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Joaquín Fonollosa

Geometría fabrorum

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3 hours ago, David Beard said:

Hi Jezzupe:

One these points, please note that the things I'm reporting observed are not fancy or mystically motivated at all.  Nor do they show any real connection to fancier large ideas like musical harmony, Fibonanci, nor Pythogorean philosophy.    What my observations report is just a very flat footed and practical workshop method, requiring nothing more than simple divider use.

 

And we can observe some difficulties in these methods 'jumping' communities'.   When we see Brescians begin to imitate the new successful Amati volute style, we see them struggle with it.

Be all evidence, these are practices that did pass individual to individual, and most easily within a cohesive community.

Not 'illuminati', just fathers, sons, and apprentices.

Keep it simple.

What? Mozart and his dad were in the Illuminati, wasn't good enough for him, he wanted his own private Grotto :lol:

All I can say is as a contractor I use ratio all the time in practical application as well as in luthier, so I agree that is/was used, quite a bit.

"Doh, shucks I was supposed to cantilever the house off the cliff 1/3 not 2/3's , clients not gonna like this' 

 

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Ok. I'm going to settle down to the post I intended to make when I logged on today.

 

I want to get at ideas of curvature and how curvature acts differently in 'circle geometry' and in 'bent sticks' or 'spline' curves.

 

There are different approaches to 'curvature', but the basic idea is that a small bit of some smooth curve will either be straight or curved.  If it's curved, then that little bit of curve will match up with a bit from some circle.  And we'll be able to say the curve bit and the circle both have the same 'curvature'.     Now one approach is to match these curvatures up with numbers that reflect how 'off straight' the curve is.  So in this approach, a straight line would have curvature a curvature of zero, and the small the circle with matching curve, the higher the curvature at a spot in our curve.

The other approach more directly associates curvature with the matching circles.   We can use the radius of the matching circle to represent the curvature.   In this approach, a straight bit has an infinite curvature as it would take an infinite circle to match a bit of straight line.

We should also note the curvatures can easily encompass a notion of directionality also.  For our purposes, we will again use the associated circle and radius.   Notice that the radius will always be perpendicular to the curve at the point where we're measuring radius.

A simple example:

1542248868_curveandcurvature.thumb.jpg.a1218fbd9c52cf6cc70fd1794852ec11.jpg

 

We can see that the 'curvature' changes considerable through the run of this curve.  But we can ask about the specific curvature at any spot along the way.

To measure at a particular point, we seek a tangent circle with matching curvature at the spot we want to measure.

1185813080_curvepoint.thumb.jpg.9a9e42d56901e5d94650422cf36a272d.jpg

Now, if we had a mathematical formula for the curve, then we could theoretically use limits to determine a unique and ideal match of tangency and curvature.   But using physical or geometric analysis, are matching will always be somewhat imperfect.  And there will actually be a small range of good matching for any level of accuracy we can achieve.

1320663409_curvatreaccuracy.thumb.jpg.2224bb9cced9cfaf906ac45b099a9b0c.jpg

 

In any event, our best match can be summarized in the perpendicular radius and center from the point we are testing.

940958704_curvatureradiusfromonepoint.thumb.jpg.72ff7b7d9cc6a916c7a6d887548c8d6c.jpg

 

And we can use this approach to test many points on the curve, and develop a picture of the curvatures in this shape:

574133582_curvaturestudy.thumb.jpg.b0cf79870c0eeb07e797b842c96381f7.jpg

 

So this a curve of unknown actual origin that I found on the internet.   It does not represent directly either simple spline bending nor circle geometry.

For the purpose of studying instruments, it seems that three kinds of shape geometry are emerging as most interesting.   One is pure geometry of circles and lines.   The second is the geometry of spline bending under stress or control points.   The third we haven't directly mentioned yet, but it's obviously relevant to the discussion.  And that would be the shapes of spline or similar when plastically bent.   That is for example when a rib is permanently bend with heat and a bending iron for example.   These curves tend to be less simple and pure than the smooth shapes gotten by stressing an elastic spline to follow a limited number of controlled points, or perhaps also constraining its length as Marty does.   These curves tend to naturally distribute the stress as much as possible, while the actual heat bending tends to accumulate through many partial bends yield less pure and simple shapes. 

We can use curvature study to help us distinguish these various shapes.

The curve we just looked at was I suspect generated as a fine computer simulation of a plastically bent wire, or similar.   I suspect this because the shape includes a sort of typical flattening of curvature at the ends, and otherwise a sort of smoothly and continuously changing radius and center of curvature.   Or maybe I'm just imagining this.  It is sort of a subtle thing.

452657144_bentcurve.thumb.jpg.cec2247e902dfa6307728d23f5440569.jpg

 

 

 

 

 

 

**********

 

Okay,  Now let's look a curve that absolutely is circle geometry, because we make so.

This means our curve will consist entirely of sections of circle arc.  And, to be smoothly joined, all that is required is that point were two different arcs join lies on the line between their centers.   If we turn the requirement upside down, it means we can draw a bit of arc and stop at a point.  Then, to continue smoothly with a new radius, we just pick a new center along this stopping point's radius.

