Joe Eagar

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About Joe Eagar

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  • Birthday 02/15/1987

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  • Woodworking Interests
    Fabricating my own stuff, killing time, etc.

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  1. That's only because there's a great deal of research, going back decades, on making them work, including solvers to detect and fix curvature problems automatically ("fairing" algorithms). And in truth, they really don't work that well. Natural shapes simply do not have high-degree, rational curvature functions. By the way, my research has been going extremely well. I'm thinking of releasing a little CAD app (assuming I can convince my company to let me, since they're going to own the patent). Trust me, if I ever manage to do that you'll never go back to bezier curves again
  2. 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).
  3. 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?
  4. 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.
  5. German auto manufactures, I assume . It seems like the sort of research the Germans would be good at.
  6. 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.
  7. 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.
  8. 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). What do you mean, curve-flat-curve? Do you mean transitions from straight lines to curves? You do realize that that is one of the definitions of a French curve, that it transitions from a straight line to an arc (it's used heavily in road and rail layout for this reason; such transitions prevent sudden changes in angular velocity).
  9. Note that unlike the Golden Ratio, this is based on a great deal of consumer research. However, if you and your client like a given design that's fine; this sort of research is based on what looks good to most people, not what looks good to everyone. Also, context doesn't matter. There is no contextual use that will make the "bad" curve look good, though as C Shaffer pointed out, the process of physically making a curve for a given context may turn it into a "good" one.
  10. The curvature at a point on a plane curve is the reciprocal of the osculating circle at that point. That's why I used the circle analogy. Industrial designers have done a lot of survey research on what curves look best to people. The result: a "fair" curve is one whose curvature function only increases or decreases (monotonic). More recent research is more specific: an ascetic curve is one whose curvature plot looks linear on a logarithmic scale. This all based on consumer surveys, by the way (manufacturers have had a strong financial interest in getting this research right). @Wtnhighlander, it does matter in furniture. If you had two woodworkers build a sculpted chair, but one could only use real-world drafting tools like splines and French curve templates, and the other had to use traditional CAD software, the former's result would "look" better than the latter's (unless the latter was using software that itself was based on French curves). This shows up a lot in manufacturing design, as well as computer graphics more generally (e.g. 3D animated films).
  11. Mathematically, a "fair" curve is one where the curvature function only increases or decreases (and, preferably, is linear if graphed on a logarithmic plot). The curvature function basically tells you, if I fitted a circle to that curve at this point, how big would it be? (It's actually one over that value). A French curve (it's also called a clothoid, Euler spiral, and Cornu spiral) has a linearly (if graphed on a linear plot) increasing curvature function. Polynomials, however, tend to have oscillating plots. Here's an example image: Notice how the bottom image has a nice, smooth shape (it's actually a bit better than what you would get from a simple French curve, but not by much). Think of each part of the curve as if it were an arc of a circle. For the top curve(starting from the left), the radius of that circle starts small, flattens out in the middle, gets small again, and then (though it's hard to see) flattens out again. The bottom curve, on the other hand, has a smooth transition of curvature (the circle radius gets gradually smaller).
  12. Joe Eagar

    Joe's Album

  13. Hi all. I was catching up on WoodTalk episodes recently and heard Shannon dissing his French curve template as being primitive in today's world of Google SketchUp. Since this is an area I actively do research in, I just had to to comment. Bezier curves (in fact, all polynomial curve splines) are not superior to French curve templates. They have mathematical flaws that make them a bit less helpful than you might think. I don't want to bore people with the math, but basically you cannot create as nice of curves with Bezier splines as if you constructed them with a French curve template, at least not in the same amount of time, since you are basically "fighting the math." Now, there is software available that uses French curve splines (see this youtube video for an Inkscape plugin), and I encourage anyone doing curves on the computer (which includes me, my research is motivated by my own needs), to use it. But let's face it: computers are not really superior to something as simple as a French curve template. If you are using such a template to lay out your work, do not switch to computer-generated Bezier splines. Your work will suffer if you do.
  14. The availability/price issue is why I ended up using dyed edge banding, instead of ordering veneer sheets. I suspect it's a matter of finding the right source; they do make plywood out of veneers, after all, so you should be able to get individual sheets at a reasonable price somewhere.