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        <e type="operand">u</e>
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        <e type="operand">1</e>
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        <e type="operand">u</e>
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        <e type="bracket">(</e>
        <e type="operand">u</e>
        <e type="operand">0</e>
        <e type="operator" args="2">≤</e>
        <e type="bracket">(</e>
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        <e type="operand">1</e>
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        <e type="operand">2</e>
        <e type="operand">u</e>
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        <e type="operand">1</e>
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        <e type="bracket">(</e>
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        <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>
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        <e type="operand">u</e>
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        <e type="bracket">(</e>
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        <e type="operand">u</e>
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        <e type="bracket">(</e>
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        <e type="operand">u</e>
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        <e type="operand">u</e>
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        <e type="operator" args="2">≤</e>
        <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>
        <e type="operator" args="2">-</e>
        <e type="bracket">(</e>
        <e type="operand">3</e>
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      <p bold="true">The Gaussian b-spline tool</p>
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        <p>Gaussian basis 'b-spline'</p>
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        <e type="operand">x</e>
        <e type="operand">2</e>
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        <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>
        <e type="operand">v</e>
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    <math>
      <input>
        <e type="operand">X</e>
        <e type="operand">1.875</e>
        <e type="operand">1.875</e>
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        <e type="operand">2.05</e>
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        <e type="operand">2.125</e>
        <e type="operand">2.125</e>
        <e type="operand">1</e>
        <e type="operand">8</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>
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      <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>
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    <math>
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        <e type="operand">X</e>
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        <e type="operand">Y</e>
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    <math>
      <input>
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        <e type="operand">u</e>
        <e type="operand">Y</e>
        <e type="function" preserve="true" args="1">transpose</e>
        <e type="function" args="2">Bsp</e>
        <e type="operator" args="2">:</e>
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    <math>
      <input>
        <e type="operand">u</e>
        <e type="function" args="1">ox</e>
        <e type="operand">u</e>
        <e type="operand">X</e>
        <e type="function" preserve="true" args="1">transpose</e>
        <e type="function" args="2">Bsp</e>
        <e type="operator" args="2">:</e>
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    <math>
      <input>
        <e type="operand">Plot</e>
        <e type="operand">t</e>
        <e type="operand">1.875</e>
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        <e type="operand">1.9</e>
        <e type="function" preserve="true" args="3">range</e>
        <e type="operator" args="2">:</e>
        <e type="operand">i</e>
        <e type="operand">1</e>
        <e type="operand">t</e>
        <e type="function" preserve="true" args="1">rows</e>
        <e type="function" preserve="true" args="2">range</e>
        <e type="operand">vx</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">ox</e>
        <e type="operator" args="2">:</e>
        <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>
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    <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" />
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      <yaxes ymin="-1.25" ymax="1.25" ytick="0.5" numberformat="General" decimalplaces="3" />
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        <e type="operand">XY</e>
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        <e type="operand">2</e>
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    <math>
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        <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>
      </input>
    </math>
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    <math>
      <input>
        <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>
        <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>
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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>
  </region>
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    <math>
      <input>
        <e type="operand">u</e>
        <e type="function" args="1">oy</e>
        <e type="operand">u</e>
        <e type="operand">Y</e>
        <e type="function" preserve="true" args="1">transpose</e>
        <e type="function" args="2">Bsp</e>
        <e type="operator" args="2">:</e>
      </input>
    </math>
  </region>
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    <math>
      <input>
        <e type="operand">u</e>
        <e type="function" args="1">ox</e>
        <e type="operand">u</e>
        <e type="operand">X</e>
        <e type="function" preserve="true" args="1">transpose</e>
        <e type="function" args="2">Bsp</e>
        <e type="operator" args="2">:</e>
      </input>
    </math>
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    <math>
      <input>
        <e type="operand">Plot</e>
        <e type="operand">t</e>
        <e type="operand">1.5</e>
        <e type="operand">7</e>
        <e type="operand">1.51</e>
        <e type="function" preserve="true" args="3">range</e>
        <e type="operator" args="2">:</e>
        <e type="operand">i</e>
        <e type="operand">1</e>
        <e type="operand">t</e>
        <e type="function" preserve="true" args="1">rows</e>
        <e type="function" preserve="true" args="2">range</e>
        <e type="operand">vx</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">ox</e>
        <e type="operator" args="2">:</e>
        <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>
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      <p>We will not eternise on that, just suggestive of some fitting techniques. You may have to scalesomething and many things  in there.</p>
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