What then characterizes a 'circle geometry' shape is stretches of constant curvature radius and center, then sudden instant jumps to a new constant radius and center.   

This is different than shapes native to bent splines.   Another way to describe the 'circle geometry' shapes is that they are smooth only in that their first derivatives are continuous.  But there second derivatives consist of constants with abrupt jumps from one constant to the next.  And the third derivatives go are zero everywhere except the arc join points where the third derivative might be viewed as either infinite or undefined.    But with bent splines, natively these take shapes that are smoothly continuous in their first and second derivatives, and suspect mostly continuous also in their third.

So that is a very pointed difference between these curve families.

Here is an example curve truly made just from joining circle arcs.   And, of course, we don't have to guess in analyzing the curvatures.  We know the centers we used.  So the curvature radii shown are of course actually accurate in this illustration.

705717317_circlecurves.thumb.jpg.7b2aa6665c83dd91da75a182daa8a17f.jpg

 

Now, is this example typical of the 'circle geometry' found in Cremona work?   No.

This example is 'circle geometry', but not 'rational circle geometry'.  And, in deed, only 'rational circle geometry' is actually observed in Cremona work.    Such a conclusion is not necessarily evident from looking at only a small number of examples.   But, looking across the whole body of examples, it becomes evident that the best understanding of Cremona examples, and the understanding that runs consistently across the whole range of their work, is that the centers and radii lengths in Cremona work are always arranged in logical and rational relationships.

This rational aspect is absent in our first example of circle geometry.

**********

Lastly, we can look at how to create a circle geometry approximation for a random smooth curve.  And why we might consider an example natively circle geometry or not.

So back to our 'bent wire' curve.   Our curvature analysis here was not created from actually knowing this curve or how it was generated.   The curvature radii were estimated, one at a time, as 'best guesses'.

474285883_curvaturestudy2.jpg.360bd35ca6a30bc25171b9d48a43c49f.jpg

 

Notice that the tighter end of this looks much like the shape of a cBout or even the lower part of a violin.    We have tighter curvature joined by a more relaxed longer radius curve.    If our analysis were absolutely accurate, and if the shape were truly a circle geometry in origin, the centers would concentrate in three spots, joined by shared radii.   But here, the centers all sort of drift around in an interesting way.     Now, if we observe a true circle geometry shape of two smaller radii arcs joined by one larger radius arc, the inaccuracy of observation will still create a drift of centers and radii between the different concentration points.    However, we should roughly except more smooth and complete smearing of lengths and path between in real bent spline geometry, and more concentration and sudden jump between centers in real circle geometry shapes.   Though both patterns can appear very similar.

Here, also notice a nice kind of curved path traced by the radii and centers.  This again tends to suggest a more natural bending origin for the shape instead of a more human contrived origin in circle geometry.

 

2010485537_curvaturenaturalbend.thumb.jpg.88628990ffa7fb717dcdc0d645c458c8.jpg

 

 

Now, to seek a circle geometry approximation, we will look for a pattern of centers and join lines the somewhat approximates the observed curvature radii.

1291889870_curvatreestimate.thumb.jpg.3c76b096ec75ef1b660dd58d8f3c9172.jpg

 

 

Starting from this, I will try to make a good approximation with circle geometry.

1851402612_curvatretrace.thumb.jpg.67ff8c7d1930378a415a6cb2149c785a.jpg

 

This trace with circle geometry isn't horribly bad.  But it also doesn't suggest the curve is naturally circle geometry.   The best approximation available does not change its shape in a way the echos the original.  The paths of the two curves differ.  And there is not expectation of an improved trace without increasing the number of circles.

If a curve is naturally circle geometry, then the best fit will be the one using the original few circles that generated the shape.  Using exactly those correct circles will create the best fit and the truest match of paths.   When a trace is merely approximating a curve, then the path differences will reveal imperfections in the fit.  But the road to a better fit will be to use more smaller segments of arc.  If you use enough arc segments, then you will merely be tracing the curvature.   The fit will become good.  But the infinitely many small segments to get a better fit also indicate a non-native fit.

This curve is not circle geometry.

 

1339034610_curvaturecompare.thumb.jpg.5a44b22050ec3cb0cc4cfa32d45a186c.jpg

 

***********

The point of this is that the shape observed in Cremona work are often 'wood bending friendly', but they are always these things:

*  Circle and line geometry

* With the centers and sizings logically and rationally related to each other or parts of the instruments

and-

* Within the traditional recipes of geometry and ration for each feature.

 

These things are not for free.   Their consistent presence across the whole body of Cremona examples is strong evidence that the instruments and molds were intentionally designed and worked in these methods from the beginning.

Moreover, it also appears likely that all these things were inherited into Cremona making from earlier precedents.

 

 

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3 hours ago, David Beard said:

Ok. I'm going to settle down to the post I intended to make when I logged on today.

