**Next message:**Anshuman Razdan: "RE: little bit off topic (about inspection)"**Previous message:**Anshuman Razdan: "RE: little bit off topic (about inspection)"**In reply to:**Anshuman Razdan: "RE: little bit off topic (about inspection)"**Next in thread:**Anshuman Razdan: "RE: little bit off topic (about inspection)"**Reply:**Anshuman Razdan: "RE: little bit off topic (about inspection)"**Reply:**Ron Ohler: "BPM"**Messages sorted by:**[ date ] [ thread ] [ subject ] [ author ] [ attachment ]

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/
*

*>
*

*>
*

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

**Next message:**Anshuman Razdan: "RE: little bit off topic (about inspection)"**Previous message:**Anshuman Razdan: "RE: little bit off topic (about inspection)"**In reply to:**Anshuman Razdan: "RE: little bit off topic (about inspection)"**Next in thread:**Anshuman Razdan: "RE: little bit off topic (about inspection)"**Reply:**Anshuman Razdan: "RE: little bit off topic (about inspection)"**Reply:**Ron Ohler: "BPM"**Messages sorted by:**[ date ] [ thread ] [ subject ] [ author ] [ attachment ]

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