[x3d-public] Sequencer interval definition

[Andreas Plesch]

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 ?

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 ?

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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