﻿<?xml version="1.0" encoding="utf-8" standalone="yes"?>
<?application progid="SMath Studio Desktop" version="0.98.6179.21440"?>
<regions>
  <settings>
    <identity>
      <id>d64f37d1-2e32-459c-8d7d-32d7e98d91fe</id>
      <revision>99</revision>
    </identity>
    <calculation>
      <precision>6</precision>
      <exponentialThreshold>5</exponentialThreshold>
      <fractions>decimal</fractions>
    </calculation>
    <pageModel active="true" printAreas="true" simpleEqualsOnly="false" printBackgroundImages="true">
      <paper id="1" orientation="Portrait" width="850" height="1100" />
      <margins left="39" right="39" top="39" bottom="39" />
      <header alignment="Center" color="#a9a9a9">&amp;[DATE] &amp;[TIME] - &amp;[FILENAME]</header>
      <footer alignment="Center" color="#a9a9a9">&amp;[PAGENUM] / &amp;[COUNT]</footer>
      <backgrounds />
    </pageModel>
    <dependencies>
      <assembly name="SMath Studio Desktop" version="0.98.6179.21440" guid="a37cba83-b69c-4c71-9992-55ff666763bd" />
      <assembly name="Math Region" version="0.98.6179.21440" guid="02f1ab51-215b-466e-a74d-5d8b1cf85e8d" />
      <assembly name="Picture Region" version="1.10.6179.21444" guid="06b5df04-393e-4be7-9107-305196fcb861" />
      <assembly name="Special Functions" version="1.11.6179.21442" guid="2814e667-4e12-48b1-8d51-194e480eabc5" />
      <assembly name="Text Region" version="1.10.6179.21446" guid="485d28c5-349a-48b6-93be-12a35a1c1e39" />
      <assembly name="Plot Region" version="1.9.6179.21450" guid="c451c2b5-798b-4f08-b9ec-b90963d1ddaa" />
    </dependencies>
    <mode debug="true" />
  </settings>
  <region id="0" left="9" top="9" width="761" height="121" color="#000000" bgColor="#ebebeb" fontSize="10">
    <math decimalPlaces="4" exponentialThreshold="3">
      <input>
        <e type="operand">vx</e>
        <e type="operand">vy</e>
        <e type="operand">char</e>
        <e type="operand">size</e>
        <e type="operand">color</e>
        <e type="function" args="5">plotG</e>
        <e type="operand">n</e>
        <e type="operand">vx</e>
        <e type="function" preserve="true" args="1">length</e>
        <e type="operator" args="2">:</e>
        <e type="operand">plot</e>
        <e type="operand">vx</e>
        <e type="operand">1</e>
        <e type="function" preserve="true" args="2">el</e>
        <e type="operand">vy</e>
        <e type="operand">1</e>
        <e type="function" preserve="true" args="2">el</e>
        <e type="operand">char</e>
        <e type="operand">size</e>
        <e type="operand">color</e>
        <e type="function" preserve="true" args="5">augment</e>
        <e type="operator" args="2">:</e>
        <e type="operand">i</e>
        <e type="operand">2</e>
        <e type="operand">n</e>
        <e type="function" preserve="true" args="2">range</e>
        <e type="operand">plot</e>
        <e type="operand">plot</e>
        <e type="operand">vx</e>
        <e type="operand">i</e>
        <e type="function" preserve="true" args="2">el</e>
        <e type="operand">vy</e>
        <e type="operand">i</e>
        <e type="function" preserve="true" args="2">el</e>
        <e type="operand">char</e>
        <e type="operand">size</e>
        <e type="operand">color</e>
        <e type="function" preserve="true" args="5">augment</e>
        <e type="function" preserve="true" args="2">stack</e>
        <e type="operator" args="2">:</e>
        <e type="function" preserve="true" args="3">for</e>
        <e type="operand">plot</e>
        <e type="operand">4</e>
        <e type="operand">1</e>
        <e type="function" preserve="true" args="6">line</e>
        <e type="operator" args="2">:</e>
      </input>
    </math>
  </region>
  <region id="1" left="9" top="153" width="704" height="24" color="#000000" bgColor="#ffffff" fontSize="10">
    <text lang="eng">
      <p>http://www.chemicalaid.com/tools/reactionstoichiometry.php?equation=S+%2B+O2+%3D+SO3</p>
    </text>
  </region>
  <region id="2" left="18" top="198" width="322" height="177" border="true" color="#000000" bgColor="#ebebeb" fontSize="10">
    <math decimalPlaces="4">
      <input>
        <e type="operand">z</e>
        <e type="operand">n</e>
