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what is a nurb curve or surface

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Message 1 of 16
Anonymous
903 Views, 15 Replies
‎12-09-2003 01:05 AM
‎12-09-2003 01:05 AM

what is a nurb curve or surface

 
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15 REPLIES 15
Message 2 of 16
Anonymous
in reply to: Anonymous
‎12-09-2003 01:17 AM
‎12-09-2003 01:17 AM

Nurbs = Nonuniform Rational B-splines, you can get a good explanation here:

http://www.cs.wpi.edu/~matt/courses/cs563/talks/nurbs.html

Steve


"fritsche" wrote in message
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>
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Message 3 of 16
Anonymous
in reply to: Anonymous
‎12-09-2003 01:27 AM
‎12-09-2003 01:27 AM

yeah that explained it...????? someone in English! If there is a B-spline, then what is a A-spline, and is the spline tool in IV considered a NURB because it is continually tangent?
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Message 4 of 16
Anonymous
in reply to: Anonymous
‎12-09-2003 01:34 AM
‎12-09-2003 01:34 AM

Maybe this will help you?

http://www.3drender.com/jbirn/ea/HeadModel.html


"fritsche" wrote in message
news:f1a4bc9.1@WebX.maYIadrTaRb...
> yeah that explained it...????? someone in English! If there is a B-spline,
then what is a A-spline, and is the spline tool in IV considered a NURB
because it is continually tangent?
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Message 5 of 16
Anonymous
in reply to: Anonymous
‎12-09-2003 01:36 AM
‎12-09-2003 01:36 AM

NURBS is an algorithm which defines curvature
with an equation that the computer can use.  Very complex curvature can be
defined with relatively simple mathematics.  The spline function is a
simple example of NURBS curvature.  The only information you need to store
in the database are the control points, inflection points and point
weights.  The curve is built from this information.

 

Pat

 

 

Pat


style="PADDING-RIGHT: 0px; PADDING-LEFT: 5px; MARGIN-LEFT: 5px; BORDER-LEFT: #000000 2px solid; MARGIN-RIGHT: 0px">
yeah
that explained it...????? someone in English! If there is a B-spline, then
what is a A-spline, and is the spline tool in IV considered a NURB because it
is continually tangent?
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Message 6 of 16
Anonymous
in reply to: Anonymous
‎12-09-2003 01:49 AM
‎12-09-2003 01:49 AM

>If there is a B-spline, then what is a A-spline

B is short for a person's name Pierre Bezier, a mathemetician and I think he spoke French not English.
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Message 7 of 16
Anonymous
in reply to: Anonymous
‎12-09-2003 01:53 AM
‎12-09-2003 01:53 AM

what do you mean by inflection points and point weights
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Message 8 of 16
Anonymous
in reply to: Anonymous
‎12-09-2003 01:53 AM
‎12-09-2003 01:53 AM

This one is pretty good:

http://www.datamation.co.uk/samples/edn/vol7/e707sp2.html


"fritsche" wrote in message
news:f1a4bc9.5@WebX.maYIadrTaRb...
> what do you mean by inflection points and point weights
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Message 9 of 16
Anonymous
in reply to: Anonymous
‎12-09-2003 02:20 AM
‎12-09-2003 02:20 AM

I believe the acronym for the B in NURBS is boundary.

"JDMATHER" wrote in message
news:f1a4bc9.4@WebX.maYIadrTaRb...
> If there is a B-spline, then what is a A-spline
> B is short for a person's name Pierre Bezier, a mathemetician and I
think he spoke French not English.
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Message 10 of 16
Anonymous
in reply to: Anonymous
‎12-09-2003 02:49 AM
‎12-09-2003 02:49 AM

An inflection point is where the center of
curvature moves from one side of the line to the other.  Essentially its
the point where a curve starts bending back on itself.  Imagine an S
shape.  The top half of the S bends around a focal point (like the
center of an arc).  The bottom half bends around a different focal
point.  The 2 focal points are on opposite sides of the S curve.  The
inflection point is where the curvature goes from being controlled by a focal
point on one side of the line to being controlled by a point on the other
side.  In this case the Inflection Point is the middle of the S.  If
you want get into the calculus of it, its any point where the second derivative
changes from + to -. 

 

Point weight is the value that determines how
strongly a control point influences curvature.  A heavier weight will cause
the curve to bend more tightly around the point.

 

Hope that helps.

 

Pat

 

 


style="PADDING-RIGHT: 0px; PADDING-LEFT: 5px; MARGIN-LEFT: 5px; BORDER-LEFT: #000000 2px solid; MARGIN-RIGHT: 0px">
what
do you mean by inflection points and point weights
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Message 11 of 16
Anonymous
in reply to: Anonymous
‎12-09-2003 05:26 AM
‎12-09-2003 05:26 AM

Non Uniform Rational Bezier Splines!

"Steve" wrote in message
news:77754E41A6BDD691B9A9FEB085B8381E@in.WebX.maYIadrTaRb...
> I believe the acronym for the B in NURBS is boundary.
>
> "JDMATHER" wrote in message
> news:f1a4bc9.4@WebX.maYIadrTaRb...
> > If there is a B-spline, then what is a A-spline
> > B is short for a person's name Pierre Bezier, a mathemetician and I
> think he spoke French not English.
>
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Message 12 of 16
Anonymous
in reply to: Anonymous
‎12-09-2003 05:36 AM
‎12-09-2003 05:36 AM

The letter B in B-spline stands for "basis".

