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
-> > -> >
-> > -> >
-> > -> > For more information about the rp-ml, see
http://ltk.hut.fi/rp-ml/
> -> >
> ->
> ->
> -> For more information about the rp-ml, see http://ltk.hut.fi/rp-ml/
>
>
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