        <e type="function" args="2">RepEnd</e>
        <e type="operand">m</e>
        <e type="operand">z</e>
        <e type="function" preserve="true" args="1">rows</e>
        <e type="operator" args="2">:</e>
        <e type="operand">i</e>
        <e type="operand">1</e>
        <e type="operand">n</e>
        <e type="function" preserve="true" args="2">range</e>
        <e type="operand">w</e>
        <e type="operand">i</e>
        <e type="function" preserve="true" args="2">el</e>
        <e type="operand">z</e>
        <e type="operand">1</e>
        <e type="function" preserve="true" args="2">el</e>
        <e type="operator" args="2">:</e>
        <e type="function" preserve="true" args="3">for</e>
        <e type="operand">i</e>
        <e type="operand">n</e>
        <e type="operand">1</e>
        <e type="operator" args="2">+</e>
        <e type="bracket">(</e>
        <e type="operand">m</e>
        <e type="operand">n</e>
        <e type="operator" args="2">+</e>
        <e type="bracket">(</e>
        <e type="function" preserve="true" args="2">range</e>
        <e type="operand">w</e>
        <e type="operand">i</e>
        <e type="function" preserve="true" args="2">el</e>
        <e type="operand">z</e>
        <e type="operand">i</e>
        <e type="operand">n</e>
        <e type="operator" args="2">-</e>
        <e type="function" preserve="true" args="2">el</e>
        <e type="operator" args="2">:</e>
        <e type="function" preserve="true" args="3">for</e>
        <e type="operand">i</e>
        <e type="operand">m</e>
        <e type="operand">n</e>
        <e type="operator" args="2">+</e>
        <e type="operand">1</e>
        <e type="operator" args="2">+</e>
        <e type="bracket">(</e>
        <e type="operand">m</e>
        <e type="operand">2</e>
        <e type="operand">n</e>
        <e type="operator" args="2">*</e>
        <e type="operator" args="2">+</e>
        <e type="bracket">(</e>
        <e type="function" preserve="true" args="2">range</e>
        <e type="operand">w</e>
        <e type="operand">i</e>
        <e type="function" preserve="true" args="2">el</e>
        <e type="operand">z</e>
        <e type="operand">m</e>
        <e type="function" preserve="true" args="2">el</e>
        <e type="operator" args="2">:</e>
        <e type="function" preserve="true" args="3">for</e>
        <e type="operand">w</e>
        <e type="operand">5</e>
        <e type="operand">1</e>
        <e type="function" preserve="true" args="7">line</e>
        <e type="operator" args="2">:</e>
      </input>
    </math>
  </region>
  <region id="3" left="351" top="198" width="79" height="135" color="#000000" bgColor="#ffffff" fontSize="10">
    <math decimalPlaces="4">
      <input>
        <e type="operand">X</e>
        <e type="operand">1.5</e>
        <e type="operand">3</e>
        <e type="operand">5</e>
        <e type="operand">7</e>
        <e type="operand">4</e>
        <e type="operand">5</e>
        <e type="operand">0.5</e>
        <e type="operator" args="1">-</e>
        <e type="operand">7</e>
        <e type="operand">1</e>
        <e type="function" preserve="true" args="9">mat</e>
        <e type="operator" args="2">:</e>
      </input>
    </math>
  </region>
  <region id="4" left="432" top="198" width="53" height="135" color="#000000" bgColor="#ffffff" fontSize="10">
    <math decimalPlaces="4">
      <input>
        <e type="operand">Y</e>
        <e type="operand">0</e>
        <e type="operand">1</e>
        <e type="operand">0</e>
        <e type="operand">4</e>
        <e type="operand">2</e>
        <e type="operand">4</e>
        <e type="operand">6</e>
        <e type="operand">7</e>
        <e type="operand">1</e>
        <e type="function" preserve="true" args="9">mat</e>
        <e type="operator" args="2">:</e>
      </input>
    </math>
  </region>
  <region id="5" left="612" top="270" width="96" height="26" color="#000000" bgColor="#ffffff" fontSize="10">
    <math decimalPlaces="4">
      <input>
        <e type="operand">t0</e>
        <e type="operand">1</e>
        <e type="function" preserve="true" args="1">time</e>
        <e type="operator" args="2">:</e>
