Scratch Building, Aircraft Design, 3D/CAD If you are starting/building a project from scratch or want to discuss design, CAD or even share 3D design images this is the place. Q&A's.

Bezier vs Spline

Reply
Old 10-06-2006, 12:13 PM
  #1
rainedave
Thread Starter
 
rainedave's Avatar
 
Join Date: Jul 2005
Location: Richmond, VA
Posts: 6,329
Gallery
My Gallery
Models
My Models
Ratings
My Feedback
Default Bezier vs Spline

Hi. In switching back and forth between cad programs I've noticed the option of drawing either Bezier curves or Spline curves. What are the differences between them? Is one better suited to certain uses and the other for different ones?

I might be wrong about this, but I seem to notice that when drawing a Spline curve the location of a point effects the entire curve more drastically than with Bezier.

Any info on these tools would be great.

Thanks, David
rainedave is offline  
Reply With Quote
Old 10-06-2006, 02:34 PM
  #2
mmattockx
 
Join Date: Apr 2005
Location: Calgary, AB, CANADA
Posts: 2,424
Gallery
My Gallery
Models
My Models
Ratings
My Feedback
Default RE: Bezier vs Spline

B-Spline Curves:

http://www.doc.ic.ac.uk/~dfg/AndysSp.../BSplines.html


Bezier Curves:

http://www.moshplant.com/direct-or/bezier/



Mark
mmattockx is offline  
Reply With Quote
Old 10-06-2006, 03:22 PM
  #3
lawsonaero
 
Join Date: Jul 2006
Location: Raleigh, NC
Posts: 30
Gallery
My Gallery
Models
My Models
Ratings
My Feedback
Default RE: Bezier vs Spline

google, wikipedia, and the terms bezier, spline, NURBS, and b-spline should get you started.

some terms to look out for: uniform, interpolated, natural.

interpolated means that a point is specified which the curve must pass through.

a bezier curve is a third order polynomial function with 4 "handles" - 2 interpolated endpoints and 2 that control curvature. bezier splines are multiple bezier curves which are tangent across each interpolated endpoint.

NURBS curves (Non Uniform Rational B-Spline) are what Autocad calls a spline. NURBS splines (yes thats redundant) allow for an extra few variables, including how interpolated each endpoint should be. this means that you can make a spline that fits more smoothly and isnt tied to exactly what data points you've picked. this is controlled by a variable called "fit tolerance" in autocad, and is a unitless number from 0 to 1, where 0 is fully interpolated.

B-splines is short for Basis splines, which is confusing but does not mean Bezier Spline.

Natural splines imply the condition that endpoints have a zero second order derivative. This means that they are the local maximum or minimum between critical points (which are the points where the first-order derivative equals zero).

I've seen someone say that splines *shouldnt* be used to draw airfoils. I think what he means is that for an airfoil to be true to its data set, it should be drawn with an interpolated line.

-Barrett
lawsonaero is offline  
Reply With Quote
Old 10-06-2006, 08:10 PM
  #4
CoosBayLumber
 
Join Date: Jan 2002
Location: San Bernardino Calif
Posts: 3,757
Gallery
My Gallery
Models
My Models
Ratings
My Feedback
Default RE: Bezier vs Spline

Well, you are confusing me, for I come at this with an Autocad point of view. For in Acad, once you do a Pedit, there is an option to "Fit Curve" If you read up the Compufoil manual this is the correct choice for smoothing for Eric only considers this option to be the one which will result in an accurate airfoil. It holds the coordinates (or endpoints) in position, and then creates a smooth curve of tangent arcs. The Spline option will instead hold the coordinates as a P.I. for each curve, then try and fit a new curvy line based upon tangents in between the points. Thus, in actuality, none of your new Polyline will actually go through the assigned coordinates. If the assigned coordinates are quite close to one another, then the variance probably will not be noticed. The Bezier type of curve instead computes a polyline based upon the tangents but adds in multi-arcs in order to obtain a jointed line in close proximity to teh noted coordinates.

Thus if you are using an airfoil program with coordinate pairs, the use the "Fit Curve option" Nice thing about the fit curve option is that you can cut it at any place and it will not recompute the lenght of the polyline and give yet another appearance.

However, if you are drawing a random polyline, like for a leader, then by all means use the Spline option for that is what it was intended for.

