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      <description />
      <author>Mathsoft Engineering &amp; Education, Inc.</author>
      <company>Mathsoft Engineering &amp; Education, Inc.</company>
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    <calculation>
      <builtInVariables array-origin="0" convergence-tolerance="0.001" constraint-tolerance="0.001" random-seed="1226606285" prn-precision="4" prn-col-width="8" />
      <calculationBehavior automatic-recalculation="true" matrix-strict-singularity-check="true" optimize-expressions="false" exact-boolean="false" strings-use-origin="false" zero-over-zero="0">
        <compatibility multiple-assignment="MC12" local-assignment="MC12" />
      </calculationBehavior>
      <units>
        <currentUnitSystem name="mks" customized="false" />
      </units>
    </calculation>
    <editor protection-level="none" view-annotations="false" view-regions="false">
      <ruler is-visible="false" ruler-unit="in" />
      <grid granularity-x="6" granularity-y="6" />
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    <fileFormat screen-dpi="96" image-type="image/png" image-quality="75" save-numeric-results="true" exclude-large-results="false" save-text-images="false" />
    <miscellaneous>
      <handbook handbook-region-tag-ub="911" can-delete-original-handbook-regions="true" can-delete-user-regions="true" can-print="true" can-copy="true" can-save="true" file-permission-mask="4294967295" />
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      <png item-idref="1" display-width="54" display-height="42" />
      <link href="./Visualiz.xmcd" title="Links to Visualization and Synthetic Images " popup="false" />
      <rendering item-idref="2" />
    </region>
    <region region-id="803" left="66" top="6.75" width="243.75" height="14.25" align-x="66" align-y="18" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag="">
      <text use-page-width="false" push-down="false" lock-width="true">
        <p style="Normal" margin-left="0" margin-right="0" text-indent="inherit" text-align="left" list-style-type="inherit" tabs="inherit">
          <b>
            <c val="#008080">VISUALIZATION AND SYNTHETIC IMAGES</c>
          </b>
        </p>
      </text>
    </region>
    <region region-id="315" left="66" top="27.75" width="110.25" height="18" align-x="66" align-y="42" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag="">
      <text use-page-width="false" push-down="false" lock-width="true">
        <p style="Normal" margin-left="0" margin-right="0" text-indent="inherit" text-align="left" list-style-type="inherit" tabs="inherit">
          <f size="16">
            <b>
              <c val="#800080">Bitmapped Type</c>
            </b>
          </f>
        </p>
      </text>
      <indexes>
        <phrase>bitmapped type</phrase>
        <phrase>type, bitmapped</phrase>
      </indexes>
    </region>
    <region region-id="304" left="6" top="54" width="344.25" height="5.25" align-x="6" align-y="54" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag="">
      <png item-idref="3" display-width="342.75" display-height="3.75" />
      <rendering item-idref="4" />
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    <region region-id="319" left="6" top="90.75" width="291" height="71.25" align-x="6" align-y="102" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag="">
      <text use-page-width="false" push-down="false" lock-width="true">
        <p style="Normal" margin-left="0" margin-right="0" text-indent="inherit" text-align="left" list-style-type="inherit" tabs="inherit">The type on this screen is a simple image in which each pixel is either on (and possibly colored) or off (white). You can produce some interesting effects by applying some of the functions in this Extension Pack to a sample of bitmapped type. Here is a sample containing a few words in various fonts and line weights:</p>
      </text>
    </region>
    <region region-id="320" left="36" top="168.75" width="162.75" height="15.75" align-x="52.5" align-y="180" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag="">
      <math optimize="false" disable-calc="false">
        <ml:define warning="WarnRedefinedBIUnit">
          <ml:id xml:space="preserve">A</ml:id>
          <ml:apply>
            <ml:id xml:space="preserve">READ_IMAGE</ml:id>
            <ml:str xml:space="preserve">type.bmp</ml:str>
          </ml:apply>
        </ml:define>
      </math>
      <rendering item-idref="5" />
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    <region region-id="907" left="54" top="198" width="181.5" height="120" align-x="144" align-y="198" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag="">
      <component hide-arguments="false" clsid-buddy="8442da2d-08d7-45ad-a4a6-f28bee6ae06a" item-idref="6" disable-calc="false">