      </input>
    </math>
  </region>
  <region id="6" left="351" top="342" width="300" height="26" color="#000000" bgColor="#ffffff" fontSize="10">
    <math decimalPlaces="4">
      <input>
        <e type="operand">Cntrl</e>
        <e type="operand">X</e>
        <e type="operand">Y</e>
        <e type="operand" style="string">.</e>
        <e type="operand">14</e>
        <e type="operand" style="string">black</e>
        <e type="function" args="5">plotG</e>
        <e type="operator" args="2">:</e>
      </input>
    </math>
  </region>
  <region id="7" left="18" top="396" width="43" height="24" color="#000000" bgColor="#ffffff" fontSize="10">
    <math decimalPlaces="4">
      <input>
        <e type="operand">r</e>
        <e type="operand">1</e>
        <e type="operator" args="2">:</e>
      </input>
    </math>
  </region>
  <region id="8" left="117" top="396" width="43" height="24" color="#000000" bgColor="#ffffff" fontSize="10">
    <math decimalPlaces="4">
      <input>
        <e type="operand">n</e>
        <e type="operand">2</e>
        <e type="operator" args="2">:</e>
      </input>
    </math>
  </region>
  <region id="9" left="18" top="432" width="139" height="49" color="#000000" bgColor="#ffffff" fontSize="10">
    <math>
      <input>
        <e type="operand">X</e>
        <e type="operand">X</e>
        <e type="operand">r</e>
        <e type="function" args="2">RepEnd</e>
        <e type="operator" args="2">:</e>
        <e type="operand">Y</e>
        <e type="operand">Y</e>
        <e type="operand">r</e>
        <e type="function" args="2">RepEnd</e>
        <e type="operator" args="2">:</e>
        <e type="operand">2</e>
        <e type="operand">1</e>
        <e type="function" preserve="true" args="4">line</e>
      </input>
    </math>
  </region>
  <region id="10" left="18" top="486" width="103" height="171" color="#000000" bgColor="#ffffe1" fontSize="10">
    <math decimalPlaces="4">
      <input>
        <e type="operand">XY</e>
        <e type="operand">1.5</e>
        <e type="operand">0</e>
        <e type="operand">1.5</e>
        <e type="operand">0</e>
        <e type="operand">3</e>
        <e type="operand">1</e>
        <e type="operand">5</e>
        <e type="operand">0</e>
        <e type="operand">7</e>
        <e type="operand">4</e>
        <e type="operand">4</e>
        <e type="operand">2</e>
        <e type="operand">5</e>
        <e type="operand">4</e>
        <e type="operand">0.5</e>
        <e type="operator" args="1">-</e>
        <e type="operand">6</e>
        <e type="operand">0.5</e>
        <e type="operator" args="1">-</e>
        <e type="operand">6</e>
        <e type="operand">9</e>
        <e type="operand">2</e>
        <e type="function" preserve="true" args="20">mat</e>
        <e type="operator" args="2">:</e>
      </input>
    </math>
  </region>
  <region id="11" left="135" top="495" width="267" height="24" color="#000000" bgColor="#ffffe1" fontSize="10">
    <text lang="eng">
      <p bold="true">&lt;= isolate the repeated polygon</p>
    </text>
  </region>
  <region id="12" left="252" top="522" width="123" height="49" color="#000000" bgColor="#ffffff" fontSize="10">
    <math>
      <input>
        <e type="operand">X</e>
        <e type="operand">XY</e>
        <e type="operand">1</e>
        <e type="function" preserve="true" args="2">col</e>
        <e type="operator" args="2">:</e>
        <e type="operand">Y</e>
        <e type="operand">XY</e>
        <e type="operand">2</e>
        <e type="function" preserve="true" args="2">col</e>
        <e type="operator" args="2">:</e>
        <e type="operand">2</e>
        <e type="operand">1</e>
        <e type="function" preserve="true" args="4">line</e>
      </input>
    </math>
  </region>
  <region id="13" left="234" top="576" width="151" height="24" color="#000000" bgColor="#80ffff" fontSize="10">
    <text lang="eng">
      <p bold="true">DeBoor 'u' vector</p>
    </text>
  </region>
  <region id="14" left="180" top="612" width="43" height="32" color="#000000" bgColor="#ffffff">
    <picture>