 

I want to get at ideas of curvature and how curvature acts differently in 'circle geometry' and in 'bent sticks' or 'spline' curves.

 

There are different approaches to 'curvature', but the basic idea is that a small bit of some smooth curve will either be straight or curved.  If it's curved, then that little bit of curve will match up with a bit from some circle.  And we'll be able to say the curve bit and the circle both have the same 'curvature'.     Now one approach is to match these curvatures up with numbers that reflect how 'off straight' the curve is.  So in this approach, a straight line would have curvature a curvature of zero, and the small the circle with matching curve, the higher the curvature at a spot in our curve.

The other approach more directly associates curvature with the matching circles.   We can use the radius of the matching circle to represent the curvature.   In this approach, a straight bit has an infinite curvature as it would take an infinite circle to match a bit of straight line.

We should also note the curvatures can easily encompass a notion of directionality also.  For our purposes, we will again use the associated circle and radius.   Notice that the radius will always be perpendicular to the curve at the point where we're measuring radius.

A simple example:

1542248868_curveandcurvature.thumb.jpg.a1218fbd9c52cf6cc70fd1794852ec11.jpg

 

We can see that the 'curvature' changes considerable through the run of this curve.  But we can ask about the specific curvature at any spot along the way.

To measure at a particular point, we seek a tangent circle with matching curvature at the spot we want to measure.

1185813080_curvepoint.thumb.jpg.9a9e42d56901e5d94650422cf36a272d.jpg

Now, if we had a mathematical formula for the curve, then we could theoretically use limits to determine a unique and ideal match of tangency and curvature.   But using physical or geometric analysis, are matching will always be somewhat imperfect.  And there will actually be a small range of good matching for any level of accuracy we can achieve.

1320663409_curvatreaccuracy.thumb.jpg.2224bb9cced9cfaf906ac45b099a9b0c.jpg

 

In any event, our best match can be summarized in the perpendicular radius and center from the point we are testing.

940958704_curvatureradiusfromonepoint.thumb.jpg.72ff7b7d9cc6a916c7a6d887548c8d6c.jpg

 

And we can use this approach to test many points on the curve, and develop a picture of the curvatures in this shape:

574133582_curvaturestudy.thumb.jpg.b0cf79870c0eeb07e797b842c96381f7.jpg

 

So this a curve of unknown actual origin that I found on the internet.   It does not represent directly either simple spline bending nor circle geometry.

For the purpose of studying instruments, it seems that three kinds of shape geometry are emerging as most interesting.   One is pure geometry of circles and lines.   The second is the geometry of spline bending under stress or control points.   The third we haven't directly mentioned yet, but it's obviously relevant to the discussion.  And that would be the shapes of spline or similar when plastically bent.   That is for example when a rib is permanently bend with heat and a bending iron for example.   These curves tend to be less simple and pure than the smooth shapes gotten by stressing an elastic spline to follow a limited number of controlled points, or perhaps also constraining its length as Marty does.   These curves tend to naturally distribute the stress as much as possible, while the actual heat bending tends to accumulate through many partial bends yield less pure and simple shapes. 

We can use curvature study to help us distinguish these various shapes.

The curve we just looked at was I suspect generated as a fine computer simulation of a plastically bent wire, or similar.   I suspect this because the shape includes a sort of typical flattening of curvature at the ends, and otherwise a sort of smoothly and continuously changing radius and center of curvature.   Or maybe I'm just imagining this.  It is sort of a subtle thing.

452657144_bentcurve.thumb.jpg.cec2247e902dfa6307728d23f5440569.jpg

 

 

 

 

 

 

**********

 

Okay,  Now let's look a curve that absolutely is circle geometry, because we make so.

This means our curve will consist entirely of sections of circle arc.  And, to be smoothly joined, all that is required is that point were two different arcs join lies on the line between their centers.   If we turn the requirement upside down, it means we can draw a bit of arc and stop at a point.  Then, to continue smoothly with a new radius, we just pick a new center along this stopping point's radius.

What then characterizes a 'circle geometry' shape is stretches of constant curvature radius and center, then sudden instant jumps to a new constant radius and center.   

This is different than shapes native to bent splines.   Another way to describe the 'circle geometry' shapes is that they are smooth only in that their first derivatives are continuous.  But there second derivatives consist of constants with abrupt jumps from one constant to the next.  And the third derivatives go are zero everywhere except the arc join points where the third derivative might be viewed as either infinite or undefined.    But with bent splines, natively these take shapes that are smoothly continuous in their first and second derivatives, and suspect mostly continuous also in their third.

So that is a very pointed difference between these curve families.

Here is an example curve truly made just from joining circle arcs.   And, of course, we don't have to guess in analyzing the curvatures.  We know the centers we used.  So the curvature radii shown are of course actually accurate in this illustration.

705717317_circlecurves.thumb.jpg.7b2aa6665c83dd91da75a182daa8a17f.jpg

 

Now, is this example typical of the 'circle geometry' found in Cremona work?   No.

