French vs. Bezier Curves

[Vyrolan]

Vyrolan:

 

http://www.hindawi.com/journals/jam/2013/732457/abs/ 

 

I know I look absurdly young (especially in the last profile picture) but I'm 27, and yes, I do active research in this area (albeit unpublished, it's part of my job).

 

My apologies if I came off as dismissive towards you.   I was merely responding to the question since it seemed to be directed towards me since I had done the air-quoting of "research".  I have no doubts there's exhaustive research on the topic and that you are well-read and knowledgeable on the topic; it was not my intention to belittle either.   I just think there's a broad range for the spectrum of formality one takes towards their curves.   You are probably somewhat to the extreme of formal end where you want to apply mathematics and make it "correct"...others are likely to the extreme informal end where they just make it "look right".   Often time I think you find very mathematical people that wish they were more "artistic" and could just make it look right rather than following a French curve or whatever.  To each his own...  I, for one, have found this thread rather interesting because I too am a very mathematical person and have often wondered about what makes the curve look correct, and fortunately for me I have people like you to provide those answers. =)

 

 

 

Im pretty sure this is why the lord made poplar. 

 

See PB is on the informal end as well. =)

[Joe Eagar]

Age has nothing to do with this, but rather backing up what you are stating.  I get the math behind it, I don't think there are many here would disagree that you get two different types of curves produced.  My point is what published "market research" states one is preferable over the other.  As I stated earlier, it really depends on the application on which type of curve is used.  

 

I linked to said research (here's another one, see first paragraph of page 2 -> http://mrl.nyu.edu/~elif/thesisprop/FarinS89.pdf ).  And yet, you are still using scare quotes.

 

Frankly, I don't think there are any applications where the curvature profile of a Bezier curve is preferable to spirals, or even B-splines (which were invented precisely to replace Bezier curves in industrial design).  This isn't a matter of context, nor is it a matter of opinion.  You might make that argument where other polynomial curves are concerned, but not with Bezier (Bernstein) polynomials.

[Joe Eagar]

  Often time I think you find very mathematical people that wish they were more "artistic" and could just make it look right rather than following a French curve or whatever.  To each his own...  I, for one, have found this thread rather interesting because I too am a very mathematical person and have often wondered about what makes the curve look correct, and fortunately for me I have people like you to provide those answers. =)

 

You're misunderstanding me.  I spent years being frustrated by the limitations of bezier curves and surfaces before I started this research.  Why?

 

Bad math limits the artist.  Think of it this way: the artist has an image of a shape in his head.  He tries to build it with curves, but those curves cannot represent that shape.  It isn't mathematically possible.  So what does the artist do?  He turns into a human constrained optimization machine.  He learns, through trial and error, to approximate his desired shape with methods that are remarkably like how you would have a computer do it.

 

A polygonal box-modeler, for example, operates in a manner remarkably similar to a multi-grid, hierarchical Guess-Seidel solver.  

 

I'm not saying artists should worry more about math.  I'm saying they should use tools that let them worry about it less.  Someone who doesn't know the mathematical reason as to why their curve looks bad, or why it's so hard to model certain parts of the human body with 3D surfaces, is still worrying about math; they just don't know it.

[Eric.]

I understand it's your field of study, Joe, so you're interested in the minutiae of mathematics...but I think you're WAY over-complicating things here and creating a crisis that doesn't really exist in the day-to-day activities in the average woodworker's shop.  If you're an architect designing some multi-billion dollar building, then yeah, you better concern yourself with the problems that your computer models might pose.  But we're cavemen with strings and nails and pliable sticks and pencils...if a curve looks good, it is good, the math be damned.  I appreciate your passion, but I think it belongs either on an engineer's or architect's forum.  Of course, I glazed over just reading the first post...others might be enjoying the brain damage you're inflicting upon them.   Either way, carry on...I'm gonna go make a compound curve with a five gallon bucket and a can of paint.

[Tpt life]

Thank you for that giggle

[Freddie]

I have a harder time making a line look straight than making it look curvy. Is there a formula to fix me?

Clamp yourself to a 6' level, leave overnight and PM us in the morning.