      <raw format="png" encoding="base64">iVBORw0KGgoAAAANSUhEUgAAACMAAAAYCAYAAABwZEQ3AAAAAXNSR0IArs4c6QAAAARnQU1BAACxjwv8YQUAAAAJcEhZcwAADsMAAA7DAcdvqGQAAACpSURBVEhLzdRNCoMwEEBhKZ5EPFnxWNKTSU8iTdvFgyojJvPjdPE2mQQ+EkjXv9ZS3a2X151qx3ya7pM8N6bC/KKW5yLvVWTCkBfKBUNWlCuGtKgQDLWiQjFUi+qkw1GdoS7F0BEqBUN7VCqGQP0FZhzGMj/mXAyI1GfaI1IwRwi65NM7Q1AophZBIZhWBLlitAhywVgRZMJ4IUiF+SLEubEmjPdNbFvLG1DzBUqJJvVOAAAAAElFTkSuQmCC</raw>
    </picture>
  </region>
  <region id="15" left="396" top="612" width="43" height="32" color="#000000" bgColor="#ffffff">
    <picture>
      <raw format="png" encoding="base64">iVBORw0KGgoAAAANSUhEUgAAACMAAAAYCAYAAABwZEQ3AAAAAXNSR0IArs4c6QAAAARnQU1BAACxjwv8YQUAAAAJcEhZcwAADsMAAA7DAcdvqGQAAADFSURBVEhLzdNbCoMwEIXhUFxJcWXFZUlXJq5EmlLKCYrnkGTSdHz4X4wzfHgJw2uL3boN/LqoC2Z6TF+IF2ZZlyPCAyMRiMyozJgsApFZVTWmGIHIDlUxphqByC5VFmNGILJTJTHNCEMnjAcCJYwnAoUrIFCYn3Mc7yM9/HfpNV0BdfqAPVHy1/ZASQxqRpGdqiwGmVFkl6oYg6pRZIeqGoOKUWRWZcagLIrMqJoxSKLIvaqfYfYdUORc1QXzKT0pcsbb4hvMKQVKjmB8dgAAAABJRU5ErkJggg==</raw>
    </picture>
  </region>
  <region id="16" left="225" top="621" width="169" height="26" color="#000000" bgColor="#ffe1e1" fontSize="10">
    <math decimalPlaces="4">
      <input>
        <e type="operand">u</e>
        <e type="operand">1</e>
        <e type="operand">X</e>
        <e type="function" preserve="true" args="1">rows</e>
        <e type="operand">n</e>
        <e type="operand">2</e>
        <e type="operator" args="2">+</e>
        <e type="bracket">(</e>
        <e type="operator" args="2">+</e>
        <e type="function" preserve="true" args="2">range</e>
        <e type="operator" args="2">:</e>
      </input>
    </math>
  </region>
  <region id="17" left="279" top="666" width="218" height="26" color="#000000" bgColor="#ffffff" fontSize="10">
    <math optimize="2" decimalPlaces="4">
      <input>
        <e type="operand">3</e>
        <e type="function" preserve="true" args="1">appVersion</e>
        <e type="operand" style="string">0.98.6179</e>
        <e type="operator" args="2">≡</e>
      </input>
    </math>
  </region>
  <region id="18" left="18" top="675" width="259" height="106" border="true" color="#000000" bgColor="#e1ffff" fontSize="10">
    <math optimize="2" decimalPlaces="4">
      <input>
        <e type="operand">v</e>
        <e type="operand">j</e>
        <e type="function" args="2">N0</e>
        <e type="operand">μ</e>
        <e type="operand">j</e>
        <e type="operand">1</e>
        <e type="operand">1</e>
        <e type="function" preserve="true" args="3">line</e>
        <e type="operator" args="2">:</e>
        <e type="operand">u</e>
        <e type="operand">μ</e>
        <e type="function" preserve="true" args="2">el</e>
        <e type="operand">v</e>
        <e type="operator" args="2">≤</e>
        <e type="bracket">(</e>
        <e type="operand">v</e>
        <e type="operand">u</e>
        <e type="operand">μ</e>
        <e type="operand">1</e>
        <e type="operator" args="2">+</e>
        <e type="function" preserve="true" args="2">el</e>
        <e type="operator" args="2">&lt;</e>
        <e type="bracket">(</e>
        <e type="operator" args="2">&amp;</e>
        <e type="operand">1</e>
        <e type="operand">0</e>
        <e type="function" preserve="true" args="3">if</e>
        <e type="operand">2</e>
        <e type="operand">1</e>
        <e type="function" preserve="true" args="4">line</e>
        <e type="operator" args="2">:</e>
      </input>
    </math>
  </region>
  <region id="19" left="279" top="693" width="161" height="65" color="#000000" bgColor="#ffe1e1" fontSize="10">
    <math decimalPlaces="4">
      <description active="true" position="Right" lang="eng">
        <p>1. correct2. wrong</p>
      </description>
      <input>
        <e type="operand">u</e>
        <e type="operand">μ</e>
        <e type="function" preserve="true" args="2">el</e>
        <e type="operand">v</e>
        <e type="operator" args="2">≤</e>
        <e type="bracket">(</e>
        <e type="operand">v</e>
        <e type="operand">u</e>
        <e type="operand">μ</e>
        <e type="operand">1</e>
        <e type="operator" args="2">+</e>
        <e type="function" preserve="true" args="2">el</e>
        <e type="operator" args="2">&lt;</e>
        <e type="bracket">(</e>