        <inputs>
          <ml:id xml:space="preserve">A</ml:id>
        </inputs>
        <outputs />
      </component>
      <rendering item-idref="7" />
    </region>
    <region region-id="521" left="6" top="330.75" width="189" height="14.25" align-x="6" align-y="342" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag="">
      <text use-page-width="false" push-down="false" lock-width="true">
        <p style="Normal" margin-left="0" margin-right="0" text-indent="inherit" text-align="left" list-style-type="inherit" tabs="inherit">Now we'll try some basic transformations:</p>
      </text>
    </region>
    <region region-id="522" left="6" top="354.75" width="106.5" height="14.25" align-x="6" align-y="366" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag="">
      <text use-page-width="false" push-down="false" lock-width="true">
        <p style="Normal" margin-left="0" margin-right="0" text-indent="inherit" text-align="left" list-style-type="inherit" tabs="inherit">Make the type <b>thicker</b><f family="Times New Roman" charset="0"><inlineAttr font-weight="normal" line-through="false">:</inlineAttr></f></p>
      </text>
      <indexes>
        <phrase>type, fatter</phrase>
      </indexes>
    </region>
    <region region-id="906" left="54" top="378" width="181.5" height="120" align-x="144" align-y="378" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag="">
      <component hide-arguments="false" clsid-buddy="8442da2d-08d7-45ad-a4a6-f28bee6ae06a" item-idref="8" disable-calc="false">
        <inputs>
          <ml:apply>
            <ml:id xml:space="preserve">erode4</ml:id>
            <ml:sequence>
              <ml:id xml:space="preserve">A</ml:id>
              <ml:real>100</ml:real>
            </ml:sequence>
          </ml:apply>
        </inputs>
        <outputs />
      </component>
      <rendering item-idref="9" />
    </region>
    <region region-id="524" left="0" top="522" width="6000" height="6" align-x="0" align-y="522" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag="">
      <pageBreak />
    </region>
    <region region-id="601" left="6" top="546.75" width="102.75" height="14.25" align-x="6" align-y="558" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag="">
      <text use-page-width="false" push-down="false" lock-width="true">
        <p style="Normal" margin-left="0" margin-right="0" text-indent="inherit" text-align="left" list-style-type="inherit" tabs="inherit">Generate <b>outline</b> type:</p>
      </text>
      <indexes>
        <phrase>type, outline</phrase>
      </indexes>
    </region>
    <region region-id="905" left="54" top="576" width="181.5" height="120" align-x="144" align-y="576" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag="">
      <component hide-arguments="false" clsid-buddy="8442da2d-08d7-45ad-a4a6-f28bee6ae06a" item-idref="10" disable-calc="false">
        <inputs>
          <ml:apply>
            <ml:minus />
            <ml:real>255</ml:real>
            <ml:parens>
              <ml:apply>
                <ml:minus />
                <ml:id xml:space="preserve">A</ml:id>
                <ml:apply>
                  <ml:id xml:space="preserve">erode4</ml:id>
                  <ml:sequence>
                    <ml:id xml:space="preserve">A</ml:id>
                    <ml:real>100</ml:real>
                  </ml:sequence>
                </ml:apply>
              </ml:apply>
            </ml:parens>
          </ml:apply>
        </inputs>
        <outputs />
      </component>
      <rendering item-idref="11" />
    </region>
    <region region-id="610" left="6" top="714.75" width="137.25" height="14.25" align-x="6" align-y="726" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag="">
      <text use-page-width="false" push-down="false" lock-width="true">
        <p style="Normal" margin-left="0" margin-right="0" text-indent="inherit" text-align="left" list-style-type="inherit" tabs="inherit">Put a <b>shadow</b> behind the type:</p>
      </text>
      <indexes>
        <phrase>type, shadow behind</phrase>
      </indexes>
    </region>
    <region region-id="611" left="36" top="738.75" width="327" height="15.75" align-x="51" align-y="750" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag="">
      <math optimize="false" disable-calc="false">
        <ml:define warning="WarnRedefinedBIUnit">
          <ml:id xml:space="preserve">T</ml:id>
          <ml:apply>
            <ml:id xml:space="preserve">putregion</ml:id>
            <ml:sequence>
              <ml:id xml:space="preserve">A</ml:id>
              <ml:apply>
                <ml:id xml:space="preserve">submatrix</ml:id>
                <ml:sequence>
                  <ml:id xml:space="preserve">A</ml:id>
