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
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
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
MC 5106 Arizona State University
Tempe AZ 85287-5106
Phone: (480) 965 5368
Fax: (480) 965 2910
-> -----Original Message-----
-> From: email@example.com
-> [mailto:firstname.lastname@example.org]On Behalf Of
-> Tommy Tucker
-> Sent: Monday, March 20, 2000 10:44 AM
-> To: Steve Pitt; email@example.com
-> Subject: RE: little bit off topic (about inspection)
-> 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
-> 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
-> 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
-> Tommy Tucker
-> (vc) 408-855-4372
-> (fx) 408-855-4360
-> > -----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
-> > ______________________________________________________
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-> > For more information about the rp-ml, see http://ltk.hut.fi/rp-ml/
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