        <e type="operator" args="2">&amp;</e>
        <e type="operand">u</e>
        <e type="operand">μ</e>
        <e type="function" preserve="true" args="2">el</e>
        <e type="operand">v</e>
        <e type="operator" args="2">≤</e>
        <e type="bracket">(</e>
        <e type="operand">v</e>
        <e type="operand">u</e>
        <e type="operand">μ</e>
        <e type="operand">1</e>
        <e type="operator" args="2">+</e>
        <e type="function" preserve="true" args="2">el</e>
        <e type="operator" args="2">≤</e>
        <e type="bracket">(</e>
        <e type="operator" args="2">&amp;</e>
        <e type="operand">2</e>
        <e type="operand">1</e>
        <e type="function" preserve="true" args="4">sys</e>
      </input>
    </math>
  </region>
  <region id="20" left="18" top="783" width="451" height="81" border="true" color="#000000" bgColor="#e1ffff" fontSize="10">
    <math optimize="2" decimalPlaces="4">
      <input>
        <e type="operand">v</e>
        <e type="operand">j</e>
        <e type="function" args="2">N1</e>
        <e type="operand">μ</e>
        <e type="operand">j</e>
        <e type="operand">1</e>
        <e type="operand">1</e>
        <e type="function" preserve="true" args="3">line</e>
        <e type="operator" args="2">:</e>
        <e type="operand">v</e>
        <e type="operand">u</e>
        <e type="operand">μ</e>
        <e type="function" preserve="true" args="2">el</e>
        <e type="operator" args="2">-</e>
        <e type="operand">u</e>
        <e type="operand">μ</e>
        <e type="operand">1</e>
        <e type="operator" args="2">+</e>
        <e type="function" preserve="true" args="2">el</e>
        <e type="operand">u</e>
        <e type="operand">μ</e>
        <e type="function" preserve="true" args="2">el</e>
        <e type="operator" args="2">-</e>
        <e type="operator" args="2">/</e>
        <e type="operand">v</e>
        <e type="operand">μ</e>
        <e type="function" args="2">N0</e>
        <e type="operator" args="2">*</e>
        <e type="operand">u</e>
        <e type="operand">μ</e>
        <e type="operand">2</e>
        <e type="operator" args="2">+</e>
        <e type="function" preserve="true" args="2">el</e>
        <e type="operand">v</e>
        <e type="operator" args="2">-</e>
        <e type="operand">u</e>
        <e type="operand">μ</e>
        <e type="operand">2</e>
        <e type="operator" args="2">+</e>
        <e type="function" preserve="true" args="2">el</e>
        <e type="operand">u</e>
        <e type="operand">μ</e>
        <e type="operand">1</e>
        <e type="operator" args="2">+</e>
        <e type="function" preserve="true" args="2">el</e>
        <e type="operator" args="2">-</e>
        <e type="operator" args="2">/</e>
        <e type="operand">v</e>
        <e type="operand">μ</e>
        <e type="operand">1</e>
        <e type="operator" args="2">+</e>
        <e type="function" args="2">N0</e>
        <e type="operator" args="2">*</e>
        <e type="operator" args="2">+</e>
        <e type="operand">2</e>
        <e type="operand">1</e>
        <e type="function" preserve="true" args="4">line</e>
        <e type="operator" args="2">:</e>
      </input>
    </math>
  </region>
  <region id="21" left="18" top="864" width="451" height="81" border="true" color="#000000" bgColor="#e1ffff" fontSize="10">
    <math optimize="2" decimalPlaces="4">
      <input>
        <e type="operand">v</e>
        <e type="operand">j</e>
        <e type="function" args="2">N2</e>
        <e type="operand">μ</e>
        <e type="operand">j</e>
        <e type="operand">1</e>
        <e type="operand">1</e>
        <e type="function" preserve="true" args="3">line</e>
        <e type="operator" args="2">:</e>
        <e type="operand">v</e>
        <e type="operand">u</e>
        <e type="operand">μ</e>
        <e type="function" preserve="true" args="2">el</e>
        <e type="operator" args="2">-</e>
        <e type="operand">u</e>
        <e type="operand">μ</e>
        <e type="operand">2</e>
        <e type="operator" args="2">+</e>
        <e type="function" preserve="true" args="2">el</e>
