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.
> -----Original Message-----
> From: Anshuman Razdan [mailto:email@example.com]
> Sent: Monday, March 20, 2000 10:59 AM
> To: 'Tommy Tucker'; 'Steve Pitt'; firstname.lastname@example.org
> Subject: RE: little bit off topic (about inspection)
> 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 !!.
> Dr. Anshuman Razdan
> Technical Director PRISM
> Email: email@example.com
> MC 5106 Arizona State University
> Tempe AZ 85287-5106
> Phone: (480) 965 5368
> Fax: (480) 965 2910
> -> -----Original Message-----
> -> From: firstname.lastname@example.org
> -> [mailto:email@example.com]On Behalf Of
> -> Tommy Tucker
> -> Sent: Monday, March 20, 2000 10:44 AM
> -> To: Steve Pitt; firstname.lastname@example.org
> -> 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
> -> email@example.com
> -> http://www.paraform.com
> -> > -----Original Message-----
> -> > From: firstname.lastname@example.org
> -> [mailto:email@example.com]On Behalf
> -> > Of Steve Pitt
> -> > Sent: Friday, March 03, 2000 3:23 AM
> -> > To: firstname.lastname@example.org
> -> > 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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