                  <ml:real>0</ml:real>
                  <ml:apply>
                    <ml:minus />
                    <ml:apply>
                      <ml:id xml:space="preserve">rows</ml:id>
                      <ml:id xml:space="preserve">A</ml:id>
                    </ml:apply>
                    <ml:real>3</ml:real>
                  </ml:apply>
                  <ml:real>0</ml:real>
                  <ml:apply>
                    <ml:minus />
                    <ml:apply>
                      <ml:id xml:space="preserve">cols</ml:id>
                      <ml:id xml:space="preserve">A</ml:id>
                    </ml:apply>
                    <ml:real>3</ml:real>
                  </ml:apply>
                </ml:sequence>
              </ml:apply>
              <ml:real>2</ml:real>
              <ml:real>2</ml:real>
            </ml:sequence>
          </ml:apply>
        </ml:define>
      </math>
      <rendering item-idref="12" />
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    <region region-id="612" left="36" top="762.75" width="112.5" height="15.75" align-x="51" align-y="774" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag="">
      <math optimize="false" disable-calc="false">
        <ml:define warning="WarnRedefinedBIUnit">
          <ml:id xml:space="preserve">S</ml:id>
          <ml:apply>
            <ml:id xml:space="preserve">scale</ml:id>
            <ml:sequence>
              <ml:id xml:space="preserve">T</ml:id>
              <ml:real>160</ml:real>
              <ml:real>255</ml:real>
            </ml:sequence>
          </ml:apply>
        </ml:define>
      </math>
      <rendering item-idref="13" />
    </region>
    <region region-id="904" left="54" top="792" width="181.5" height="120" align-x="144" align-y="792" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag="">
      <component hide-arguments="false" clsid-buddy="8442da2d-08d7-45ad-a4a6-f28bee6ae06a" item-idref="14" disable-calc="false">
        <inputs>
          <ml:apply>
            <ml:id xml:space="preserve">and</ml:id>
            <ml:sequence>
              <ml:id xml:space="preserve">S</ml:id>
              <ml:id xml:space="preserve">A</ml:id>
            </ml:sequence>
          </ml:apply>
        </inputs>
        <outputs />
      </component>
      <rendering item-idref="15" />
    </region>
    <region region-id="618" left="12" top="930.75" width="163.5" height="14.25" align-x="12" align-y="942" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag="">
      <text use-page-width="false" push-down="false" lock-width="true">
        <p style="Normal" margin-left="0" margin-right="0" text-indent="inherit" text-align="left" list-style-type="inherit" tabs="inherit">Make a <b>cross-stitch</b> sampler effect:</p>
      </text>
      <indexes>
        <phrase>type, cross-stitch sampler</phrase>
      </indexes>
    </region>
    <region region-id="903" left="54" top="960" width="181.5" height="120" align-x="144" align-y="960" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag="">
      <component hide-arguments="false" clsid-buddy="8442da2d-08d7-45ad-a4a6-f28bee6ae06a" item-idref="16" disable-calc="false">
        <inputs>
          <ml:apply>
            <ml:id xml:space="preserve">diacrisp</ml:id>
            <ml:id xml:space="preserve">A</ml:id>
          </ml:apply>
        </inputs>
        <outputs />
      </component>
      <rendering item-idref="17" />
    </region>
    <region region-id="629" left="0" top="1098" width="6000" height="6" align-x="0" align-y="1098" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag="">
      <pageBreak />
    </region>
    <region region-id="630" left="6" top="1110.75" width="288.75" height="14.25" align-x="6" align-y="1122" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag="">
      <text use-page-width="false" push-down="false" lock-width="true">
        <p style="Normal" margin-left="0" margin-right="0" text-indent="inherit" text-align="left" list-style-type="inherit" tabs="inherit">Fill the image with <b>randomly placed copies</b> of the original type:</p>
      </text>
    </region>
    <region region-id="631" left="6" top="1134.75" width="114.75" height="14.25" align-x="6" align-y="1146" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag="">
      <text use-page-width="false" push-down="false" lock-width="true">
        <p style="Normal" margin-left="0" margin-right="0" text-indent="inherit" text-align="left" list-style-type="inherit" tabs="inherit">Set the number of copies:</p>
      </text>
    </region>
    <region region-id="632" left="36" top="1158.75" width="33.75" height="15.75" align-x="53.25" align-y="1170" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag="">
      <math optimize="false" disable-calc="false">
