[x3d-public] Sequencer interval definition

[vmarchetti at kshell.com]

For more on the [a,b) denoting an interval a <= x < b, see http://mathworld.wolfram.com/Half-ClosedInterval.html

However, I agree that for the practcal problem of clarifying the spec language, we should know how existing browsers have interpreted the currrent language.

Vince Marchetti

> On Sep 30, 2017, at 11:47 PM, Andreas Plesch <andreasplesch at gmail.com> wrote:
> 
> 
> 
> On Sep 30, 2017 7:49 PM, "vmarchetti at kshell.com" <vmarchetti at kshell.com> wrote:
> 
> > On Sep 4, 2017, at 11:45 AM, Andreas Plesch <andreasplesch at gmail.com> wrote:
> >
> > Resending this without html formatting to ensure proper transmission:
> >
> > 30.2.4 defines how sequencer values are assigned to key intervals:
> >
> > http://www.web3d.org/documents/specifications/19775-1/V3.3/Part01/components/utils.html#SequencingEvents
> >
> > (−infinity, t0), [t0, t1), [t1, t2), ... , [tn-1, +infinity)
> >
> > are the intervals.
> >
> > The square bracket [ seems to indicate that the limiting value does not belong to the interval. Is that the case ?
> 
> I'm more used to the square bracket indicating a closed boundary, so that the for the interval denoted [a,b) ; x is in the interval a <= x < b
> so a is an element of the interval but b is not. Take the view that neither +infinity nor -infinity is a number; so (-infinity,a) is just shorthand for the set x < a, while [a,+infinity) is x >= a.
> 
> VRML97 seems to be when the bracket for the interval was introduced:
> 
> http://tecfa.unige.ch/guides/vrml/vrml97/spec/part1/concepts.html#4.6.8
> 
> But it is not accompanied by an explanation. For interpolators it may not matter if the limit is included in the interval since the function is continuous.
> 
> For sequencers, the function produces different values depending on from which side an interval limit is approached.
> 
> I guess it is time to look up how various browsers behave at sequencer interval limits.
> 
> 
> 
> >
> > For example, in the second interval [t0, t1) t0 does not belong to the interval but t1 does.
> > I have seen other notations where this interval would be described as ]t0, t1] which I would offer as a suggestion for an improvement.
> >
> > The next question is about the piecewise function definition:
> >
> > f(t) = v_n, if t_n <= t < t_(n-1)
> >
> > Given that the keys t_i are given in a monotonically non-decreasing order, t_n is always larger (or equal to) than t_(n-1). Therefore, a t larger than t_n can never be smaller than t_(n-1). But this is the condition described in the function for value v_n. There is no possible t which can fulfill this condition.
> > Presumably this condition was designed as:
> >
> > f(t) = v_n, if t_n >= t > t_(n-1)
> >
> > If this is the case I can submit a spec. comment but I very much would appreciate additional eyes on that since it seems like a rather fundamental oversight. Did I overlook something ?
> >
> 
> My set of eyes agrees with yours that the formula form in the v 3.3 version of section 30.2.4 is incorrect, I would propose a corrected version:
> 
> f(t)    =  v_i, if t_{i-1}   ≤ t < t_{i}  for  1 <= i < n-1
>         = v_0, if t < t_0,
>         = v_{n−1}, if t ≥ t_{n−1}
> 
> 
> Looks good to me if [ is meant to include the limit in the interval.
> 
> Andreas
> 
> 
> 
> 
> 
> > The Interpolator component spec. may provide additional insight:
> >
> > http://www.web3d.org/documents/specifications/19775-1/V3.3/Part01/components/interp.html#Linearinterpolation
> >
> > Here the equivalent piecewise function definition is:
> >
> > f(t) = linterp(t, v_i, v_(i+1)),    if t_i <= t <= t_(i+1),
> >
> > Note that the interval condition here is between t_i and t_(i+1) and not t_(i-1). So this is correct. But why change for Sequencer to t_(n-1) ? Perhaps there is a reason ?
> >
> > Also note that i is used rather than n which is also more correct since n is reserved for the fixed, total number of keys, whereas i is the variable index depending on the whatever time t is considered.
> >
> > -Andreas
> >
> > --
> > Andreas Plesch
> > Waltham, MA 02453
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