AR
I can't really say how I intend to provide an initial guess without giving
away a few secrets, but my point is that searching thousands of polygons in
a tessellated model for millions of points costs more than the 3-5
iterations. I agree that using a tessellated model is a good idea, but
don't think you buy a whole lot of time by dropping the 3-5 iterations and
seriously doubt the same level of accuracy can be achieved. If you add
more polygons to the tessellation just to make the approximation reasonable,
the situation gets worse.
Are you doing some research in this area? Maybe there is some opportunity
for collaboration.
Tommy Tucker
(vc) 408-855-4372
(fx) 408-855-4360
tommy@paraform.com
http://www.paraform.com
> -----Original Message-----
> From: Anshuman Razdan [mailto:razdan@asu.edu]
> Sent: Monday, March 20, 2000 2:07 PM
> To: 'Tommy Tucker'; 'Steve Pitt'; rp-ml@bart.lpt.fi
> Subject: RE: little bit off topic (about inspection)
>
>
> Tommy
> Good point - good initial guess - that's where the key is.
> So how do u
> intend to provide a good guess. What about points that happen to lie close
> to patch boundaries? But imagine 3-5 iterations for million points on a
> complicated part. I will let you do the floating point calculations.
>
> AR
>
> -> -----Original Message-----
> -> From: owner-rp-ml@ltk.hut.fi
> -> [mailto:owner-rp-ml@ltk.hut.fi]On Behalf Of
> -> Tommy Tucker
> -> Sent: Monday, March 20, 2000 1:15 PM
> -> To: razdan@asu.edu; 'Steve Pitt'; rp-ml@bart.lpt.fi
> -> Subject: RE: little bit off topic (about inspection)
> ->
> ->
> -> What if you use the result from the reasonable tessellation
> -> to provide good
> -> initial guesses to the Newton method? My experience is that
> -> given a good
> -> initial guess, Newton's method will converge in 3-5
> -> iterations. This is a
> -> small additional cost compared to searching the tessellation.
> ->
> -> Tommy Tucker
> -> (vc) 408-855-4372
> -> (fx) 408-855-4360
> -> tommy@paraform.com
> -> http://www.paraform.com
> ->
> -> > -----Original Message-----
> -> > From: Anshuman Razdan [mailto:razdan@asu.edu]
> -> > Sent: Monday, March 20, 2000 10:59 AM
> -> > To: 'Tommy Tucker'; 'Steve Pitt'; rp-ml@bart.lpt.fi
> -> > Subject: RE: little bit off topic (about inspection)
> -> >
> -> >
> -> > Hi
> -> > A very interesting discussion indeed. Here is my input
> -> > coming from a Free
> -> > form modeling perspective.
> -> >
> -> > So Why is it difficult to spec free form geometry?
> -> >
> -> > By freeform I am assuming you mean parametric (and not
> -> parametric as in
> -> > associative) geometric curves and surfaces. Which in turn
> -> means mostly B
> -> > Spline and NURB - a variant of B Spline curves and surfaces. Even
> -> > though the
> -> > parametric surfaces are mathematically represented in the
> -> solid(surface)
> -> > modeling kernels, the display, manufacture (STL file) etc
> -> always requires
> -> > them to be tessellated to a certain resolution. So imagine
> -> a curve being
> -> > represented by a chunk of st. lines. Now these lines may be short
> -> > and within
> -> > "tolerance" but still are not accurate representation.
> -> Another problem is
> -> > that unlike algebraic curves and surfaces there is no "root"
> -> > solving to see
> -> > if a point is numerically on the curve or surface. All
> -> techniques are
> -> > numerical like Newton's method to find how close a point is to
> -> > the curve or
> -> > surface and usually expensive to perform.
> -> >
> -> > Another problem is ... more theoretical but when designing
> -> algorithms we
> -> > have to consider all possibilities... A parametric
> -> curve/surface has the
> -> > play of domain and range. I.e. you pick a point in the U,V
> -> domain of the
> -> > surface and you can get a point on the surface. This mapping is
> -> > unique i.e.
> -> > for every point in the domain there is a unique point in the
> -> > range. However,
> -> > the inverse is not true. For example if a curve self
> -> intersects. The point
> -> > of intersection maps to two different points in the domain
> -> (although
> -> > individual mapping of each point in domain maps to unique point
> -> > which is the
> -> > intersection point).
> -> >
> -> > So how does it play into finding the nearest point
> -> problem. For something
> -> > like a Newton's method to work you must start with a
> -> initial good guess
> -> > otherwise the solution may not converge. And the guess is
> -> in the parameter
> -> > domain. So if you apply a techniques to map the point (scanned
> -> > point) to the
> -> > domain of the surface and you start with a wrong inverse
> -> mapping you will
> -> > possible never converge to the solution.
> -> >
> -> > So what is "good enough" solution. Approximate the free form
> -> > surface with a
> -> > reasonable tessellation and then compare the scanned points to this
> -> > tessellation - so now you are comparing the scanned data
> -> to a close enough
> -> > approximation of the surface. Now is it good enough - that
> -> depends. On
> -> > tolerances used, how good the approximation of the
> -> original surface is,
> -> > noise in the scanned data etc etc. If you compared every
> -> scanned point to
> -> > the original NURB surface model you could take literally days to
> -> > create the
> -> > color map.