        <ml:define warning="WarnRedefinedBIUnit">
          <ml:id xml:space="preserve">N</ml:id>
          <ml:real>6</ml:real>
        </ml:define>
      </math>
      <rendering item-idref="18" />
    </region>
    <region region-id="633" left="78" top="1158.75" width="68.25" height="15.75" align-x="92.25" align-y="1170" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag="">
      <math optimize="false" disable-calc="false">
        <ml:define>
          <ml:id xml:space="preserve">k</ml:id>
          <ml:range>
            <ml:real>0</ml:real>
            <ml:apply>
              <ml:minus />
              <ml:id xml:space="preserve">N</ml:id>
              <ml:real>1</ml:real>
            </ml:apply>
          </ml:range>
        </ml:define>
      </math>
      <rendering item-idref="19" />
    </region>
    <region region-id="634" left="36" top="1182.75" width="133.5" height="17.25" align-x="153" align-y="1194" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag="">
      <math optimize="false" disable-calc="false">
        <ml:define warning="WarnRedefinedBIUnit">
          <ml:apply>
            <ml:indexer />
            <ml:id xml:space="preserve">H</ml:id>
            <ml:sequence>
              <ml:apply>
                <ml:minus />
                <ml:apply>
                  <ml:id xml:space="preserve">rows</ml:id>
                  <ml:id xml:space="preserve">A</ml:id>
                </ml:apply>
                <ml:real>1</ml:real>
              </ml:apply>
              <ml:apply>
                <ml:minus />
                <ml:apply>
                  <ml:id xml:space="preserve">cols</ml:id>
                  <ml:id xml:space="preserve">A</ml:id>
                </ml:apply>
                <ml:real>1</ml:real>
              </ml:apply>
            </ml:sequence>
          </ml:apply>
          <ml:real>0</ml:real>
        </ml:define>
      </math>
      <rendering item-idref="20" />
    </region>
    <region region-id="635" left="6" top="1212.75" width="189" height="14.25" align-x="6" align-y="1224" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag="">
      <text use-page-width="false" push-down="false" lock-width="true">
        <p style="Normal" margin-left="0" margin-right="0" text-indent="inherit" text-align="left" list-style-type="inherit" tabs="inherit">The FFT can be used to make the copies </p>
      </text>
    </region>
    <region region-id="636" left="36" top="1236.75" width="261.75" height="17.25" align-x="281.25" align-y="1248" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag="">
      <math optimize="false" disable-calc="false">
        <ml:define warning="WarnRedefinedUDScalar">
          <ml:apply>
            <ml:indexer />
            <ml:id xml:space="preserve">H</ml:id>
            <ml:sequence>
              <ml:apply>
                <ml:id xml:space="preserve">floor</ml:id>
                <ml:apply>
                  <ml:id xml:space="preserve">rnd</ml:id>
                  <ml:apply>
                    <ml:minus />
                    <ml:apply>
                      <ml:id xml:space="preserve">rows</ml:id>
                      <ml:id xml:space="preserve">A</ml:id>
                    </ml:apply>
                    <ml:real>1</ml:real>
                  </ml:apply>
                </ml:apply>
              </ml:apply>
              <ml:apply>
                <ml:plus />
                <ml:apply>
                  <ml:id xml:space="preserve">floor</ml:id>
                  <ml:apply>
                    <ml:id xml:space="preserve">rnd</ml:id>
                    <ml:apply>
                      <ml:minus />
                      <ml:apply>
                        <ml:id xml:space="preserve">cols</ml:id>
                        <ml:id xml:space="preserve">A</ml:id>
                      </ml:apply>
                      <ml:real>1</ml:real>
                    </ml:apply>
                  </ml:apply>
                </ml:apply>
                <ml:apply>
                  <ml:mult style="default" />
                  <ml:real>0</ml:real>
                  <ml:id xml:space="preserve">k</ml:id>
                </ml:apply>
              </ml:apply>
            </ml:sequence>
          </ml:apply>
          <ml:real>1</ml:real>
        </ml:define>
      </math>
      <rendering item-idref="21" />
    </region>
    <region region-id="911" left="324" top="1236.75" width="103.5" height="28.5" align-x="324" align-y="1248" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag="">
      <text use-page-width="false" push-down="false" lock-width="true">
        <p style="Normal" margin-left="0" margin-right="0" text-indent="inherit" text-align="left" list-style-type="inherit" tabs="inherit">recompute for different patterns</p>
