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<p class="MsoNormal">Today Dick and I refined prose and reconciled multiple comments in Mantis 1093 and 1185.</p>
<p class="MsoNormal"><br>
We think that the equations for X3DSequencer computations are now clearer, especially when several keys are identical (which is allowed in a monotonically non-decreasing sequence). We thank Yves Piguet, Roy Walmsley and Andreas Plesch for fundamental contributions.</p>
<p class="MsoNormal"><o:p> </o:p></p>
<ul style="margin-top:0in" type="disc">
<li class="MsoListParagraph" style="margin-left:0in;mso-list:l0 level1 lfo1">30.2.4 Sequencing single field (SF) events - Discrete value sequencing function
</li><li class="MsoListParagraph" style="margin-left:0in;mso-list:l0 level1 lfo1">https://www.web3d.org/member-only/mantis/view.php?id=1185</li></ul>
<p class="MsoNormal"><o:p> </o:p></p>
<ul style="margin-top:0in" type="disc">
<li class="MsoListParagraph" style="margin-left:0in;mso-list:l0 level1 lfo1">30.2.4 Sequencing Single Field (SF) events - Notation in sequencing function</li><li class="MsoListParagraph" style="margin-left:0in;mso-list:l0 level1 lfo1">https://www.web3d.org/member-only/mantis/view.php?id=1093</li></ul>
<p class="MsoNormal"><o:p> </o:p></p>
<p class="MsoNormal">Results online as follows. All comments welcome.<o:p></o:p></p>
<p class="MsoNormal"><o:p> </o:p></p>
<ul style="margin-top:0in" type="disc">
<li class="MsoListParagraph" style="margin-left:0in;mso-list:l0 level1 lfo1">30.2.4 Sequencing Single Field (SF) events<o:p></o:p></li><li class="MsoListParagraph" style="margin-left:0in;mso-list:l0 level1 lfo1">https://www.web3d.org/specifications/X3Dv4Draft/ISO-IEC19775-1v4-CD1/Part01/components/eventUtilities.html#SequencingEvents<o:p></o:p></li></ul>
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<p class="MsoNormal" style="border:none;padding:0in"><o:p> </o:p></p>
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<h2>30.2.4 Sequencing Single Field (SF) events <span style="font-size:18.0pt"><o:p></o:p></span></h2>
<p>Sequencer nodes allow content authors to generate a specific sequence of discrete events over the course of a TimeSensor's output. They are derived from the abstract node type
<i>X3DSequencerNode</i> and thus share the signature fields of <i>set_fraction</i> (SFFloat [in]) and
<i>key</i> (MFFloat [in,out]). </p>
<p>The <i>set_fraction</i> inputOnly field receives an SFFloat event and causes the sequencing function to evaluate, resulting in a
<i>value_changed</i> output event with the same timestamp as the <i>set_fraction</i> event. The sequencer node sends only one
<i>value_changed</i> output event per <i>key</i>[i] interval. <span class="proposed">
<span style="background:yellow;mso-highlight:yellow">Such sequenced values are not interpolated.</span></span> The usage of the
<i>keyValue</i> and output fields are dependent on the type of the Sequencer. </p>
<p>BooleanSequencer and IntegerSequencer output a single-value field to <i>value_changed</i>. Each value in the
<i>keyValue</i> field corresponds in order to the parameter value in the <i>key</i> field. Results are undefined if the number of values in the
<i>key</i> field of a sequencer is not the same as the number of values in the <i>
keyValue</i> field. </p>
<p>The specified X3D sequencer nodes are designed for discrete events along a timeline. Each of these nodes defines a piecewise-linear function,
<i>f(t)</i>, on the interval ( <i>−infinity, +infinity)</i>. The piecewise-linear function is defined by
<i>n</i> values of <i>t</i>, called <i>key</i>, and the <i>n</i> corresponding values of
<i>f(t)</i>, called <i>keyValue</i>. The keys shall be monotonically non-decreasing, otherwise the results are undefined. The keys are not restricted to any interval.
</p>
<p>Each of these nodes evaluates <i>f(t)</i> given any value of <i>t</i> (via the
<i>fraction</i> field) as follows: Let the <i>n</i> keys <i>t<sub>0</sub>, t<sub>1</sub>, t<sub>2</sub>, ..., t<sub>n-1</sub></i> partition the domain (
<i>-infinity, +infinity</i>) into the <i>n+</i>1 subintervals given by (− <i>infinity</i>,
<i>t<sub>0</sub>), [t<sub>0</sub>, t<sub>1</sub>), [t<sub>1</sub>, t<sub>2</sub>), ..., [t<sub>n-1</sub>, +infinity)</i>. Also, let the
<i>n</i> values <i>v<sub>0</sub>, v<sub>1</sub>, v<sub>2</sub>, ..., v<sub>n-1</sub></i> be the values of
<i>f(t)</i> at the associated key values. The discrete value sequencing function,
<i>f(t)</i>, is defined to be:</p>
<div>
<p><s> <i>f(t)</i> = <i>v<sub>n</sub>, if t<sub>n</sub> ≤ t < t<sub>n-1</sub></i><br>
= <i>v<sub>0</sub></i>, if <i>t ≤ t<sub>0</sub></i>,<br>
= <i>v<sub>n−1</sub></i>, if <i>t ≥ t<sub>n−1</sub></i><o:p></o:p></s></p>
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<div>
<p> <i><span style="background:yellow;mso-highlight:yellow">f(t)</span></i><span style="background:yellow;mso-highlight:yellow"> =
<i>v<sub>i</sub></i> , if t<sub>i</sub> ≤ t < t<sub>n-1</sub> for 0 ≤ i < n-1;<br>
= <i>v<sub>i</sub></i> , if t = t<sub>i</sub> = t<sub>i+1</sub>;<br>
= <i>v<sub>0</sub></i> , if <i>t ≤ t<sub>0</sub></i>;<br>
= <i>v<sub>n−1</sub></i> , if <i>t ≥ t<sub>n−1</sub></i><o:p></o:p></span></p>
<div style="mso-element:para-border-div;border:none;border-bottom:solid windowtext 1.0pt;padding:0in 0in 1.0pt 0in">
<p style="border:none;padding:0in"><span style="background:yellow;mso-highlight:yellow">Note that if more than one key/keyValue pairs are provided for the same key, only the first defined value for keyValue is used.</span>
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<p class="MsoNormal">all the best, Don<br>
<span style="font-size:10.0pt;font-family:"Courier New"">-- <br>
Don Brutzman Naval Postgraduate School, Code USW/Br brutzman@nps.edu<br>
Watkins 270, MOVES Institute, Monterey CA 93943-5000 USA +1.831.656.2149<br>
X3D graphics, virtual worlds, navy robotics <a href="http://faculty.nps.edu/brutzman">
http://faculty.nps.edu/brutzman</a></span><o:p></o:p></p>
<p class="MsoNormal"><o:p> </o:p></p>
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