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      <header alignment="Center" color="#a9a9a9">&amp;[DATE] &amp;[TIME] - &amp;[FILENAME]</header>
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        <p>     plotG</p>
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          <e type="operand" style="string">char</e>
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          <e type="operand">size</e>
          <e type="operator" args="2">≡</e>
          <e type="operand">c</e>
          <e type="operand" style="string">color</e>
          <e type="operator" args="2">≡</e>
          <e type="operand">1</e>
          <e type="operand">3</e>
          <e type="function" preserve="true" args="5">mat</e>
          <e type="operand">n</e>
          <e type="operand">vx</e>
          <e type="function" preserve="true" args="1">length</e>
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          <e type="operand">vx</e>
          <e type="operand">1</e>
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          <e type="operand">vy</e>
          <e type="operand">1</e>
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          <e type="operand">a</e>
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          <e type="operand">2</e>
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          <e type="operand">plot</e>
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          <e type="operand">i</e>
          <e type="function" preserve="true" args="2">el</e>
          <e type="operand">a</e>
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          <e type="function" preserve="true" args="5">augment</e>
          <e type="function" preserve="true" args="2">stack</e>
          <e type="operator" args="2">:</e>
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          <e type="operand">plot</e>
          <e type="operand">5</e>
          <e type="operand">1</e>
          <e type="function" preserve="true" args="7">line</e>
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    <math>
      <input>
        <e type="operand">u</e>
        <e type="function" args="1">b</e>
        <e type="operand">0</e>
        <e type="operand">u</e>
        <e type="operand">2</e>
        <e type="operator" args="1">-</e>
        <e type="operator" args="2">≤</e>
        <e type="operand">1</e>
        <e type="operand">6</e>
        <e type="operator" args="2">/</e>
        <e type="operand">2</e>
        <e type="operand">u</e>
        <e type="operator" args="2">+</e>
        <e type="bracket">(</e>
        <e type="operand">3</e>
        <e type="operator" args="2">^</e>
        <e type="operator" args="2">*</e>
        <e type="operand">2</e>
        <e type="operator" args="1">-</e>
        <e type="operand">u</e>
        <e type="operator" args="2">≤</e>
        <e type="bracket">(</e>
        <e type="operand">u</e>
        <e type="operand">1</e>
        <e type="operator" args="1">-</e>
        <e type="operator" args="2">≤</e>
        <e type="bracket">(</e>
        <e type="operator" args="2">&amp;</e>
        <e type="operand">1</e>
        <e type="operand">6</e>
        <e type="operator" args="2">/</e>
        <e type="operand">2</e>
        <e type="operand">u</e>
        <e type="operator" args="2">+</e>
        <e type="bracket">(</e>
        <e type="operand">3</e>
        <e type="operator" args="2">^</e>
        <e type="operator" args="2">*</e>
        <e type="operand">2</e>
        <e type="operand">3</e>
        <e type="operator" args="2">/</e>
        <e type="operand">1</e>
        <e type="operand">u</e>
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        <e type="bracket">(</e>
        <e type="operand">3</e>
        <e type="operator" args="2">^</e>
        <e type="operator" args="2">*</e>
        <e type="operator" args="2">-</e>
        <e type="operand">1</e>
        <e type="operator" args="1">-</e>
        <e type="operand">u</e>
        <e type="operator" args="2">≤</e>
        <e type="bracket">(</e>
        <e type="operand">u</e>
        <e type="operand">0</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">3</e>
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        <e type="operand">1</e>
        <e type="operand">u</e>
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        <e type="bracket">(</e>
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        <e type="operand">1</e>
        <e type="operand">6</e>
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        <e type="operand">2</e>