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    </region>
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      <math optimize="false" disable-calc="false">
        <ml:define>
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            <ml:id xml:space="preserve">Re</ml:id>
            <ml:apply>
              <ml:id xml:space="preserve">ICFFT</ml:id>
              <ml:apply>
                <ml:vectorize />
                <ml:apply>
                  <ml:mult style="default" />
                  <ml:apply>
                    <ml:id xml:space="preserve">CFFT</ml:id>
                    <ml:id xml:space="preserve">A</ml:id>
                  </ml:apply>
                  <ml:apply>
                    <ml:id xml:space="preserve">CFFT</ml:id>
                    <ml:id xml:space="preserve">H</ml:id>
                  </ml:apply>
                </ml:apply>
              </ml:apply>
            </ml:apply>
          </ml:apply>
        </ml:define>
      </math>
      <rendering item-idref="22" />
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    <region region-id="902" left="54" top="1296" width="181.5" height="120" align-x="144" align-y="1296" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag="">
      <component hide-arguments="false" clsid-buddy="8442da2d-08d7-45ad-a4a6-f28bee6ae06a" item-idref="23" disable-calc="false">
        <inputs>
          <ml:apply>
            <ml:mult style="default" />
            <ml:id xml:space="preserve">P</ml:id>
            <ml:real>10000</ml:real>
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        </inputs>
        <outputs />
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    </region>
    <region region-id="541" left="6" top="1428.75" width="322.5" height="14.25" align-x="6" align-y="1440" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag="">
      <text use-page-width="false" push-down="false" lock-width="true">
        <p style="Normal" margin-left="0" margin-right="0" text-indent="inherit" text-align="left" list-style-type="inherit" tabs="inherit">Make an <b>embossed</b> effect using the row and column gradient functions:</p>
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      <indexes>
        <phrase>type, embossed</phrase>
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    <region region-id="542" left="36" top="1452.75" width="90.75" height="15.75" align-x="60" align-y="1464" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag="">
      <math optimize="false" disable-calc="false">
        <ml:define>
          <ml:id xml:space="preserve">GR</ml:id>
          <ml:apply>
            <ml:id xml:space="preserve">rowgrad</ml:id>
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        </ml:define>
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    </region>
    <region region-id="543" left="36" top="1476.75" width="87" height="15.75" align-x="60.75" align-y="1488" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag="">
      <math optimize="false" disable-calc="false">
        <ml:define>
          <ml:id xml:space="preserve">GC</ml:id>
          <ml:apply>
            <ml:id xml:space="preserve">colgrad</ml:id>
            <ml:id xml:space="preserve">A</ml:id>
          </ml:apply>
        </ml:define>
      </math>
      <rendering item-idref="26" />
    </region>
    <region region-id="544" left="36" top="1500.75" width="189.75" height="15.75" align-x="52.5" align-y="1512" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag="">
      <math optimize="false" disable-calc="false">
        <ml:define warning="WarnRedefinedBIUnit">
          <ml:id xml:space="preserve">G</ml:id>
          <ml:apply>
            <ml:id xml:space="preserve">gaussconv</ml:id>
            <ml:sequence>
              <ml:apply>
                <ml:neg />
                <ml:parens>
                  <ml:apply>
                    <ml:id xml:space="preserve">or</ml:id>
                    <ml:sequence>
                      <ml:id xml:space="preserve">GR</ml:id>
                      <ml:id xml:space="preserve">GC</ml:id>
                    </ml:sequence>
                  </ml:apply>
                </ml:parens>
              </ml:apply>
              <ml:real>.0003</ml:real>
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          </ml:apply>
        </ml:define>
      </math>
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    </region>
    <region region-id="901" left="54" top="1530" width="181.5" height="120" align-x="144" align-y="1530" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag="">
      <component hide-arguments="false" clsid-buddy="8442da2d-08d7-45ad-a4a6-f28bee6ae06a" item-idref="28" disable-calc="false">
        <inputs>
          <ml:apply>
            <ml:id xml:space="preserve">scale</ml:id>