This example is 'circle geometry', but not 'rational circle geometry'.  And, in deed, only 'rational circle geometry' is actually observed in Cremona work.    Such a conclusion is not necessarily evident from looking at only a small number of examples.   But, looking across the whole body of examples, it becomes evident that the best understanding of Cremona examples, and the understanding that runs consistently across the whole range of their work, is that the centers and radii lengths in Cremona work are always arranged in logical and rational relationships.

This rational aspect is absent in our first example of circle geometry.

**********

Lastly, we can look at how to create a circle geometry approximation for a random smooth curve.  And why we might consider an example natively circle geometry or not.

So back to our 'bent wire' curve.   Our curvature analysis here was not created from actually knowing this curve or how it was generated.   The curvature radii were estimated, one at a time, as 'best guesses'.

474285883_curvaturestudy2.jpg.360bd35ca6a30bc25171b9d48a43c49f.jpg

 

Notice that the tighter end of this looks much like the shape of a cBout or even the lower part of a violin.    We have tighter curvature joined by a more relaxed longer radius curve.    If our analysis were absolutely accurate, and if the shape were truly a circle geometry in origin, the centers would concentrate in three spots, joined by shared radii.   But here, the centers all sort of drift around in an interesting way.     Now, if we observe a true circle geometry shape of two smaller radii arcs joined by one larger radius arc, the inaccuracy of observation will still create a drift of centers and radii between the different concentration points.    However, we should roughly except more smooth and complete smearing of lengths and path between in real bent spline geometry, and more concentration and sudden jump between centers in real circle geometry shapes.   Though both patterns can appear very similar.

Here, also notice a nice kind of curved path traced by the radii and centers.  This again tends to suggest a more natural bending origin for the shape instead of a more human contrived origin in circle geometry.

 

2010485537_curvaturenaturalbend.thumb.jpg.88628990ffa7fb717dcdc0d645c458c8.jpg

 

 

Now, to seek a circle geometry approximation, we will look for a pattern of centers and join lines the somewhat approximates the observed curvature radii.

1291889870_curvatreestimate.thumb.jpg.3c76b096ec75ef1b660dd58d8f3c9172.jpg

 

 

Starting from this, I will try to make a good approximation with circle geometry.

1851402612_curvatretrace.thumb.jpg.67ff8c7d1930378a415a6cb2149c785a.jpg

 

This trace with circle geometry isn't horribly bad.  But it also doesn't suggest the curve is naturally circle geometry.   The best approximation available does not change its shape in a way the echos the original.  The paths of the two curves differ.  And there is not expectation of an improved trace without increasing the number of circles.

If a curve is naturally circle geometry, then the best fit will be the one using the original few circles that generated the shape.  Using exactly those correct circles will create the best fit and the truest match of paths.   When a trace is merely approximating a curve, then the path differences will reveal imperfections in the fit.  But the road to a better fit will be to use more smaller segments of arc.  If you use enough arc segments, then you will merely be tracing the curvature.   The fit will become good.  But the infinitely many small segments to get a better fit also indicate a non-native fit.

This curve is not circle geometry.

 

1339034610_curvaturecompare.thumb.jpg.5a44b22050ec3cb0cc4cfa32d45a186c.jpg

 

***********

The point of this is that the shape observed in Cremona work are often 'wood bending friendly', but they are always these things:

*  Circle and line geometry

* With the centers and sizings logically and rationally related to each other or parts of the instruments

and-

* Within the traditional recipes of geometry and ration for each feature.

 

These things are not for free.   Their consistent presence across the whole body of Cremona examples is strong evidence that the instruments and molds were intentionally designed and worked in these methods from the beginning.

Moreover, it also appears likely that all these things were inherited into Cremona making from earlier precedents.

 

 

Hey, I thought you said this wasn't gonna be complex :D I mean I was one of those sons of a father son construction company but I don't ever remember talking about this over dinner :lol:

I'll try to absorb this.

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Sorry.  I doubt that the old makers ever had to debate with a skeptic about whether or not they worked using dividers or just by bending the wood.   Discussions about how we can separate these possibilities through observations centuries later get complex.

But when we settle down to just working proportions and shapes by the traditional divider recipes, that is easy.

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Ok.   Here's another bit.

 

When we want to we can use a kind of empirical approach to begin an analysis of a shape.  

I'm going to use this to look at the Strad guitar.   Because the image quality is low, and because I don't have dozens of other analyzes of Strad guitars to draw understanding from, I have very little expectation about what exactly we might find in this guitar.   Though, being a Cremona and Strad product, I will be surprised if it doesn't turn out to use methods that are closely related to the violin methods.

I'm going to demonstrate a method that can help sort things out when you really have no idea what you might be looking at.   

The basic idea is to try and determine perpendiculars to the shape.   We know that the curvature radii lay along such lines.   With a fuzzy or indefinite image, or when viewing a damaged edge, estimating such perpendiculars isn't necessarily straightforward.    Maybe I've made this overly complicated. But what I did is use two thin lines as guides to tangency along the outer edge and along the purfling line.  These aught to generally agree.   Then I used a main line to estimate the perpendicular, and two side lines to say, 'certainly the prependicular falls within these bounds'. 