[phinds]

Thanks for the post and explanation Joe Edgar ... very cogent discussion. Like Eric, I absolutely see a "good" and a "bad" curve and your explanation for why each is each is excellent. I had not previously been aware that Bezier curves produced such inferior results.
 

[wtnhighlander]

From the first research paper referenced by Joe Eagar:

"This curve preserves the monotonicity of curvature and is said to produce visually pleasing curves."

Can anyone clarify exactly who says this?

[Joe Eagar]

From the first research paper referenced by Joe Eagar:

"This curve preserves the monotonicity of curvature and is said to produce visually pleasing curves."

Can anyone clarify exactly who says this?

 

German auto manufactures, I assume  .  It seems like the sort of research the Germans would be good at.

[Joe Eagar]

I understand it's your field of study, Joe, so you're interested in the minutiae of mathematics...but I think you're WAY over-complicating things here and creating a crisis that doesn't really exist in the day-to-day activities in the average woodworker's shop.  If you're an architect designing some multi-billion dollar building, then yeah, you better concern yourself with the problems that your computer models might pose.  But we're cavemen with strings and nails and pliable sticks and pencils...if a curve looks good, it is good, the math be damned.  I appreciate your passion, but I think it belongs either on an engineer's or architect's forum.  Of course, I glazed over just reading the first post...others might be enjoying the brain damage you're inflicting upon them.   Either way, carry on...I'm gonna go make a compound curve with a five gallon bucket and a can of paint.

 

I just felt bad catching up on the podcasts.  I felt bad after hearing Shannon/Marc/Matt express shame for using "old-school" curve layout tools.  I want to make sure everyone knows said tools are far superior to most computer software.

[Joe Eagar]

Thank you for that giggle

Any chance you can YouTube demo the program you suggest Joe while interacting with Sketchup?

 

I don't really use SketchUp.  I'm curious, are people printing out paper templates, or are they using (real-world) splines to transfer what's on the computer screen to a piece of wood?

[wtnhighlander]

I don't really use SketchUp. I'm curious, are people printing out paper templates, or are they using (real-world) splines to transfer what's on the computer screen to a piece of wood?

I use Sketchup to validate dimensions and joinery. I never use it to make templates. In fact, almost all of my final design and layout is done with a pencil right on the wood. No plans, other than the basic idea and general dimensions in my head. Short of high-qualty sheet goods (maybe), it seems that the material always varies too much for plans to be af any real use.

[pghmyn]

I understand it's your field of study, Joe, so you're interested in the minutiae of mathematics...but I think you're WAY over-complicating things here and creating a crisis that doesn't really exist in the day-to-day activities in the average woodworker's shop.  If you're an architect designing some multi-billion dollar building, then yeah, you better concern yourself with the problems that your computer models might pose.  But we're cavemen with strings and nails and pliable sticks and pencils...if a curve looks good, it is good, the math be damned.  I appreciate your passion, but I think it belongs either on an engineer's or architect's forum.  Of course, I glazed over just reading the first post...others might be enjoying the brain damage you're inflicting upon them.   Either way, carry on...I'm gonna go make a compound curve with a five gallon bucket and a can of paint.

I'd have to agree here. Curves are such an essential part to design, both for aesthetics and functionality. A combination of the two are even better.

 

But for this particular application, the in depth look at curves and the mathematical curvature are too much for my taste. Not talking down to your arguments, because anything including math and design will peak my interest.

 

Woodworking is a form of art. It doesn't matter how you conceive it, design it, build it, or finish it. There will always be more than one way to do it. That is what makes this medium so amazing to work with.

 

Although, I must say, I did like looking back into the concept of curvature. It's been a little while since derivations including that have been on my paper

[Eric.]

Once upon a time in a land far, far away about 100 miles from here, near the beginning of my semester of Calculus II, I was sitting in class and I realized that everything I was learning there meant absolutely nothing to me and always would.  I put my book in my bag, got up, walked out, and never thought about math ever, EVER again.  And I intend to keep it that way.

 

[krtwood]

I don't really use SketchUp.  I'm curious, are people printing out paper templates, or are they using (real-world) splines to transfer what's on the computer screen to a piece of wood?