Wm.
CoosBayLumber is offline  
Reply With Quote
Old 10-06-2006, 08:46 PM
  #5
jstrawn
 
Join Date: Feb 2004
Location: Wichita, KS
Posts: 43
Gallery
My Gallery
Models
My Models
Ratings
My Feedback
Default RE: Bezier vs Spline

At least for NURBS, B-Spline means Bezier Spline.

In all cases, it refers to the math behind the actual calculation of the curve. Each CAD program utilizes slightly different math. Things have gotten a little better over the years, but there is still some error when moving from one system to the other.
jstrawn is offline  
Reply With Quote
Old 10-07-2006, 08:55 AM
  #6
rainedave
Thread Starter
 
rainedave's Avatar
 
Join Date: Jul 2005
Location: Richmond, VA
Posts: 6,329
Gallery
My Gallery
Models
My Models
Ratings
My Feedback
Default RE: Bezier vs Spline

Thanks, everyone. This gives me another thing to research and read up on. I've been piling up quite a list of topics I need to research lately. I've always been sort of a library "hermit" (in fact archival research is what I was trained to do). The internet is great for people like me. The skill is in determining what is junk and what is accurate.
rainedave is offline  
Reply With Quote
Old 10-07-2006, 09:23 AM
  #7
lawsonaero
 
Join Date: Jul 2006
Location: Raleigh, NC
Posts: 30
Gallery
My Gallery
Models
My Models
Ratings
My Feedback
Default RE: Bezier vs Spline

Quote:
ORIGINAL: CoosBayLumber

Well, you are confusing me, for I come at this with an Autocad point of view. For in Acad, once you do a Pedit, there is an option to "Fit Curve" If you read up the Compufoil manual this is the correct choice for smoothing for Eric only considers this option to be the one which will result in an accurate airfoil. It holds the coordinates (or endpoints) in position, and then creates a smooth curve of tangent arcs. The Spline option will instead hold the coordinates as a P.I. for each curve, then try and fit a new curvy line based upon tangents in between the points. Thus, in actuality, none of your new Polyline will actually go through the assigned coordinates. If the assigned coordinates are quite close to one another, then the variance probably will not be noticed. The Bezier type of curve instead computes a polyline based upon the tangents but adds in multi-arcs in order to obtain a jointed line in close proximity to teh noted coordinates.

Thus if you are using an airfoil program with coordinate pairs, the use the "Fit Curve option" Nice thing about the fit curve option is that you can cut it at any place and it will not recompute the lenght of the polyline and give yet another appearance.

However, if you are drawing a random polyline, like for a leader, then by all means use the Spline option for that is what it was intended for.

Wm.
William,

"fit curve" is the same as setting tolerance = 0.0 make sense now?
lawsonaero is offline  
Reply With Quote
Old 10-07-2006, 11:18 AM
  #8
RRW_SOAR
 
Join Date: Jan 2003
Location: Lost Andes, CHILE
Posts: 80
Gallery
My Gallery
Models
My Models
Ratings
My Feedback
Default RE: Bezier vs Spline

Hi,

Just like rainedave, I was wandering about B-Splines and Bzier Curves, and got some math info about them.

But the main reason I was doing this research was to learn how to use or draw with these tools in AutoCAD, and here I'd like you to give me a hand, How can I draw with Splines?

For example, I'd like to draw a very simple fuse shape, for a sailplane, so nothing like doing scale things. Are there any tricks, hints or tips to draw with Splines?

BTW. I'm using AutoCAD 2005.
RRW_SOAR is offline  
Reply With Quote
Old 10-08-2006, 10:31 AM
  #9
mikeperik
 
Join Date: Jan 2005
Location: Batavia, IL
Posts: 90
Gallery
My Gallery
Models
My Models
Ratings
My Feedback
Default RE: Bezier vs Spline

Does the choice of using bezier or splines matter if you're going to be sending your design to a laser cutter? Do they have a preference? I though one type allowed for faster cut times.

Mike
mikeperik is offline  
Reply With Quote
Old 10-08-2006, 02:54 PM
  #10
rainedave
Thread Starter
 
rainedave's Avatar
 
Join Date: Jul 2005
Location: Richmond, VA
Posts: 6,329
Gallery
My Gallery
Models
My Models
Ratings
My Feedback
Default RE: Bezier vs Spline

When I command my cad program to create an offset spline (parallel curve), the new spline it creates has about ten to twenty times more points on the spline that the original one that I drew. I would guess that creates more work for the laser cutter than a spline with only three or four points on it.