        <e type="operand">u</e>
        <e type="operand">μ</e>
        <e type="function" preserve="true" args="2">el</e>
        <e type="operator" args="2">-</e>
        <e type="operator" args="2">/</e>
        <e type="operand">v</e>
        <e type="operand">μ</e>
        <e type="function" args="2">N1</e>
        <e type="operator" args="2">*</e>
        <e type="operand">u</e>
        <e type="operand">μ</e>
        <e type="operand">3</e>
        <e type="operator" args="2">+</e>
        <e type="function" preserve="true" args="2">el</e>
        <e type="operand">v</e>
        <e type="operator" args="2">-</e>
        <e type="operand">u</e>
        <e type="operand">μ</e>
        <e type="operand">3</e>
        <e type="operator" args="2">+</e>
        <e type="function" preserve="true" args="2">el</e>
        <e type="operand">u</e>
        <e type="operand">μ</e>
        <e type="operand">1</e>
        <e type="operator" args="2">+</e>
        <e type="function" preserve="true" args="2">el</e>
        <e type="operator" args="2">-</e>
        <e type="operator" args="2">/</e>
        <e type="operand">v</e>
        <e type="operand">μ</e>
        <e type="operand">1</e>
        <e type="operator" args="2">+</e>
        <e type="function" args="2">N1</e>
        <e type="operator" args="2">*</e>
        <e type="operator" args="2">+</e>
        <e type="operand">2</e>
        <e type="operand">1</e>
        <e type="function" preserve="true" args="4">line</e>
        <e type="operator" args="2">:</e>
      </input>
    </math>
  </region>
  <region id="22" left="18" top="1044" width="160" height="97" color="#000000" bgColor="#ffff80" fontSize="10">
    <math optimize="2" decimalPlaces="4">
      <input>
        <e type="operand">v</e>
        <e type="operand">j</e>
        <e type="function" args="2">N</e>
        <e type="operand">μ</e>
        <e type="operand">j</e>
        <e type="operand">1</e>
        <e type="operand">1</e>
        <e type="function" preserve="true" args="3">line</e>
        <e type="operator" args="2">:</e>
        <e type="operand">v</e>
        <e type="operand">μ</e>
        <e type="function" args="2">N1</e>
        <e type="operand">2</e>
        <e type="operand">1</e>
        <e type="function" preserve="true" args="4">line</e>
        <e type="operand">μ</e>
        <e type="operand">j</e>
        <e type="operand">1</e>
        <e type="operand">1</e>
        <e type="function" preserve="true" args="3">line</e>
        <e type="operator" args="2">:</e>
        <e type="operand">v</e>
        <e type="operand">μ</e>
        <e type="function" args="2">N2</e>
        <e type="operand">2</e>
        <e type="operand">1</e>
        <e type="function" preserve="true" args="4">line</e>
        <e type="operand">2</e>
        <e type="operand">1</e>
        <e type="function" preserve="true" args="4">mat</e>
        <e type="operator" args="2">:</e>
      </input>
    </math>
  </region>
  <region id="23" left="198" top="1062" width="262" height="24" color="#000000" bgColor="#ffff80" fontSize="10">
    <text lang="eng">
      <p bold="true">Collect the respective De boor </p>
    </text>
  </region>
  <region id="24" left="198" top="1098" width="53" height="24" color="#000000" bgColor="#ffff80" fontSize="10">
    <math decimalPlaces="4">
      <input>
        <e type="operand">n</e>
      </input>
      <result action="numeric">
        <e type="operand">2</e>
      </result>
    </math>
  </region>
  <region id="25" left="252" top="1098" width="273" height="24" color="#000000" bgColor="#ffff80" fontSize="10">
    <text lang="eng">
      <p>&lt;= Spline order, set from above  </p>
    </text>
  </region>
  <region id="26" left="18" top="1152" width="234" height="68" border="true" color="#000000" bgColor="#ffe1e1" fontSize="10">
    <math decimalPlaces="4">
      <description active="true" position="Top" lang="eng">
        <p>Defined as local definition</p>
      </description>
      <input>
        <e type="operand">v</e>
        <e type="function" args="1">Sx</e>
        <e type="operand">v</e>
        <e type="operand">k</e>
        <e type="function" args="2">N</e>
        <e type="operand">n</e>
