problems with NUBS

[Robert Orosz <roboro@AUTO-TROL.com>]

All,

I've spent the better part of the past two days trying to fulfill one of my
action items, namely, generate a CGM file with NUBS in it for the test
suite.  Along the way, I've encountered a number of problems which lead me
to ask the question: "Are NUBS and NURBS absolutely required for WebCGM
2.0?"  If the answer is yes, then there are some problems which need to be
worked out.  I'll describe the issues below in the order that I encountered
them.

1) Profile should require clamped splines.  This one is easy and appears to
be resolved; the Model Profile as specified in the WebCGM 2.0 draft profile
PPF does not specify that splines should be clamped.  This is apparently a
transcription error and will be corrected.  Interestingly, the ATA made the
exact same error.

2) The parameter end value parameter.  I had a recollection that the NUBS
specification in CGM92 had a defect, namely, that the parameter end value
was incorrectly specified to be less than the n-th knot value.  Since CGM99
was supposed to have all of the defect corrections in place, I looked at the
NUBS specification in CGM99.  I was dismayed to discover that it was
unchanged with respect to the parameter end value parameter of NUBS and
NURBS.  I then went searching for that defect report (8632-1/065).  This was
frustrating at first until I discovered that Lofton is an excellent document
repository!  He sent me a copy of that report.  I read it and was dismayed
to discover that it too was unchanged with respect to the parameter end
value parameter of NUBS and NURBS.  So, that probably explains why CGM99 had
no changes for parameter end value.  Other changes from 8632-1/065 are
incorporated into CGM99.

Lofton then sent me another defect report (8632:1999-1/001) which addresses
the issue of the parameter value.  It states that the end value shall be
less than or equal to the (n+1)st knot value.  However, he does not know the
status of this defect report.

3) Interval over which the higher order basis functions are non-zero.  I
noticed this discrepancy while reading 8632-1/065.  It states that the
interval over which the higher order (k > 1) basis functions evaluate to
non-zero is T[i] <= t <= T[i+k].  However, CGM99 gives the interval as T[i]
<= t < T[i+k].  So, B[i,k](t) = 0 when t = T[i+k} according to CGM99.  It
does not equal 0 according to the 8632-1/065 defect report, and you must
evaluate the two terms in the basis function to obtain the value.

The 8632-1/065 defect report states: "The CGM defects editor has convened an
ad hoc committee of NURBS and CGM experts. ...", so that tends to make me
believe it over CGM99.  However, I'm not a NURBS expert myself, so I have no
idea which is correct.  It's possible that the numerators of the two terms
in the basis function evaluate to 0 when t = T[i+k] in which case there is
no discrepancy.  I haven't checked this possibility.  Like I said, I'm not a
NURBS expert.

I'm reluctant to spend any more time on this until these issues are
resolved.

Regards,

Rob