The first screen shot is the spline I drew. The second one is the spline that the parallel spline tool generated from mine. You can see how many more points there are on the generated spline.
Attached Thumbnails
Click image for larger version

Name:	Zx70626.gif
Views:	191
Size:	5.5 KB
ID:	537149   Click image for larger version

Name:	Je11024.gif
Views:	236
Size:	11.2 KB
ID:	537150  
rainedave is offline  
Reply With Quote
Old 10-09-2006, 09:22 AM
  #11
CoosBayLumber
 
Join Date: Jan 2002
Location: San Bernardino Calif
Posts: 3,757
Gallery
My Gallery
Models
My Models
Ratings
My Feedback
Default RE: Bezier vs Spline

Mike:

You bettcha it makes a difference.

The more points, short distance in between the coordinates, will determine the cutting quality via slowing the eye of the laser down. For the software has to calculate the coordinates of the step points, which usually slows it down. And thus burning the wood just a bit harder.

We have been working around this situation by assigning a different advance speed to the eye as it goes around multi-multi point lines such as the splined areas. To correct this increases costs, and is only done when the customer orders numerous copies in the order. Thus if you order one or two copies, you get a lower quality, than that for 10 or more copies. For if the customer is slow witted, they will not notice the extra burning time. Is always easiest to cut parts using fewer quantity of lines, than hundereds of calculated ones which will burn up. And when the complaint comes in that the parts on that order for 100 came out looking better than that for the two, then it takes time to explain just how.....


Wm.
CoosBayLumber is offline  
Reply With Quote
Old 10-09-2006, 09:45 AM
  #12
mikeperik
 
Join Date: Jan 2005
Location: Batavia, IL
Posts: 90
Gallery
My Gallery
Models
My Models
Ratings
My Feedback
Default RE: Bezier vs Spline

So, what you're saying is that if I'm putting a design together that I may want to have laser cut. I should use more segments when making curves instead of trying to get the longest curved segment I can. Correct?
mikeperik is offline  
Reply With Quote
Old 10-09-2006, 10:45 AM
  #13
rainedave
Thread Starter
 
rainedave's Avatar
 
Join Date: Jul 2005
Location: Richmond, VA
Posts: 6,329
Gallery
My Gallery
Models
My Models
Ratings
My Feedback
Default RE: Bezier vs Spline

Yes, I have the same question. Of the two screen shots I posted, which one does a laser cutter prefer?
rainedave is offline  
Reply With Quote
Old 10-09-2006, 07:02 PM
  #14
SoCal GliderGuider
 
Join Date: Mar 2004
Location: SoCal, CA
Posts: 1,195
Gallery
My Gallery
Models
My Models
Ratings
My Feedback
Default RE: Bezier vs Spline

Most laser cutters prefer straight lines and arcs. These can be cantenated into a simple polyline. Splines and other high level curve sets just confuse most laser cutter software/hardware.
SoCal GliderGuider is offline  
Reply With Quote
Old 10-09-2006, 09:19 PM
  #15
rainedave
Thread Starter
 
rainedave's Avatar
 
Join Date: Jul 2005
Location: Richmond, VA
Posts: 6,329
Gallery
My Gallery
Models
My Models
Ratings
My Feedback
Default RE: Bezier vs Spline

So, you're suggesting to not send any splines at all to a cutter? That will mean a lot of re-drawing for me![X(]
rainedave is offline  
Reply With Quote
Old 10-10-2006, 10:32 PM
  #16
SoCal GliderGuider
 
Join Date: Mar 2004
Location: SoCal, CA
Posts: 1,195
Gallery
My Gallery
Models
My Models
Ratings
My Feedback
Default RE: Bezier vs Spline

Depends on the software. I know of a gent that uses Corel draw and dedicated drivers from the same company that his laser cutter came from. Corel (as well as the Adobe products) use splines for their flowing lines. Another laser cutter that I've sent data to will only accept the simple polylines (think acad calls them 2d polylines) and the flow of the lines has to be presorted. Recently he bought an optomizing driver that is supposed to do the sorting prior to compilining the cutting file. I haven't sent him any work so I don't know how well his driver/compiler works.

Most of the CAM programs will translate the data as necessary for the target cutter/mill.

So you have to ask which and what they (the laser cutter) may prefer.
SoCal GliderGuider is offline  
Reply With Quote
Reply


Thread Tools
Search this Thread
Display Modes

Posting Rules
You may not post new threads
You may not post replies
You may not post attachments
You may not edit your posts

BB code is On
Smilies are On
[IMG] code is On
HTML code is Off



All times are GMT -8. The time now is 02:36 AM.