as an example of how a 'cusp' can manifest with different shapes.)



I recognize how Smith's idea of a 'cusp' could very well also relate to how a 'triradius' typically manifests in practice - because due to the nature of how how fingerprints develop (in terms of 'forces' acting pressure in the skin)... I can visualize that when studying the details of any triradius in practice, it will very likely nearly alwas display a characteristic that is typically also seen in a 'cusp'.

So, regarding Loesch's comment about how a 'triradius' typically manifests in practice with an 'asymmetric' shape... I would not be surprized if that notification can not be traced back to passages in the work of Penrose.


And finally for the F.B.I. perspective: I can easily relate Smith's 'cusp' with what the F.B.I. calls a 'meeting of two ridges' (see page 9)

Patti wrote:

Martijn (admin) wrote:

Patti wrote:

Martijn (admin) wrote:

Patti wrote:

In fig. 139 you are looking at 3 ridges meeting at the center type of triradius. A Star triradius as I would describe it.

The FBI focal point delta is exactly the same location as Penrose etal. i.e. the middle of 3 ridges meeting at the center.

Patti, does your comment implicate that you now finally recognize as well my point?

(My point is: that in the F.B.I. approach the concept of a 'bifurcation' relates to a rather wide range of manifestation shapes - including examples which can very well be described in the scientific approach as a 'triradius')

(1) If you agree that the FBI interchanges a splitting bifurcation at times with one of the angles of the Penrose's F or G examples, then 'yes' I agree that the FBI has a multiple use of the term 'bifurcation'.

(2) I think this isn't helpful on their part, but only is an issue to those of us who mix the FBI's rules with the scientific communities' methods.

(3) I would imagine Cummins & Midlo would add a paragraph relating to that misuse of a term if they were alive today.

(4) Using a bifurcation as the all-purpose fbi delta point does not always get the same results when using the scientific method. Both methods should always have the same results, or one of the methods is being incorrectly applied.

Patti... ; sounds to me that you made at least some progress in recognizing that the F.B.I. really has only one single 'label' available that could be used for describing a 'triradius': the word 'bifurcation'.

By the way, the implication of this point is that the F.B.I. has basically implicitely declared the word 'triradius' as ... outdated and completely irrelevant.


And this is also confirmed by internet statistics - a few weeks ago I did some research on internet statistics in the 'Google Scholar', and I found that since the 1980's the word 'delta' became gradually much more popular in scientific publications related to fingerprints. And in the past few years the word triradius is only still quite often used in the perspective of the palmar triradii (especially regarding the 'axial triadius').


Now regarding your points 1-3:

Ad 1) Sounds find with me.

Ad 2) Sure.

Ad 3) I think that Cummins & Midlo would actually have embraced the F.B.I. perspective, because it is really much more detailed. There is nothing 'misleading' (quoted from you words Patti) about the F.B.I.'s system. And the F.B.I. also does not 'misuse' (also quoted from your words) the word bifurcation.... especially since earlier today I have also identified how Loesch has started to describe explicitely that the idea of a perfect 'triradius' is basically only an imaginary concept - because in practice ridges do not develop straight, they always have a small 'curve' resulting in smaller or larger 'asymmetrical' shapes.

Ad 4) Well, all I can say is that in all 'complex' fingerprint examples that we have discussed so far I was able to find the same result (in terms of 'pattern type' & ridge count) with both methods - and after our lengthy discussions so far, Lynn was able to confirm my assessment for the Disney print and the two fingerprint examples from Kiwihands' hands.

I think only you have labeled a triradius a bifurcation. The triradius is 3 ridges. The delta or triradial point is a 'focal point' at the center of these 3 ridges.

I don't think either of you have confirmed anything with the Disney prints other than none of the prints uploaded are of the quality to make absolute statements.

Patti, you must have forgotten my earlier quote from Craig A. Coppock's book (page 74):

"J - Triradius: an intersection of seperate ridges often found in the delta areas. A triradius is similar in appearance to a bifurcation yet, with a greater angle between the seperate ridge intersections."

http://books.google.com/books?id=7HMmmypL2DwC


And regarding your words:

"The triradius is 3 ridges. The delta or triradial point is a 'focal point' at the center of these 3 ridges."

Of course!

But regarding your earlier comments where you described the F.B.I.'s use of the word 'bifurcation' as 'misleading' + 'misusing'... Coppock's definition of a 'triradius' actually explicitely confirms that my conclusions is correct - because I am certainly not the first person who recognized that the F.B.I.'s multi-concept of a 'bifurcation' includes the typical variation shapes of how a 'triradius' typically manifests in practice.

So Patti, please be aware that if you 'reject' the green words above... then you do not only disagree with me, but then you are implicitely also rejecting some significant parts of the F.B.I. book & Coppock's book.

I hope you will give it another attempt to put everything in perspective.

Patti wrote:Martijn,
Lynn carefully explained to you that this comparison was only a visual, looks like, comparison. They are not describing a triradius as a bifurcation.

A " Y " shape looks similar to a shape 3 with ridges meeting at the center, especially if it is not symmetrical.

"J - Triradius: an intersection of seperate ridges often found in the delta areas. A triradius is similar in appearance to a bifurcation yet, with a greater angle between the seperate ridge intersections."

Martijn (admin) wrote:

Patti wrote:Martijn,
Lynn carefully explained to you that this comparison was only a visual, looks like, comparison. They are not describing a triradius as a bifurcation.

A " Y " shape looks similar to a shape 3 with ridges meeting at the center, especially if it is not symmetrical.

Sorry, I don't understand what you are saying (since you did not specify to which comment of mine you made that response) ...

Patti, are you suggesting that Lynn made such a comment after I earlier introduced the quote from Coppock's book?

"J. Triradius (An intersection of seperate ridges often found in the delta areas. A triradius is similar in appearance to a bifurcation yet, with a greater angle between the seperate ridge intersections.)"

You seem to have completely misinterpreted this Martijn. He's just saying that a triraidus LOOKS SIMILAR TO a bifurcation, but with wider angles.
That's as far as the similarity goes.

Earlier on the same page he states that a bifurcation is a dividing ridge.
Here he says a triradius is an intersection of ridges. An intersection is where lines meet or cross.
Elsewhere a bifurcation is variously described as a forking ridge, a splitting ridge.A bifurcation is not the same thing as a triradius.