SO, here is one of my little test figures set against the fuzzy out line of the guitar's shape:

1176545179_anempiricalmethod.thumb.jpg.afafbe54509d8a179ba6206d980bb264.jpg

 

By repeating this process around the guitar outline, I got the following:1185848996_empirical1.thumb.jpg.d3677bcdd687644ff106722edc6f403f.jpg

 

To me, the pattern of this looks very familiar and like circle geometry typical. All very similar to violin stuff.

And here I've rough circle areas where I would expect circle geometry centers, and marked areas the appear to be straight line segments.

2094302434_empiricalappraoch.thumb.jpg.30722a6d561d50582e8c580327bbd5ee.jpg

 

This leads us rather directly to the following initial gross interpretation of the geometry present in this guitar.

1848022705_empirical2.thumb.jpg.43fe8cfd0b9a1e1246779d24abdb562b.jpg

 

 

And if we clean things up a bit, we find a cleaner fit with rational circle geometry.   However, the cBout radii appear to near to LB in diameter, but not exactly so.   Better fit to the actual sides shape appears somewhat larger than LB on one side, and somewhat smaller on the other.   Perhaps this is where the inexactness of side bending was absorbed in the guitar design??

 

236110468_empiricalcleaned.thumb.jpg.b4b89a3fb19ef6968e4396233028f55b.jpg

 

This has been an interesting exercise.  But not too much should be read into on example.  If we had dozens of such examples showing essential the same patterns and methods, then we could begin to say something about conclusions and methods.

Happily, the body of Cremona violin examples do allow such many dozens of examples.

 

 

empirical cleaned.jpg

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David, following my experience,  the way you work is too approximative to convince, for example we do not agree about the measurement of the easiest arc to measure !!

for me the black circle is the better one. Why do you persit to prefer the red circle  against the evidence?  Is it because that match your theory of the "cremonese traditional geometry" ?

It is not a correct approach for me.

Again, my conviction is that circles has been used rather than ellyps but it is difficult to prove. May be I miss something It seems to me that your geometrical method  of research could  generate more approximations than the original outline itself! 

My opinion is that the best way to know what is the value of this technique (bendind) is to try it. I have asked to Marty to give me the process to draw the strad guitar and until now the only response I get is that it is better to use a carbon rod....  For me I understand that the quality of the shape will depend of the quality of the material. How I can manage the quality of the rod with the form- we will see 


What I know for sure, it is that the setting of the main dimensions done, the drawing of the shape with a compas take me less that 60 seconds
(I can easily give the demonstration of that)
How many time it will take with the carbon rod?

We will see if the supposed efficiency of the method can be accepted as a good argument against the use of the compass.

 

 

1775388063_Capturedecran2019-10-03a10_34_58.png.f7cf126b5bfae6bb94d2d3a87c3eded0.png

Using the most accurate method to research the centers , their measurements are less that the third of the width in the both sides

637536580_Capturedecran2019-10-07a14_27_26.thumb.png.79d066fb09f23d85de77fb79ddc89409.png

 

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Great writing David! I guess this stuff can be too technical for many folks around here.

What SW are you using (I guess Photoshop/Illustrator combo?).

BTW, there are tools in most CAD software packs for curve analysis that will display the local radii of any curve just like you do. It is very important in some design areas to know what type of curvature you have i.e. if your curves (or surfaces derived from them) are simple arc geometry (that would be called tangent continuous) than it will show in light reflections (assuming they are perfectly made) even though they are smooth to "hand".

If the local radii of joining curves "transition smoothly" from one curve to another than you have curvature continuous shape. I  guess that any naturally bent piece of wood will show curvature continuous curvature (curves like parabola, catenary, ellipse etc will be as well curvature continuous)

Sure Strad forms were hand made and the violin around them as well so the geometry will be a bit blurred but as seen in Davids renderings of the guitar the similar radii at spots are stil just too clear to be purely random. And the multiply repeating ratios showing among so many examples would be highly improbable being just random occurence. Statistically I dare to speculate (I don't have tme to do any closer approximation) the probability of drawing new violin shape freehand or using just bent sticks for curves (without tracing existing shape) will contain such ratios and circles with probability smaller than 5%, and if you repeat that several times (think different strad forms or other instruments) the probability will go rapidly down... that would pretty much statistically prove that circle geometry and simple ratios of radii were at the origins of these shapes.

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4 hours ago, HoGo said:

the probability of drawing new violin shape freehand or using just bent sticks for curves (without tracing existing shape) will contain such ratios and circles with probability smaller than 5%, and if you repeat that several times (think different strad forms or other instruments) the probability will go rapidly down... that would pretty much statistically prove that circle geometry and simple ratios of radii were at the origins of these shapes.