Glenn
Autodesk Inventor Team

"Ed O'Halloran" wrote in message
news:D2E0A7701E13C0EEA5486858CCA2E82E@in.WebX.maYIadrTaRb...
> Non Uniform Rational Bezier Splines!
>
> "Steve" wrote in message
> news:77754E41A6BDD691B9A9FEB085B8381E@in.WebX.maYIadrTaRb...
> > I believe the acronym for the B in NURBS is boundary.
> >
> > "JDMATHER" wrote in message
> > news:f1a4bc9.4@WebX.maYIadrTaRb...
> > > If there is a B-spline, then what is a A-spline
> > > B is short for a person's name Pierre Bezier, a mathemetician and I
> > think he spoke French not English.
> >
>
>
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Message 13 of 16
Anonymous
in reply to: Anonymous
‎12-09-2003 05:53 AM
‎12-09-2003 05:53 AM

Hmmm, interesting. "Boundary" was from memory so I could be wrong about
that. I've heard Bezier used in this context before but have been told more
than once that it was incorrect. This is the first time I've heard it called
"basis".

Steve

"Glenn Chun (Autodesk)" wrote in message
news:5ED1BDF1422E54D70A09DD5B8FC342C5@in.WebX.maYIadrTaRb...
> The letter B in B-spline stands for "basis".
>
> Glenn
> Autodesk Inventor Team
>
> "Ed O'Halloran" wrote in message
> news:D2E0A7701E13C0EEA5486858CCA2E82E@in.WebX.maYIadrTaRb...
> > Non Uniform Rational Bezier Splines!
> >
> > "Steve" wrote in message
> > news:77754E41A6BDD691B9A9FEB085B8381E@in.WebX.maYIadrTaRb...
> > > I believe the acronym for the B in NURBS is boundary.
> > >
> > > "JDMATHER" wrote in message
> > > news:f1a4bc9.4@WebX.maYIadrTaRb...
> > > > If there is a B-spline, then what is a A-spline
> > > > B is short for a person's name Pierre Bezier, a mathemetician and
I
> > > think he spoke French not English.
> > >
> >
> >
>
>
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Message 14 of 16
Anonymous
in reply to: Anonymous
‎12-09-2003 06:25 AM
‎12-09-2003 06:25 AM

I did find this:

In 1946, Schoenberg had introduced such a basis for piecewise polynomials,
the B-splines ("B" for "basis").

The writer was was Paul Davis from the Worcester Polytechnic Institute.

I wonder if he had anything to do with trignometric B-splines?

Steve

"Glenn Chun (Autodesk)" wrote in message
news:5ED1BDF1422E54D70A09DD5B8FC342C5@in.WebX.maYIadrTaRb...
> The letter B in B-spline stands for "basis".
>
> Glenn
> Autodesk Inventor Team
>
> "Ed O'Halloran" wrote in message
> news:D2E0A7701E13C0EEA5486858CCA2E82E@in.WebX.maYIadrTaRb...
> > Non Uniform Rational Bezier Splines!
> >
> > "Steve" wrote in message
> > news:77754E41A6BDD691B9A9FEB085B8381E@in.WebX.maYIadrTaRb...
> > > I believe the acronym for the B in NURBS is boundary.
> > >
> > > "JDMATHER" wrote in message
> > > news:f1a4bc9.4@WebX.maYIadrTaRb...
> > > > If there is a B-spline, then what is a A-spline
> > > > B is short for a person's name Pierre Bezier, a mathemetician and
I
> > > think he spoke French not English.
> > >
> >
> >
>
>
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Message 15 of 16
Anonymous
in reply to: Anonymous
‎12-09-2003 06:50 AM
‎12-09-2003 06:50 AM

Steve,

You were probably thinking about B-rep (boundary representation).

Cheers,
Glenn

"Steve" wrote in message
news:295DEAA70B5EE8A0706E923A592B54B1@in.WebX.maYIadrTaRb...
> Hmmm, interesting. "Boundary" was from memory so I could be wrong about
> that. I've heard Bezier used in this context before but have been told
more
> than once that it was incorrect. This is the first time I've heard it
called
> "basis".
>
> Steve
>
> "Glenn Chun (Autodesk)" wrote in message
> news:5ED1BDF1422E54D70A09DD5B8FC342C5@in.WebX.maYIadrTaRb...
> > The letter B in B-spline stands for "basis".
> >
> > Glenn
> > Autodesk Inventor Team
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Message 16 of 16
Anonymous
in reply to: Anonymous
‎12-09-2003 06:59 AM
‎12-09-2003 06:59 AM

Yes, deformation!

I have a good memory, it's just short.

Steve

"Glenn Chun (Autodesk)" wrote in message
news:5EA8FE8D93B8A8F6DA6BDB101F1911C1@in.WebX.maYIadrTaRb...
> Steve,
>
> You were probably thinking about B-rep (boundary representation).
>
> Cheers,
> Glenn
>
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