Bezier Curve Chine

From what I understand

From what i gather the idea is to create a model which can be defined by a simple grid of bezier curves, this makes it possible to define and press small plate sections into shape and then weld them together to make a compound curved surface.

In fact almost all modern construction uses some form of bezier curves, cars, airplanes but making them from a patchwork would be way to labor intensive so if they are made from metal they are usually pressed/formed into a female mold.

One way to think of it is radius chine gone mad, where the entire hull is made from variable radius plates precut by cnc and pressed variable radius shape.

I doubt it's ever going to be a popular method but there might be some people out there willing to make 10km of welds on a 30ft boat

jarl
http://dallur.com

 

From a manual drafting perpsective, it means you can construct the curve using drawing instruments, such as compass & straightedge, and no computation. There are similar methods for constructing conic sections.

From a computer perspective, Bezier curves are easy to construct because they are fast to compute (polynomial equations, no trancendental functions), C0 continuity is assured by co-locating the end points of adjacent segments, C1 continuity is assured by making the control points on either side of a node co-linear, and C2 continuity is assured by making the control points equidistant from the node. The curve always lies within the convex hull of the control points, so one can get an idea of what the curve's shape is just by looking at the control points. The free-form curves in Microsoft drawing objects used by Excel, Powerpoint and Word are Bezier curves.

B-splines are different from Bezier curves. B-splines are polynomial splines that provide the smoothest curve with least support. For example, if you change a control point of a cubic B-spline curve, you only affect the curve at the adjacent control points and there is no change to the curve outside of that. Similarly, the curve at a given control point is only affected by that control point and the two adjacent control points. So it is very easy to make local changes in a B-spline curve or surface without having to adjust all the other control points. A B-spline curve can also have a variety of conditions specified at the ends, whether to extrapolate as a constant slope, or constant curvature, etc.

 

This is far beyond me, but I am reading to try to get the jist of the usage of bezier curves as I have used them in mapmaking in Illustrator. and they are just fun to mess with. But I have to agree that while they make design "elegant" I don't see how they could possibly simplify construction of ANYTHING. A cnc machine will understand this much better than the human mind which is easily driven mad by the infinite number of control points along the lines.

 

Lines I've seen shown for Bezier hulls looked like radiused chine hulls.
If one wanted to accomplish the same thing, without kilometers of welding, and the resulting distortion, one would be far better off to build an origami hull, then piece by piece, fit in a radiused chine.
Radiused chine plates can be easily bent by hand, without the need for a brake press.

 

Brent
How would you go about bendind a 3 or 4 foot wide peice of 10 gage or 3/16" into a 18 to 24" radius ?
Tom

 

LyndonJ

The Bezier curve construction method is neither a constant radius chine (How Boring) or a Variable Radius Chine method (Not quite as Boring). Both of these methods are Radius in nature, meaning Arc of a Circle. The variable radius chine method just changes the radius somewhat along the length of the hull, still a simple Arc of a Circle.

And, yes, it does have to do with "Bezier" curves. A bezier curve is a B-spline curve whose type is one less than the number of control points. See "dskira" reply above. His animation shows a type 3 (cubic) B-spline. The curve used in the example sailboat is a type 2 B-spline since it has only three controll points.

Effectively it creates a true round surface at the turn of the chine.

The sample boat is designed using the bezier curve method and has a shell thickness of 3/16". Maybe on larger craft you could get up to 1/4" thickness for shell plating. I therefore do not see a cold form bending problem since thicker material will never be used.

Additionally if three (3) degree bends in aluminum could cause a failure, maybe we should not be building boats from aluminum. We have to form the material somehow! Is aluminum a viable material for boat building or not?

Do the bending plane line up through the next section? Each plate is developed separately from each other. I have checked into this. No they do not line up exactly. But they do line up close enough for the work we have at hand. This is not the space shuttle where a .030 thousands of an inch really matters.

With my many years of experience in the metal fabrication trade a Rolling Machine with a very skilled operator would never achieve the accuracy required for these complex developments. Using a Press Break is the only way to go in the forming of the shell plating.