            <ml:sequence>
              <ml:id xml:space="preserve">G</ml:id>
              <ml:real>0</ml:real>
              <ml:real>255</ml:real>
            </ml:sequence>
          </ml:apply>
        </inputs>
        <outputs />
      </component>
      <rendering item-idref="29" />
    </region>
    <region region-id="697" left="0" top="1668" width="6000" height="6" align-x="0" align-y="1668" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag="">
      <pageBreak />
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    <region region-id="804" left="6" top="1686.75" width="325.5" height="85.5" align-x="6" align-y="1698" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag="">
      <text use-page-width="false" push-down="false" lock-width="true">
        <p style="Normal" margin-left="0" margin-right="0" text-indent="inherit" text-align="left" list-style-type="inherit" tabs="inherit">All of these mimic the sort of text manipulation features you might expect to find in a reasonable painting program. The only trouble is, they don't conserve font features, that is, they readily round corners on sans serif fonts, and square edges on serif fonts. This may give you some insight as to why PostScript and TrueType fonts are required for more sophisticated font processing.</p>
      </text>
    </region>
    <region region-id="805" left="6" top="1782.75" width="329.25" height="128.25" align-x="6" align-y="1794" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag="">
      <text use-page-width="false" push-down="false" lock-width="true">
        <p style="Normal" margin-left="0" margin-right="0" text-indent="inherit" text-align="left" list-style-type="inherit" tabs="inherit">A different approach to modifying the type image is to transform </p>
        <p style="Normal" margin-left="0" margin-right="0" text-indent="inherit" text-align="left" list-style-type="inherit" tabs="inherit">the locations of the black pixels directly. In <f family="Times New Roman" charset="0"><inlineAttr font-weight="normal" line-through="false">Mathcad, i</inlineAttr></f>t's easiest to do this if each pixel is stored as a complex number, since one value can then hold two coordinates. These values can be generated by making a list of complex numbers representing the coordinates within the image of each black pixel. The origin is the lower left corner.</p>
        <p style="Normal" margin-left="0" margin-right="0" text-indent="inherit" text-align="left" list-style-type="inherit" tabs="inherit" />
        <p style="Normal" margin-left="0" margin-right="0" text-indent="inherit" text-align="left" list-style-type="inherit" tabs="inherit">This computation takes a while, but once the locations are stored, subsequent interesting transformations are very speedy.</p>
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    </region>
    <region region-id="806" left="36" top="1920.75" width="86.25" height="15.75" align-x="52.5" align-y="1932" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag="">
      <math optimize="false" disable-calc="false">
        <ml:define warning="WarnRedefinedUDScalar">
          <ml:id xml:space="preserve">H</ml:id>
          <ml:apply>
            <ml:minus />
            <ml:apply>
              <ml:id xml:space="preserve">rows</ml:id>
              <ml:id xml:space="preserve">A</ml:id>
            </ml:apply>
            <ml:real>1</ml:real>
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      </math>
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    </region>
    <region region-id="807" left="144" top="1920.75" width="84.75" height="15.75" align-x="163.5" align-y="1932" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag="">
      <math optimize="false" disable-calc="false">
        <ml:define warning="WarnRedefinedBIUnit">
          <ml:id xml:space="preserve">W</ml:id>
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            <ml:minus />
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              <ml:id xml:space="preserve">A</ml:id>
            </ml:apply>
            <ml:real>1</ml:real>
          </ml:apply>
        </ml:define>
      </math>
      <rendering item-idref="31" />
    </region>
    <region region-id="854" left="36" top="1944.75" width="211.5" height="183.75" align-x="52.5" align-y="1956" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag="">
      <math optimize="false" disable-calc="false">
        <ml:define warning="WarnRedefinedBIUnit">
          <ml:id xml:space="preserve">C</ml:id>
          <ml:program>
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              <ml:id xml:space="preserve">p</ml:id>
              <ml:real>0</ml:real>
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            <ml:localDefine>