        <e type="operand">u</e>
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        <e type="bracket">(</e>
        <e type="operand">3</e>
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        <e type="operator" args="2">*</e>
        <e type="operator" args="2">+</e>
        <e type="operand">0</e>
        <e type="operand">u</e>
        <e type="operator" args="2">≤</e>
        <e type="bracket">(</e>
        <e type="operand">u</e>
        <e type="operand">1</e>
        <e type="operator" args="2">≤</e>
        <e type="bracket">(</e>
        <e type="operator" args="2">&amp;</e>
        <e type="operand">1</e>
        <e type="operand">6</e>
        <e type="operator" args="2">/</e>
        <e type="operand">2</e>
        <e type="operand">u</e>
        <e type="operator" args="2">-</e>
        <e type="bracket">(</e>
        <e type="operand">3</e>
        <e type="operator" args="2">^</e>
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        <e type="operand">1</e>
        <e type="operand">u</e>
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        <e type="bracket">(</e>
        <e type="operand">u</e>
        <e type="operand">2</e>
        <e type="operator" args="2">≤</e>
        <e type="bracket">(</e>
        <e type="operator" args="2">&amp;</e>
        <e type="operand">0</e>
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    <text lang="eng">
      <p bold="true">The Gaussian b-spline</p>
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  <region id="5" left="414" top="270" width="240" height="158" border="true" color="#000000" bgColor="#ffffff" fontSize="10">
    <plot type="2d" render="lines" scale_x="8.51545251715269" scale_y="3.4522712143931" scale_z="29.3976516024975" rotate_x="0" rotate_y="0" rotate_z="0" transpose_x="0" transpose_y="0" transpose_z="0">
      <description active="true" position="Top" lang="eng">
        <p>Gaussian basis 'b-spline'</p>
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      <input>
        <e type="operand">2</e>
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        <e type="operand">x</e>
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        <e type="operand">x</e>
        <e type="operand">2</e>
        <e type="operator" args="2">≤</e>
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        <e type="operand">x</e>
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        <e type="operand" style="string">Undefined</e>
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      <input>
        <e type="operand">0</e>
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        <e type="operand">0.6667</e>
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    <math>
      <input>
        <e type="operand">u</e>
        <e type="operand">v</e>
        <e type="function" args="2">Bsp</e>
        <e type="operand">v</e>
        <e type="operand">m</e>
        <e type="function" preserve="true" args="2">el</e>
        <e type="operand">u</e>
        <e type="operand">m</e>
        <e type="operator" args="2">-</e>
        <e type="function" args="1">b</e>
        <e type="operator" args="2">*</e>
        <e type="bracket">(</e>
        <e type="operand">m</e>
        <e type="operand">1</e>
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        <e type="function" preserve="true" args="4">sum</e>
        <e type="operator" args="2">:</e>
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    <math>
      <input>
        <e type="operand">X</e>
        <e type="operand">1.875</e>
        <e type="operand">1.875</e>
        <e type="operand">1.95</e>
        <e type="operand">2</e>
        <e type="operand">2.05</e>
        <e type="operand">2.125</e>
        <e type="operand">2.125</e>
        <e type="operand">2.125</e>
        <e type="operand">1</e>
        <e type="operand">8</e>
        <e type="function" preserve="true" args="10">mat</e>
        <e type="operator" args="2">:</e>
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    <math>
      <input>
        <e type="operand">Y</e>
        <e type="operand">1</e>
        <e type="operand">1</e>
        <e type="operand">1</e>
        <e type="operand">0</e>
        <e type="operand">1</e>
        <e type="operator" args="1">-</e>
        <e type="operand">1</e>
        <e type="operator" args="1">-</e>
        <e type="operand">1</e>
        <e type="operator" args="1">-</e>
        <e type="operand">1</e>
        <e type="operator" args="1">-</e>