        <e type="function" preserve="true" args="2">el</e>
        <e type="operand">X</e>
        <e type="operand">k</e>
        <e type="function" preserve="true" args="2">el</e>
        <e type="operator" args="2">*</e>
        <e type="bracket">(</e>
        <e type="operand">k</e>
        <e type="operand">1</e>
        <e type="operand">X</e>
        <e type="function" preserve="true" args="1">rows</e>
        <e type="function" preserve="true" args="4">sum</e>
        <e type="operand">1</e>
        <e type="operand">1</e>
        <e type="function" preserve="true" args="3">line</e>
        <e type="operator" args="2">:</e>
      </input>
    </math>
  </region>
  <region id="27" left="405" top="1152" width="234" height="68" border="true" color="#000000" bgColor="#ffe1e1" fontSize="10">
    <math decimalPlaces="4">
      <description active="true" position="Top" lang="eng">
        <p>Defined as local definition</p>
      </description>
      <input>
        <e type="operand">v</e>
        <e type="function" args="1">Sy</e>
        <e type="operand">v</e>
        <e type="operand">k</e>
        <e type="function" args="2">N</e>
        <e type="operand">n</e>
        <e type="function" preserve="true" args="2">el</e>
        <e type="operand">Y</e>
        <e type="operand">k</e>
        <e type="function" preserve="true" args="2">el</e>
        <e type="operator" args="2">*</e>
        <e type="bracket">(</e>
        <e type="operand">k</e>
        <e type="operand">1</e>
        <e type="operand">X</e>
        <e type="function" preserve="true" args="1">rows</e>
        <e type="function" preserve="true" args="4">sum</e>
        <e type="operand">1</e>
        <e type="operand">1</e>
        <e type="function" preserve="true" args="3">line</e>
        <e type="operator" args="2">:</e>
      </input>
    </math>
  </region>
  <region id="28" left="18" top="1260" width="138" height="24" color="#000000" bgColor="#80ff00" fontSize="10">
    <math decimalPlaces="4">
      <input>
        <e type="operand">vx</e>
        <e type="operand">3</e>
        <e type="operand">10</e>
        <e type="operand">3.05</e>
        <e type="function" preserve="true" args="3">range</e>
        <e type="operator" args="2">:</e>
      </input>
    </math>
  </region>
  <region id="29" left="171" top="1260" width="335" height="24" color="#000000" bgColor="#80ff00" fontSize="10">
    <text lang="eng">
      <p>&lt;= n=2 populate for more points at will </p>
    </text>
  </region>
  <region id="30" left="18" top="1323" width="176" height="54" border="true" color="#000000" bgColor="#ffffff" fontSize="10">
    <math optimize="2" decimalPlaces="4">
      <input>
        <e type="operand">i</e>
        <e type="operand">1</e>
        <e type="operand">vx</e>
        <e type="function" preserve="true" args="1">rows</e>
        <e type="function" preserve="true" args="2">range</e>
        <e type="operand">SX</e>
        <e type="operand">i</e>
        <e type="function" preserve="true" args="2">el</e>
        <e type="operand">vx</e>
        <e type="operand">i</e>
        <e type="function" preserve="true" args="2">el</e>
        <e type="function" args="1">Sx</e>
        <e type="function" preserve="true" args="1">eval</e>
        <e type="operator" args="2">:</e>
        <e type="function" preserve="true" args="3">for</e>
      </input>
    </math>
  </region>
  <region id="31" left="405" top="1323" width="176" height="54" border="true" color="#000000" bgColor="#ffffff" fontSize="10">
    <math optimize="2" decimalPlaces="4">
      <input>
        <e type="operand">i</e>
        <e type="operand">1</e>
        <e type="operand">vx</e>
        <e type="function" preserve="true" args="1">rows</e>
        <e type="function" preserve="true" args="2">range</e>
        <e type="operand">SY</e>
        <e type="operand">i</e>
        <e type="function" preserve="true" args="2">el</e>
        <e type="operand">vx</e>
        <e type="operand">i</e>
        <e type="function" preserve="true" args="2">el</e>
        <e type="function" args="1">Sy</e>
        <e type="function" preserve="true" args="1">eval</e>
        <e type="operator" args="2">:</e>