"Will go rapidly down..". Yes that is exactly what's happen at the end of the Cremonese golden age - As soon as they start to build their form from existing ribs garland rather than an original mold 

the decline is very quick more and more straight lines appears before the corners which is the sign of the increasing of a natural tendency of a bent rib

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5 hours ago, francoisdenis said:

>

>

My opinion is that the best way to know what is the value of this technique (bendind) is to try it. I have asked to Marty to give me the process to draw the strad guitar and until now the only response I get is that it is better to use a carbon rod....  For me I understand that the quality of the shape will depend of the quality of the material. How I can manage the quality of the rod with the form- we will see 


What I know for sure, it is that the setting of the main dimensions done, the drawing of the shape with a compas take me less that 60 seconds
(I can easily give the demonstration of that)
How many time it will take with the carbon rod?

We will see if the supposed efficiency of the method can be accepted as a good argument against the use of the compass.

>

 

 

I'm sorry for not helping more.  But if you play around a little you will quickly learn all you need to know.  As with any drawing method you first have to chose your length of the instrument and bout widths. 

This is one of the advantages of using bent ribs--you don't need a lot of detailed instructions.  People in Spain, Italy, Germany, France... don't need translations.  The wood doesn't know where it is or what century it is.

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34 minutes ago, Marty Kasprzyk said:

I'm sorry for not helping more.  But if you play around a little you will quickly learn all you need to know.  As with any drawing method you first have to chose your length of the instrument and bout widths. 

This is one of the advantages of using bent ribs--you don't need a lot of detailed instructions.  People in Spain, Italy, Germany, France... don't need translations.  The wood doesn't know where it is or what century it is.

Ok I will try and will come back to you- but your advise is carbone fiber or wood?

 

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28 minutes ago, francoisdenis said:

Ok I will try and will come back to you- but your advise is carbone fiber or wood?

 

the advantage of CF is that it is more resistant to breaking if the "wrong" amount of force or pressure is applied.

one of the ways to make this easier is to use a piece of material that is well longer than you need , once placed over a paper template {if you are trying to reconstruct a shape} you can simply use the template to set the over all length of the instrument , then using the clamps at each end you can shorten or lengthen your rod/strip to meet the length requirements.

that being said any material that will bend yet have a tendency to revert to its original state will work.....

I feel the advantage of this method is dependent on what one is doing.

Meaning if you are a person who for what ever reason needs/wants to make a new template every time, for the same model, then I suppose getting down your compass drawing skills as you are suggesting is a great and fast way to repetitively draw form scratch a particular shape/model.

Whereas the REAL benefit of this method is for people who 1. design there own shapes and models, 2 like to use their eye to determine whatever final shape  it is they want/like.

In music there are people who play "copy tunes" , a large portion of "classical"music is "copy tunes" ie.people playing music written by someone else.

then there are those who play "originals" , which is simply playing music that is their own compositions.

I feel instruments are the same thing, and that this method is great for people who "come up with" their own shapes, like myself.

 

 

 

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13 hours ago, David Beard said:

>

I want to get at ideas of curvature and how curvature acts differently in 'circle geometry' and in 'bent sticks' or 'spline' curves.

>

A simple example:

1542248868_curveandcurvature.thumb.jpg.a1218fbd9c52cf6cc70fd1794852ec11.jpg

What then characterizes a 'circle geometry' shape is stretches of constant curvature radius and center, then sudden instant jumps to a new constant radius and center.   

This is different than shapes native to bent splines.   Another way to describe the 'circle geometry' shapes is that they are smooth only in that their first derivatives are continuous.  But there second derivatives consist of constants with abrupt jumps from one constant to the next.  And the third derivatives go are zero everywhere except the arc join points where the third derivative might be viewed as either infinite or undefined.    But with bent splines, natively these take shapes that are smoothly continuous in their first and second derivatives, and suspect mostly continuous also in their third.

So that is a very pointed difference between these curve families.

 

 

 

 

 

 

I hate to be a jerk about all this.                   

But we haven't discussed the reasons why bent splines look so attractive compared to circle constructions.  The first derivative of a curve is the slope of the curve at the tangent points along the curve. The second derivative is the local curvature along the curve which is a measure of how the first derivative is changes along the curve.  The third derivative is how the second derivative or curvature changes along the curve.

David mentioned that with bent splines have smooth changes in the third derivative--there are no abrupt changes in the curvature--the changes are smooth and continuous.  These always look beautiful and graceful to me.

I think the curves of the upper and lower bouts of a violin and the entire guitar shape also have a continuously and smoothly changing radius of curvature.  This can't be done with circle constructions.

Attached are a bent wood rib and a bent wire overlays on David's curve example.  I think these simple bend shapes are more attractive because these materials naturally bend into shapes that avoid sudden changes in curvature.

If you are studying motion.  The first derivative is your velocity at a particular time.  The second derivative is acceleration or how fast your velocity is changing. The third derivative is jerk or how fast your acceleration is changing.  Jerks can be unpleasant.