              <ml:apply>
                <ml:indexer />
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                <ml:id xml:space="preserve">p</ml:id>
              </ml:apply>
              <ml:real>0</ml:real>
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            <ml:for>
              <ml:id xml:space="preserve">m</ml:id>
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                <ml:real>0</ml:real>
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              </ml:range>
              <ml:for>
                <ml:id xml:space="preserve">n</ml:id>
                <ml:range>
                  <ml:real>0</ml:real>
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                </ml:range>
                <ml:ifThen>
                  <ml:apply>
                    <ml:equal />
                    <ml:apply>
                      <ml:indexer />
                      <ml:id xml:space="preserve">A</ml:id>
                      <ml:sequence>
                        <ml:apply>
                          <ml:minus />
                          <ml:id xml:space="preserve">H</ml:id>
                          <ml:id xml:space="preserve">m</ml:id>
                        </ml:apply>
                        <ml:id xml:space="preserve">n</ml:id>
                      </ml:sequence>
                    </ml:apply>
                    <ml:real>0</ml:real>
                  </ml:apply>
                  <ml:program>
                    <ml:localDefine>
                      <ml:id xml:space="preserve">p</ml:id>
                      <ml:apply>
                        <ml:plus />
                        <ml:id xml:space="preserve">p</ml:id>
                        <ml:real>1</ml:real>
                      </ml:apply>
                    </ml:localDefine>
                    <ml:localDefine>
                      <ml:apply>
                        <ml:indexer />
                        <ml:id xml:space="preserve">C</ml:id>
                        <ml:id xml:space="preserve">p</ml:id>
                      </ml:apply>
                      <ml:apply>
                        <ml:plus />
                        <ml:id xml:space="preserve">n</ml:id>
                        <ml:apply>
                          <ml:mult style="default" />
                          <ml:imag symbol="i">1</ml:imag>
                          <ml:parens>
                            <ml:apply>
                              <ml:minus />
                              <ml:id xml:space="preserve">m</ml:id>
                              <ml:apply>
                                <ml:div />
                                <ml:apply>
                                  <ml:plus />
                                  <ml:id xml:space="preserve">H</ml:id>
                                  <ml:real>1</ml:real>
                                </ml:apply>
                                <ml:real>2</ml:real>
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                            </ml:apply>
                          </ml:parens>
                        </ml:apply>
                      </ml:apply>
                    </ml:localDefine>
                  </ml:program>
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      <math optimize="false" disable-calc="false">
        <ml:define>
          <ml:id xml:space="preserve">r</ml:id>
          <ml:range>
            <ml:real>1</ml:real>
            <ml:apply>
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              </ml:apply>
              <ml:real>1</ml:real>
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        </ml:define>
      </math>
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      <math optimize="false" disable-calc="false">
        <ml:define warning="WarnRedefinedBIUnit">
          <ml:id xml:space="preserve">m</ml:id>
          <ml:range>
            <ml:real>0</ml:real>
            <ml:id xml:space="preserve">H</ml:id>
          </ml:range>
        </ml:define>
      </math>
      <rendering item-idref="34" />
    </region>
    <region region-id="858" left="246" top="2148.75" width="51" height="15.75" align-x="259.5" align-y="2160" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag="">
      <math optimize="false" disable-calc="false">
        <ml:define>
          <ml:id xml:space="preserve">n</ml:id>
          <ml:range>
            <ml:real>0</ml:real>
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          </ml:range>
        </ml:define>
      </math>
      <rendering item-idref="35" />
    </region>
    <region region-id="851" left="12" top="2178" width="6000" height="6" align-x="12" align-y="2178" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag="">
      <pageBreak />
    </region>
