[x3d-public] Sequencer interval definition

[Andreas Plesch]

Hi Vince,

wolfram is good enough for me. Let me check at least my sequencer x3dom
code, and perhaps come up with a simple test.

-Andreas



On Sun, Oct 1, 2017 at 9:42 PM, vmarchetti at kshell.com <vmarchetti at kshell.com
> wrote:

> 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
> > > _______________________________________________
> > > x3d-public mailing list
> > > x3d-public at web3d.org
> > > http://web3d.org/mailman/listinfo/x3d-public_web3d.org
> >
> >
>
>


-- 
Andreas Plesch
Waltham, MA 02453
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