> -> >
> -> > Hope above is useful - more than u wanted to know but I
> -> wanted to convey
> -> > that even though Parametric surfaces are wonderful gifts
> -> to man kind they
> -> > have their own set of problems !!.
> -> >
> -> >
> -> > AR
> -> > ---------------------------------
> -> > Dr. Anshuman Razdan
> -> > Technical Director PRISM
> -> > Email: razdan@asu.edu
> -> > http://prism.asu.edu/~razdan
> -> > MC 5106 Arizona State University
> -> > Tempe AZ 85287-5106
> -> > Phone: (480) 965 5368
> -> > Fax: (480) 965 2910
> -> >
> -> >
> -> >
> -> > -> -----Original Message-----
> -> > -> From: owner-rp-ml@ltk.hut.fi
> -> > -> [mailto:owner-rp-ml@ltk.hut.fi]On Behalf Of
> -> > -> Tommy Tucker
> -> > -> Sent: Monday, March 20, 2000 10:44 AM
> -> > -> To: Steve Pitt; rp-ml@bart.lpt.fi
> -> > -> Subject: RE: little bit off topic (about inspection)
> -> > ->
> -> > ->
> -> > -> Steve,
> -> > ->
> -> > -> I thought your question was very interesting and was
> -> > -> surprised not to see
> -> > -> more discussion. Scanners and three-dimensional measurement
> -> > -> equipment have
> -> > -> been discussed a lot on this list, but this is a subject
> -> > -> that rarely comes
> -> > -> up. Everyone thinks its great to inspect free-form shapes
> -> > -> but doesn't say a
> -> > -> whole lot about what they mean by it.
> -> > ->
> -> > -> The main advantage in free-form surface inspection using
> -> > -> scanning/digitizing
> -> > -> technology has been the use of color mapping the errors from
> -> > -> measured points
> -> > -> to CAD surfaces. You raise an interesting question as to
> -> > -> whether this is
> -> > -> enough. Most of the other features you mentioned require a
> -> > -> tolerance.
> -> > -> Free-form surfaces should to, but how are these spec'd out?
> -> > -> Any input from
> -> > -> others on the list would be appreciated. My company is in a
> -> > -> position to
> -> > -> provide real innovation in this area based on input received.
> -> > ->
> -> > -> One area I have seen a tolerance used for free-form surfaces
> -> > -> is turbine
> -> > -> blades. Generally, these are spec'd out by cross-sections
> -> > -> along the blade's
> -> > -> length. This has always bothered me because it takes a 3D
> -> > -> geometry and
> -> > -> simplifies it to 2D. With modern modeling systems, why
> -> can't a 3D
> -> > -> tolerancing scheme be imposed? In any event, you may want
> -> > -> to look into
> -> > -> turbine blade inspection and how inspection planning is
> -> > -> performed for these
> -> > -> products.
> -> > ->
> -> > -> Tommy Tucker
> -> > -> (vc) 408-855-4372
> -> > -> (fx) 408-855-4360
> -> > -> tommy@paraform.com
> -> > -> http://www.paraform.com
> -> > ->
> -> > -> > -----Original Message-----
> -> > -> > From: owner-rp-ml@bart.lpt.fi
> -> > -> [mailto:owner-rp-ml@bart.lpt.fi]On Behalf
> -> > -> > Of Steve Pitt
> -> > -> > Sent: Friday, March 03, 2000 3:23 AM
> -> > -> > To: rp-ml@bart.lpt.fi
> -> > -> > Subject: little bit off topic (about inspection)
> -> > -> >
> -> > -> >
> -> > -> > Hello List,
> -> > -> > I am Ph. D. student and my research topic is about
> -> > -> inspection planning.
> -> > -> > I have a question about inspection.
> -> > -> > For inspection of freeform surface, what should be inspected?
> -> > -> > There exist a lot of inspection features such as plane,
> -> > -> cylinder, etc.
> -> > -> > In that case, sampling several points is enough.
> -> > -> > But I think that freeform surfaces are different from
> -> the features.
> -> > -> > Just is it enough to see the difference between point data and
> -> > -> > the original
> -> > -> > surface?
> -> > -> > Or the surface which is reconstructed from point data must be
> -> > -> > compared with
> -> > -> > the original one?
> -> > -> > Which way is a CMM used for inspecting freeform surface?
> -> > -> > I respect the answer from anyone who has expriences for
> -> > -> freeform surface
> -> > -> > inspection.
> -> > -> > Tnank you in advance.
> -> > -> >
> -> > -> > Steve Pitt
> -> > -> >
> -> > -> > ______________________________________________________
> -> > -> > Get Your Private, Free Email at http://www.hotmail.com
> -> > -> >
> -> > -> >
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> > -> >
> > ->
> > ->
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> >
> >
>
>
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