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  1. #1
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    Default Bezier curves vs. segmented curves

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    I am looking for an explanation between smooth "bezier" curves and the curved shapes comprised of short straight lines. Thanks.

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    Super Member Pablo Ferral's Avatar
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    Here is an explanation of a bezier curve:
    https://en.wikipedia.org/wiki/B%C3%A9zier_curve

    You have described segment curves very well yourself.

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    Default What is the Qualitative Difference Between Bezier vs. Segmented Curve

    I guess I'm looking for the difference between the two in their creation and application, especially when using CNC. When I receive files for laser cutting that are bezier shapes, they cut smoothly. However, often when I receive files (dxf) that are segmented, they cut in a jerky fashion and not as smooth. Upon magnification, the bezier shapes are curves but the other ones are comprised of short, straight segments. How do I instruct my clients to produce the smooth curves in their CAD software?

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    Quite possibly, the short segmented curve was originally an AutoCAD Spline (Nurbs curve) that the was converted to a polyline. Many CAM packages do not support interpolated curve entities, Nurbs or Beziers, thus AutoCAD users tend to supply curve types with which they have had previous success.

    It sounds like your setup can handle Beziers, at least: Does it offer any conversion Nurbs/Spline to Beziers? If so, tell the customers to leave the curves as splines, and you will deal with them on your end.

    Get back to us. I'd be interested to know if your setup does allow for the conversion. An add-in is possible that would allow AutoCAD to reproduce the curves as Beziers.

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    Quote Originally Posted by spiderartist View Post
    I am looking for an explanation between smooth "bezier" curves and the curved shapes comprised of short straight lines. Thanks.
    If you convert a polyline to a spline using the PEDIT S option you are creating a curve known as a B-spline. A B-spline can be considered as a series of Bezier splines connected end to end. Both Bezier and B-spline splines are defined in the database by their Control Vertices (CV’s) not the points through which they pass when created in AutoCAD. A Bezier spline is an nth ordered polynomial. If you convert a polyline created with 4 CV’s in AutoCAD to a spline you will get a 3rd ordered Bezier spline. A major difference of a B-spline and a Bezier spline is that you can do some local editing of a B-spline without affecting the total B-spline. Bezier and B-spline splines are smooth curves but for display and toolpath purposes are evaluated as small straight segments. You can see the precision to which they are evaluated on polyline splines by changing the splinsegs value (the default is .

    In reality, a CNC tool is approximating all smooth curves as a series of straight segments. Some machine tools can use a smooth spline as input and determine appropriate spline evaluation parameters (similar to splinesegs) to generate segments as small as necessary to yield a curve that is smooth enough. If a “segmented curve” is given to the machine tool then it must use the segments it is given and cannot calculate a finer approximation.

    NURBS are a more sophisticated type of curve than B-splines that provide additional benefits such as the ability to exactly represent an arc, contain sharp corners, straight segments, and other features.
    ~Lee


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    My machine works fine with curves created in vector illustration software, such as CorelDraw or Adobe Illustrator. Sometimes when I import a dxf file into either program, it works fine and sometimes it doesn't. I would love to find out what to tell clients with files created in CAD software how to prepare them before sending them to me so that it eliminates the problems.

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    This is more illuminating about the distinctions in terminology that I'm not familiar with since I'm using vector illustration software to design for the CNC machine. If I understand you correctly, any curved vector line sent to a CNC machine is interpreted as tiny straight segments when it cuts the shape, regardless of how many or few points/nodes are on the curve, yes? My objective is to import dxf/dwg files that are ready to cut smoothly without my having to re-draw them in my illustration software.

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    As a test, what shows up in your CAM software after importing this file?
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    Quote Originally Posted by spiderartist View Post
    ... If I understand you correctly, any curved vector line sent to a CNC machine is interpreted as tiny straight segments when it cuts the shape, regardless of how many or few points/nodes are on the curve, yes? ...
    Yes. At a very basic level a machine tool drives the cutter from one location to the next location in a straight line. Those two locations may be calculated from smooth curves that may be defined mathematically in a variety of ways including, Bezier, B-spline, NURBS, or from a definition of an arc (center, radius, start angle, end angle for example).
    I believe Adobe Illustrator uses Bezier splines. When you manipulate a direction line in Illustrator you are actually changing the location of one of the Bezier spline’s control vertices (CVs).

    http://www.dummies.com/how-to/conten...lustrator.html

    I created two splines in AutoCAD. One of them I used the convert polyline to spline technique and for the other I used the spline command. Thus, the first is a B-spline and the second is a NURBS spline. I then created a dxf file. The dxf file outputs the chords of the B-spline. For example,

    Code:
    ...  (a portion of the DXF file)
    AcDbVertex
    100
    AcDb2dVertex
     10
    4.330213794252784
     20
    20.04452757003263
     30
    Etc.
    The ends of each chord approximating the smooth curve are define with vertex statements.

    For the “spline” splines (NURBS), DXF outputs the CVs of the NURBS Spline. For example,
    Code:
    ...
    AcDbSpline
    210  (210 refers to the normal vector of the plane, in this case 0,0,1
    0.0
    220
    0.0
    230
    1.0
     70
    
    …
    10      (this is the first CV)
    4.330213794252784
     20
    10.06624276901642
     30
    0.0
     10   (this is the 2nd CV)
    7.195453161635128
     20
    16.82283924633528
     30
    0.0
     10
    12.92593200081521
     20
    16.73334787835272
     30
    0.0
    I suspect your post-processor doesn’t know how to handle AutoCAD NURBS splines and requires the explicit x,y,z coordinates of each chord of the spline.

    Lee

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    Default Spl2arcs

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    Sometimes ago I got the request for changing a SPLINE into a LWPOLYLINE consisting of tangential ARCs considering a given tolerance.
    So I suppose NC-machines can handle LWPOLYLINES more easy than SPLINES.
    Regards
    Jochen
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