IMG_2600small.jpg

IMG_2601small.jpg

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9 hours ago, David Beard said:

 

 

empirical cleaned.jpg

 

Well, this looks familiar. Here it is one more time.  I think my step-by-step explanation from a few pages ago is easier to understand though.  Anyone can play along with a compass and straightedge :)  No computer required.

 

 

 

pla_13.thumb.png.0b0c98be8ac59e40977f8ee97d9ca3e7.png

 

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4 minutes ago, Kevin Kelly said:

 

Well, this looks familiar. Here it is one more time.  I think my step-by-step explanation from a few pages ago is easier to understand though.  Anyone can play along with a compass and straightedge :)  No computer required.

 

 

 

pla_13.thumb.png.0b0c98be8ac59e40977f8ee97d9ca3e7.png

 

Looks pretty straight forward to me, again, I'm not really sure what the differences in opinion between you, David and Denis is

It's pretty clear that one can use ratios, along with "circles" and a straight edge to make a 98% complete shape where only a wee"connecting of the dots" has to happen.

I do wish someone would summarize what seems to be the 3 guys differences between their approaches , We have Denis, we have David and we have Kevins, we have lots of disagreeing .

For example, I'm not sure if this was the way it was done,but regardless it works fine, so I'm not sure why someone would call this method "wrong" 

 

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One difference in approach only emerges once you pass through the opening gates.    We haven't much done that yet.   Mostly we stuck in a sword battle at the castle gates, with bend sticks and volute/spiral blocking the entrance.

Once you go in the castle, things begin to look different.  And we can begin to see in more complete detail.

On difference that emerges is that the Cremona work is not symmetric or ideal.    So that works against the continuing success of methods the work every detail out ideal and ahead of time.

Countless details show us the the Cremona work actual builds off of the variances that arise during building.    The asymmetries of corner work are one of the most obvious of these cases.  But there are a great many.

 

A main difference among our approach is that I kept asking 'how far does this geometry stuff go?"     My approach strips away the aspects that prevent us from following the asymmetric aspects of Cremona work.  And it pushes forward to find the geometry and ratio recipes behind all the features instead of just some.

Also, I've put a great emphasis on scouring out the aspects that apply to only a few examples.  And I've tried very hard to find the patterns and variations that put the full range of Cremona work under one cohesive understanding.

Obviously I'm partisan.  But that is my take on how these three approaches primarily differ. 

However, in my eyes, these three approaches are much more in consonance than in dissonance.

 

 

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42 minutes ago, Marty Kasprzyk said:

 

I hate to be a jerk about all this.                   

But we haven't discussed the reasons why bent splines look so attractive compared to circle constructions.  The first derivative of a curve is the slope of the curve at the tangent points along the curve. The second derivative is the local curvature along the curve which is a measure of how the first derivative is changes along the curve.  The third derivative is how the second derivative or curvature changes along the curve.

David mentioned that with bent splines have smooth changes in the third derivative--there are no abrupt changes in the curvature--the changes are smooth and continuous.  These always look beautiful and graceful to me.

I think the curves of the upper and lower bouts of a violin and the entire guitar shape also have a continuously and smoothly changing radius of curvature.  This can't be done with circle constructions.

Attached are a bent wood rib and a bent wire overlays on David's curve example.  I think these simple bend shapes are more attractive because these materials naturally bend into shapes that avoid sudden changes in curvature.

If you are studying motion.  The first derivative is your velocity at a particular time.  The second derivative is acceleration or how fast your velocity is changing. The third derivative is jerk or how fast your acceleration is changing.  Jerks can be unpleasant.

IMG_2600small.jpg

IMG_2601small.jpg

Yes, yes.

You've just explained why you prefer the shapes you prefer.   

However, the evidence shows that the Cremona masters didn't follow your advice.  Instead they worked a traditional ration circle geometry that is not bent spline shaped, but only bending friendly and somewhat reminiscent of bent spline shapes.

Go figure!    Maybe they should have followed you advice.  But they didn't.

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3 hours ago, Marty Kasprzyk said:

 

I hate to be a jerk about all this.                   

But we haven't discussed the reasons why bent splines look so attractive compared to circle constructions.  The first derivative of a curve is the slope of the curve at the tangent points along the curve. The second derivative is the local curvature along the curve which is a measure of how the first derivative is changes along the curve.  The third derivative is how the second derivative or curvature changes along the curve.

David mentioned that with bent splines have smooth changes in the third derivative--there are no abrupt changes in the curvature--the changes are smooth and continuous.  These always look beautiful and graceful to me.

I think the curves of the upper and lower bouts of a violin and the entire guitar shape also have a continuously and smoothly changing radius of curvature.  This can't be done with circle constructions.

Attached are a bent wood rib and a bent wire overlays on David's curve example.  I think these simple bend shapes are more attractive because these materials naturally bend into shapes that avoid sudden changes in curvature.

If you are studying motion.  The first derivative is your velocity at a particular time.  The second derivative is acceleration or how fast your velocity is changing. The third derivative is jerk or how fast your acceleration is changing.  Jerks can be unpleasant.