        <e type="operand">1</e>
        <e type="operand">8</e>
        <e type="function" preserve="true" args="10">mat</e>
        <e type="operator" args="2">:</e>
      </input>
    </math>
  </region>
  <region id="10" left="315" top="648" width="385" height="120" color="#000000" bgColor="#ffffff" fontSize="10">
    <text lang="eng">
      <p>The XY plot allows to plot in the reverse X direction. The choice of the control pointsis by "user". You may have to trick the ranging of 't'. "Plot" is an export. Thereis no limit in the length of X, Y. With thiskind of spline, you always have to at leastduplicate end points [here RHS is triplicate] </p>
    </text>
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    <math>
      <input>
        <e type="operand">XY</e>
        <e type="operand">X</e>
        <e type="function" preserve="true" args="1">transpose</e>
        <e type="operand">Y</e>
        <e type="function" preserve="true" args="1">transpose</e>
        <e type="function" preserve="true" args="2">augment</e>
        <e type="operator" args="2">:</e>
      </input>
    </math>
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    <math>
      <input>
        <e type="operand">u</e>
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        <e type="operand">u</e>
        <e type="operand">Y</e>
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        <e type="function" args="2">Bsp</e>
        <e type="operator" args="2">:</e>
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        <e type="operand">u</e>
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        <e type="operand">u</e>
        <e type="operand">X</e>
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        <e type="operand">Points</e>
        <e type="operand">X</e>
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        <e type="operand">Y</e>
        <e type="function" preserve="true" args="1">transpose</e>
        <e type="operand" style="string">.</e>
        <e type="operand">15</e>
        <e type="operand" style="string">black</e>
        <e type="function" args="5">plotG</e>
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        <e type="operand">Plot</e>
        <e type="operand">t</e>
        <e type="operand">1.875</e>
        <e type="operand">6</e>
        <e type="operand">1.9</e>
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        <e type="operand">i</e>
        <e type="operand">1</e>
        <e type="operand">t</e>
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        <e type="function" preserve="true" args="2">range</e>
        <e type="operand">vx</e>
        <e type="operand">i</e>
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        <e type="operand">t</e>
        <e type="operand">i</e>
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        <e type="operand">vy</e>
        <e type="operand">i</e>
        <e type="function" preserve="true" args="2">el</e>
        <e type="operand">t</e>
        <e type="operand">i</e>
        <e type="function" preserve="true" args="2">el</e>
        <e type="function" args="1">oy</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="function" preserve="true" args="3">for</e>
        <e type="operand">vx</e>
        <e type="operand">vy</e>
        <e type="function" preserve="true" args="2">augment</e>
        <e type="operand">3</e>
        <e type="operand">1</e>
        <e type="function" preserve="true" args="5">line</e>
        <e type="operator" args="2">:</e>
      </input>
    </math>
  </region>
  <region id="16" left="270" top="864" width="386" height="206" border="true" color="#000000" bgColor="#ffffff" fontSize="10">
    <xyplot width="376" height="198" smoothing="false" points="100">
      <propertiessource index="1" sourcetype="PropertyGrid" />
      <grid gridcolor="LightGray" gridpattern="Solid" gridthickness="1" isxgrid="true" isygrid="true" />
      <xaxes xmin="1.75" xmax="2.25" xtick="0.125" numberformat="General" decimalplaces="3" />
      <yaxes ymin="-1.25" ymax="1.25" ytick="0.5" numberformat="General" decimalplaces="3" />
      <y2axes isy2axis="false" y2min="-1" y2max="1" y2tick="0.5" numberformat="General" decimalplaces="3" />
      <title2d title="Gaussian Robotics" titlefont="Times New Roman, 14.25pt, style=Bold" titlefontcolor="Black" />
      <xylabel labelfont="Arial, 11.25pt" labelfontcolor="Black" tickfont="Arial, 9.75pt" tickfontcolor="Black" xlabel="x" ylabel="y" y2label="y2" />
