[x3d-public] Sequencer interval definition

Mon Oct 2 08:59:11 PDT 2017

Hi –

Note that standards documents are intended for experts in the field. Mathematical notation should be a standard part of this expertise and need not be explained.

n  Dick

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From: Andreas Plesch [mailto:andreasplesch at gmail.com] 
Sent: Monday, October 2, 2017 8:28 AM
To: puk Richard
Cc: X3D Graphics public mailing list; vmarchetti at kshell.com
Subject: RE: [x3d-public] Sequencer interval definition

Thanks, this is very reasonable. For the less mathematically fluent, it may still be helpful to add an explanation, perhaps in the tooltips.

If there aren't any more suggestions with regards to Vince's proposal for a corrected function definition, I could submit the function as a standards comment.

Andreas

On Oct 2, 2017 1:16 AM, "Richard F. Puk" <puk at igraphics.com> wrote:

Hi –

As editor of these standards, we used normal mathematical notation. We consider infinity as a number that cannot be expressed. This is why there is always an indication of an open interval  whenever infinity (+ or -) is at one end of the interval.

n  Dick

/******************************************

| Richard F. Puk, Ph.D., President

| Intelligraphics Incorporated

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| Carlsbad, CA <https://maps.google.com/?q=7644+Cortina+Court+%7C+Carlsbad,+CA%C2%A0+92009&entry=gmail&source=g>   92009-8206

| Tel: +1-760-753-9027 <tel:(760)%20753-9027>   Mobile:  +1-760-809-9027 <tel:(760)%20809-9027> 

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From: x3d-public [mailto:x3d-public-bounces at web3d.org] On Behalf Of Andreas Plesch
Sent: Saturday, September 30, 2017 10:47 PM
To: vmarchetti at kshell.com
Cc: X3D Graphics public mailing list
Subject: Re: [x3d-public] Sequencer interval definition

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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