Dskira,

I Like your animation, well done. What I am looking at is a Type 3 (cubic) B-spline or a Bezier curve.

What is the relationship between easy construction and the Bezier curve method of construction?

The bezier curve method produces a true round section at the turn of the chine between developable surfaces. Not just Arcs of a circle as with the constant and variable radius chine methods.

Full size patterns of the shell plating are provided along with the bend lines for cold forming in a press break. The method is consistent and predictable! The plating will fit seamlessly into the frame work.

The constant and variable radius chine methods call for a lot of heating, slicing of the material, clamping, pulling the material and in general forcing the material into place.

Skilled people are needed to do this. The bezier method does away with all this. The added benefit is a True round hull at the turn of the chine!

Thank you all for your comments!

Dennis Schaffer

 

"The bezier curve method produces a true round section at the turn of the chine between developable surfaces."

Could this method also be used in developable wood construction by shaping the turn of the chine using bezier curves and then planking that area, between adjacent developable surfaces, by filling in with strip planking?

 

S. Wind

I'm with DSKIRA on this. There is no resemblance between a bezier curve and what you are describing.

Also the Bezier is not a spline curve or a B spline curve they are different the B spline is whats called a generalisation of the bezier and spline would be more accurate a description.

Note that a bezier curve does not lie on the control points.

This round-ish surface connecting two flat developable parts of the hull is a rounded chine. it's just not a constant curve.

In fact it approximates rounded since it's a collection of small flat surfaces. As shown on the website. Created by creasing the plate to approximate a curved surface. Just like the computer graphics use small triangles to represent curved surfaces.

Take a cross section of that connecting surface and you don't have a bezier curve, you've just broken the non-developable surface into an approximation using many small flat sections. What's that called in the PC graphics industry ?

It's clever but I still cant see where bezier comes into it..

 

If you want to design for constant curves you have to use nurbs (non uniform b splines) that produce actual smooth surfaces, rather than Bezier curves which are point to point geometry used to produce faceted surfaces made up of polygons and faces (those flat triangle things) which must be shaded to be made to appear to be smooth. In computer animation it is common to use polygons for most man made objects and nurbs for characters and organic shapes.

 

Damn, isn't that the basis of Picasso's cubism? I am lost but learning. Carry on, Gentlemen.

 

The chine strips I see in the Bezier shape are far narrower than 4 ft. These can be easily bent by hand with the bending arangement I have shown in my book, (which you have.) Simply put ,it is a couple of plates welded at the chine with a length of pipe between them an inch off the chine. You simply put the strip in and bend it by hand. Sometimes I have had to add a piece on the end to give me more length and leverage.
If you have a brake press , cutting a slit out of a piece of four inch or bigger , heavy walled pipe , to fit over the blade , makes the kinks less sharp and obvious and more gradual.
I was a brake press operator for many years .

 

use those bezier curves daily in 3d. alway's admired the correct terminology but
altho autodesk certified i never really learned how many and what types splines there are
and what they'r all good for ( anyone can recommend a book i havent got yet? )

 

Call it what you want. This has nothing to do with bezier curves other than the pretty picture. Your construction method is nothing more than the same method used for creating 'round' ductwork. It will look fairly crappy I think when put into practice. Think : nice, straight, fair topsides, then a transition into several small 'facets'. Maybe if you put enough fairing compound on there, you can hide it but that seems silly.

It is difficult to deceive with boat hulls. Either you hang it all out there like a man with a big chine (see Y-M Tanton's Artica/Antartica) or you make damn sure your bottom is as smooth and round as Heidi Klum's ***. Anything in between will be like wearing spandex over stretch marks.

 

If the boat will be painted then the faceting can be hidden under fairing compound. If the boat is left bare then the faceting will be visible.

 

Using fairing compund is the worst method possible. It show the lake of knoweldge of the builder.
The fairing I saw in some boat was so thicc than it just fail after few years.
Fairing compund should not exist in any yard.
Always built an honnest hull. If it show sign of hungry horse, so be it.
Daniel