      <legend isbordervisible="true" islegendvisible="true" legendbackcolor="WhiteSmoke" legendbordercolor="Black" legendfont="Arial, 8pt" legendposition="SouthWest" textcolor="Black" />
      <traces>
        <trace seriesname="----- XY ----- " isy2data="false" isvisible="true" plotmethod="Lines" linecolor="Blue" linethickness="1" linepattern="Solid" symbolsize="8" symboltype="None" symbolborderthickness="1" symbolbordercolor="Black" symbolfillcolor="White" />
        <trace seriesname="Gaussian fillet" isy2data="false" isvisible="true" plotmethod="Lines" linecolor="Red" linethickness="1" linepattern="Solid" symbolsize="8" symboltype="None" symbolborderthickness="1" symbolbordercolor="Black" symbolfillcolor="White" />
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        <e type="operand">XY</e>
        <e type="operand">Plot</e>
        <e type="operand">2</e>
        <e type="operand">1</e>
        <e type="function" preserve="true" args="4">sys</e>
      </input>
    </xyplot>
  </region>
  <region id="17" left="18" top="927" width="240" height="158" border="true" color="#000000" bgColor="#ffffff" fontSize="10">
    <plot type="2d" render="lines" scale_x="5.93426043030063" scale_y="69.3181247169315" scale_z="411.351804610331" rotate_x="0" rotate_y="0" rotate_z="0" transpose_x="-1280" transpose_y="4" transpose_z="0">
      <input>
        <e type="operand">XY</e>
        <e type="operand">Plot</e>
        <e type="operand">Points</e>
        <e type="operand">3</e>
        <e type="operand">1</e>
        <e type="function" preserve="true" args="5">sys</e>
      </input>
    </plot>
  </region>
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      <input>
        <e type="operand">X</e>
        <e type="operand">0.5</e>
        <e type="operand">0.5</e>
        <e type="operand">2</e>
        <e type="operand">2</e>
        <e type="operand">2</e>
        <e type="operand">3</e>
        <e type="operand">3</e>
        <e type="operand">3</e>
        <e type="operand">1</e>
        <e type="operand">8</e>
        <e type="function" preserve="true" args="10">mat</e>
        <e type="operator" args="2">:</e>
        <e type="operand">Y</e>
        <e type="operand">0.5</e>
        <e type="operand">0.5</e>
        <e type="operand">0.5</e>
        <e type="operand">2</e>
        <e type="operand">1</e>
        <e type="operator" args="1">-</e>
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    <math evaluate="false" exponentialThreshold="3">
      <input>
        <e type="operand">M</e>
        <e type="operand">Min</e>
        <e type="operand">Max</e>
        <e type="function" args="3">Scale</e>
        <e type="operand">Max</e>
        <e type="operand">Min</e>
        <e type="operator" args="2">-</e>
        <e type="bracket">(</e>
        <e type="operand">M</e>
        <e type="operand">M</e>
        <e type="function" preserve="true" args="1">min</e>
        <e type="operator" args="2">-</e>
        <e type="operand">M</e>
        <e type="function" preserve="true" args="1">max</e>
        <e type="operand">M</e>
        <e type="function" preserve="true" args="1">min</e>
        <e type="operator" args="2">-</e>
        <e type="operator" args="2">/</e>
        <e type="bracket">(</e>
        <e type="operator" args="2">*</e>
        <e type="operand">Min</e>
        <e type="operator" args="2">+</e>
        <e type="operator" args="2">:</e>
      </input>
    </math>
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    <math fractionType="fraction">
      <input>
        <e type="operand">x</e>
        <e type="function" args="1">J</e>
        <e type="operand">1</e>
        <e type="operator" args="1">-</e>
        <e type="function" args="1">b</e>
        <e type="operator" args="2">:</e>
        <e type="operand">x</e>
        <e type="function" args="1">J</e>
        <e type="operand">0</e>
        <e type="function" args="1">b</e>
        <e type="operator" args="2">:</e>
        <e type="operand">2</e>
        <e type="operand">1</e>
        <e type="function" preserve="true" args="4">mat</e>
      </input>
      <result action="numeric">
        <e type="operand">1</e>
        <e type="operand">6</e>
        <e type="operator" args="2">/</e>
        <e type="operand">2</e>
        <e type="operand">3</e>
        <e type="operator" args="2">/</e>
        <e type="operand">2</e>
        <e type="operand">1</e>
        <e type="function" preserve="true" args="4">mat</e>
      </result>
    </math>
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