IMG_2600small.jpg

IMG_2601small.jpg

This is just showing example of the second derivative with abrupt change. The original curve has abrupt change in curvature (radii), the third derivative in that spot doesn't exist, so your wire cannot aproximate it close enough without adding a node in the "flat spot". So you need at least two connected splines for that curve.

When I have the time I will try to trace the guitar or some good violin into Rhino and show its curvature analysis. Where can I find the source pic of the guitar and what are the sizes for correct sizing?

 

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On 10/07/2019 at 3:11 PM, HoGo said:

This is just showing example of the second derivative with abrupt change. The original curve has abrupt change in curvature (radii), the third derivative in that spot doesn't exist, so your wire cannot aproximate it close enough without adding a node in the "flat spot". So you need at least two connected splines for that curve.

When I have the time I will try to trace the guitar or some good violin into Rhino and show its curvature analysis. Where can I find the source pic of the guitar and what are the sizes for correct sizing?

 

Most photos I get on the internet are small pixel size and don't have good resolution when blown up to large sizes.

A good a high resolution photo of the 1688 Stradivari Hill guitar can be purchased from the Ashmolean Museum:  ashmoleanprints.com                      accession number WA1939.32

The National Music Museum at the University of South Dakota has photos of the 1700  Stradivari Rawlins guitar.  They may be able to supply a high resolution photo to you.

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9 hours ago, francoisdenis said:

My last post has been deleted  :((...any reason for that?

I was wondering where that went...I had gone back to reread it and "poof, gone" 

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4 hours ago, jezzupe said:

I was wondering where that went...I had gone back to reread it and "poof, gone" 

Is it because there was a link to  a Wiki article? 

https://fr.wikipedia.org/wiki/Anse_de_panier

Unfortunately only in french - I took time to resume and translate some parts...:(

history, comparaison between ellyps and "anse de panier"  advantage and disadvantage (can we use "basket handle" in english ?)

with some remarks about the practice  " The discontinuity of the shape can be hampered by unsightly angles that stoneworkers are not always able to correct"

about the drawing process, I am struck that geometry remains analytic. Constructions derive from the solution of equations

530098587_Capturedecran2019-10-09a20_26_30.png.3dbad7dbe0b0469a668201e0f67a0754.png

they seem to ignore the elegant solution based on the intersection of the same circle....

104880380_Capturedecran2019-10-08a10_08_10.thumb.png.f4521c23d284d6ceca6cea1dd601f2c6.png

like some of us here....

 

 

 

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The maestronet server crashed and likely was refreshed from backup so some posts got lost due to that  - actually I was just writing response to one of those when the site went down before I could post it.

5 hours ago, Marty Kasprzyk said:

Most photos I get on the internet are small pixel size and don't have good resolution when blown up to large sizes.

A good a high resolution photo of the 1688 Stradivari Hill guitar can be purchased from the Ashmolean Museum:  ashmoleanprints.com                      accession number WA1939.32

The National Music Museum at the University of South Dakota has photos of the 1700  Stradivari Rawlins guitar.  They may be able to supply a high resolution photo to you.

For this simple experiment  better internet photos are sometimes enough, but we ned real size to make sure the width/length ratio is correct to start with (othewise we would get ellipse geometry instead of circle).

Many years ago I drew set of F-5 mandolin drawings using mostly internet pics and few basic measurements as source. Later I got more first hand info and exact measurements of instruments (Including CT scan) and even original mould tracings and found out that I was surprisingly close (well within woodworking error or wood shrinkage/expansion).

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16 hours ago, HoGo said:

For this simple experiment  better internet photos are sometimes enough, but we ned real size to make sure the width/length ratio is correct to start with (othewise we would get ellipse geometry instead of circle).

You are right - following my experience, the quality of an analysis depends on the quality of the info

This kind of bad pictures  (as the Strad guitar) ought to be considered cautiously wether we don"t have the original measurements 

 

 

 

 

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On 9/14/2019 at 11:49 PM, francoisdenis said:

Peter-K 

That 's probably a part of the true story! 

Nevertheless,  don't forget that the climax of the creativity in instruments making occured from 1450 to 1550 and the violin is only one of the latest 

invention of this incredibly creative period. The fact that all these other inventions that we know only from painting or engraving 

have disapeared did not gave to the violin a label of superiority for the design

Sorry about the late response!

I follow the thread when I have time, i think that the Amati legacy should get all the attention - the rest is (as I wrote - copycat)

You wont't find the perfection in Strad/del Gesu as they = optimization (squeezing/extending) for "power" etc...

 

 

 

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On 10/6/2019 at 9:15 PM, David Beard said:

Ok. I'm going to settle down to the post I intended to make when I log

 

How difficult do you want to make this ?   Yes,  curvature is by definition one divided by the radius of curvature.  And whatever you want to represent can be done in polar coordinates which you can understand if you google it.

You can make a radius of curvature a function of the angle of rotation.  It is not necessary to do all of this fudging around with shapes.   You can define a curve in polar coordinates and find some simple graphing program to give the image.

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