        <e type="function" preserve="true" args="3">for</e>
      </input>
    </math>
  </region>
  <region id="32" left="198" top="1350" width="194" height="26" color="#000000" bgColor="#ff8080" fontSize="10">
    <math decimalPlaces="4">
      <input>
        <e type="operand">DeBoor</e>
        <e type="operand">SX</e>
        <e type="operand">SY</e>
        <e type="function" preserve="true" args="2">augment</e>
        <e type="operator" args="2">:</e>
      </input>
    </math>
  </region>
  <region id="33" left="585" top="1350" width="166" height="26" color="#000000" bgColor="#ffffff" fontSize="10">
    <math decimalPlaces="1">
      <input>
        <e type="operand">1</e>
        <e type="function" preserve="true" args="1">time</e>
        <e type="operand">t0</e>
        <e type="operator" args="2">-</e>
      </input>
      <result action="numeric">
        <e type="operand">22.1</e>
        <e type="operand" style="unit">s</e>
        <e type="operator" args="2">*</e>
      </result>
    </math>
  </region>
  <region id="34" left="18" top="1386" width="453" height="225" color="#000000" bgColor="#ffffff" fontSize="10">
    <plot type="2d" render="lines" scale_x="2.56694234247213" scale_y="3.99186354168441" scale_z="10.2468835505205" rotate_x="0" rotate_y="0" rotate_z="0" transpose_x="-157" transpose_y="-91" transpose_z="0">
      <description active="true" position="Top" lang="eng">
        <p>De Boor parametric order 2 wrt Smath ... kind of Convex Hull</p>
      </description>
      <input>
        <e type="operand">XY</e>
        <e type="operand">DeBoor</e>
        <e type="operand">Cntrl</e>
        <e type="operand">3</e>
        <e type="operand">1</e>
        <e type="function" preserve="true" args="5">sys</e>
      </input>
    </plot>
  </region>
  <region id="35" left="495" top="1386" width="240" height="158" color="#000000" bgColor="#ffffff" fontSize="10">
    <plot type="2d" render="points" scale_x="2.05912285796665" scale_y="2.85311670611" scale_z="5.87491782599762" rotate_x="0" rotate_y="0" rotate_z="0" transpose_x="-176" transpose_y="-58" transpose_z="0">
      <description active="true" position="Top" lang="eng">
        <p>De Boor components </p>
      </description>
      <input>
        <e type="operand">vx</e>
        <e type="operand">SX</e>
        <e type="function" preserve="true" args="2">augment</e>
        <e type="operand">vx</e>
        <e type="operand">SY</e>
        <e type="function" preserve="true" args="2">augment</e>
        <e type="operand">2</e>
        <e type="operand">1</e>
        <e type="function" preserve="true" args="4">sys</e>
      </input>
    </plot>
  </region>
  <region id="36" left="495" top="1620" width="156" height="26" color="#000000" bgColor="#ffffff" fontSize="10">
    <math>
      <input>
        <e type="operand">DeBoor</e>
        <e type="function" preserve="true" args="1">rows</e>
      </input>
      <result action="numeric">
        <e type="operand">141</e>
      </result>
    </math>
  </region>
  <region id="37" left="495" top="1647" width="240" height="158" color="#000000" bgColor="#ffffff" fontSize="10">
    <plot type="2d" render="lines" scale_x="1.771561" scale_y="1.61051" scale_z="2.85311670611" rotate_x="0" rotate_y="0" rotate_z="0" transpose_x="-87" transpose_y="-43" transpose_z="0">
      <input>
        <e type="operand">x</e>
        <e type="function" args="1">Sx</e>
        <e type="operand">x</e>
        <e type="function" args="1">Sy</e>
        <e type="operand">2</e>
        <e type="operand">1</e>
        <e type="function" preserve="true" args="4">sys</e>
      </input>
    </plot>
  </region>
  <region id="38" left="207" top="1692" width="80" height="80" color="#000000" bgColor="#ffffff">
    <picture>
      <raw format="png" encoding="base64">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</raw>
    </picture>
  </region>
  <region id="39" left="162" top="1773" width="176" height="24" color="#000000" bgColor="#ffffff" fontSize="10">
    <text lang="eng">
      <p>jmGiraud: 2016/09/12</p>
    </text>
  </region>
  <region id="40" top="1845" color="#000000" bgColor="#ffe1e1">
    <area single="true" collapsed="true" />
  </region>
</regions>