 

I have a small cnc machine, so sometimes I will work out a part in CAD and machine a template or the part itself directly from there.  Other times I will work out what I want on paper, scan it, vectorize it, and then cnc it from there.  When I'm working on a curve in CAD I will usually have plenty of control points and I'll be tweaking the curve in more ways than just relying on the handles from two control points.  I like bringing the template into the computer because a) I don't have to fuss around with getting it sanded just right and I can throw away the physical template but still reproduce it again exactly if i need it later.  But I will also sometimes print out paper templates for things.  It just depends on the situation.

 

As far as the "good" and "bad" curves, no design element exists in a vacuum.  Maybe you are putting a curve on the end of the arm rest of an adirondack chair to soften it a bit.  You want something more than just rounding the corners but you don't want a perfectly flowing curve either because that doesn't match anything else on the chair.  So maybe the "bad" curve is exactly what you need.

[Joe Eagar]

I have a small cnc machine, so sometimes I will work out a part in CAD and machine a template or the part itself directly from there.  Other times I will work out what I want on paper, scan it, vectorize it, and then cnc it from there.  When I'm working on a curve in CAD I will usually have plenty of control points and I'll be tweaking the curve in more ways than just relying on the handles from two control points.  I like bringing the template into the computer because a) I don't have to fuss around with getting it sanded just right and I can throw away the physical template but still reproduce it again exactly if i need it later.  But I will also sometimes print out paper templates for things.  It just depends on the situation.

 

As far as the "good" and "bad" curves, no design element exists in a vacuum.  Maybe you are putting a curve on the end of the arm rest of an adirondack chair to soften it a bit.  You want something more than just rounding the corners but you don't want a perfectly flowing curve either because that doesn't match anything else on the chair.  So maybe the "bad" curve is exactly what you need.

 

That's the problem.  You shouldn't need so many control points.  Like I said, what you are doing is solving a constrained optimization problem, which you've learned to do by trial and error.  All artists who work with polynomial curves (and surfaces) learn to do this, whether they know the math behind it or not.

 

By the way, my motivation for doing this research is so CNC/3D printer owners can make stuff as high-quality as industrial manufacturers--without having to worry about the math (or pay patent royalties). 

[weithman5]

i always liked the analog thermometer (speedometer, fuel gauge...) because i knew that it had the potential of being exact, even if i could not read it to as many significant digits as a new digital one.

 

I always liked the curve slots in the grill of my 1984 cj7 as opposed to the straight ones they made in later years.

 

i am a former submarine officer, thank goodness for curved tubes.

[dwacker]

Brassiere curves

 

[weithman5]

Brassiere curves

 

 

shaper for the win

[Tpt life]

Um, yeah. Just imagining telling my wife that her curves are not fair...

Eager, I truly do appreciate the conversation. I think as practical guys, many of us lack the desire to engage the software in the artistic the way you do. I know at the outset I did not imagine the practical application applying to railroad tracks so maybe I am limited. Many of us engage our curves in three dimensional objects through a little trial and error. Sketchup gives a framework and let's us imagine, but we trust our eye or even our hands. Again, thanks for the head scratcher.

[Janello]

Brassiere curves

 

And there you have it, folks. Need more proof that Brassier curves are "good curves"?

[Joe Eagar]

And there you have it, folks. Need more proof that Brassier curves are "good curves"?

 

They look fake. 

[pghmyn]

I wonder if the artist who made that used the sagulator at all.

[Rick A McQuay]

I'm wondering if the issue isn't being exaggerated by the examples given in post 3. The initial point was that French curves are better than bezier curves then two examples were labeled good and bad but the "bad" example has obvious faults that could easily be tweaked by adjusting one or two control points.

[TheFatBaron]

I'm wondering if the issue isn't being exaggerated by the examples given in post 3. The initial point was that French curves are better than bezier curves then two examples were labeled good and bad but the "bad" example has obvious faults that could easily be tweaked by adjusting one or two control points.

 

This.

 

If bezier curves were inherently bad, the entire design field would be in rough shape, give how many of our tools make extensive use of bezier curves. The inability of a user to use the tools well is not always a reflection on the tool.