    <region region-id="814" left="6" top="2190.75" width="325.5" height="42.75" align-x="6" align-y="2202" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag="">
      <text use-page-width="false" push-down="false" lock-width="true">
        <p style="Normal" margin-left="0" margin-right="0" text-indent="inherit" text-align="left" list-style-type="inherit" tabs="inherit">Now we're in business. Most transformations move the black pixels to noninteger locations, so each location is rounded to the nearest integer-coordinate point. A function that does this is</p>
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    <region region-id="815" left="36" top="2244.75" width="45" height="14.25" align-x="36" align-y="2256" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag="">
      <text use-page-width="false" push-down="false" lock-width="true">
        <p style="Normal" margin-left="0" margin-right="0" text-indent="inherit" text-align="left" list-style-type="inherit" tabs="inherit">Rounding:</p>
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    <region region-id="816" left="102" top="2244.75" width="102" height="15.75" align-x="135" align-y="2256" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag="">
      <math optimize="false" disable-calc="false">
        <ml:define>
          <ml:function>
            <ml:id xml:space="preserve">rd</ml:id>
            <ml:boundVars>
              <ml:id xml:space="preserve">x</ml:id>
            </ml:boundVars>
          </ml:function>
          <ml:apply>
            <ml:id xml:space="preserve">floor</ml:id>
            <ml:apply>
              <ml:plus />
              <ml:id xml:space="preserve">x</ml:id>
              <ml:real>.5</ml:real>
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          </ml:apply>
        </ml:define>
      </math>
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    </region>
    <region region-id="828" left="6" top="2268.75" width="191.25" height="14.25" align-x="6" align-y="2280" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag="">
      <text use-page-width="false" push-down="false" lock-width="true">
        <p style="Normal" margin-left="0" margin-right="0" text-indent="inherit" text-align="left" list-style-type="inherit" tabs="inherit">A simple transformation makes <b>italic</b> type:</p>
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      <indexes>
        <phrase>italic type</phrase>
        <phrase>type, italic</phrase>
      </indexes>
    </region>
    <region region-id="818" left="36" top="2292.75" width="103.5" height="28.5" align-x="36" align-y="2304" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag="">
      <text use-page-width="false" push-down="false" lock-width="true">
        <p style="Normal" margin-left="0" margin-right="0" text-indent="inherit" text-align="left" list-style-type="inherit" tabs="inherit">Set the degree of slant (between -1 and 1):</p>
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    </region>
    <region region-id="819" left="168" top="2298.75" width="32.25" height="15.75" align-x="180.75" align-y="2310" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag="">
      <math optimize="false" disable-calc="false">
        <ml:define warning="WarnRedefinedBIUnit">
          <ml:id xml:space="preserve">s</ml:id>
          <ml:real>.5</ml:real>
        </ml:define>
      </math>
      <rendering item-idref="37" />
    </region>
    <region region-id="824" left="36" top="2334.75" width="87" height="14.25" align-x="36" align-y="2346" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag="">
      <text use-page-width="false" push-down="false" lock-width="true">
        <p style="Normal" margin-left="0" margin-right="0" text-indent="inherit" text-align="left" list-style-type="inherit" tabs="inherit">The transformation:</p>
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    </region>
    <region region-id="821" left="162" top="2334.75" width="88.5" height="15.75" align-x="187.5" align-y="2346" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag="">
      <math optimize="false" disable-calc="false">
        <ml:define>
          <ml:function>
            <ml:id xml:space="preserve">f</ml:id>
            <ml:boundVars>
              <ml:id xml:space="preserve">z</ml:id>
            </ml:boundVars>
          </ml:function>
          <ml:apply>
            <ml:plus />
            <ml:id xml:space="preserve">z</ml:id>
            <ml:apply>
              <ml:mult style="default" />
              <ml:id xml:space="preserve">s</ml:id>
              <ml:apply>
                <ml:id xml:space="preserve">Im</ml:id>
                <ml:id xml:space="preserve">z</ml:id>
              </ml:apply>
            </ml:apply>
          </ml:apply>
        </ml:define>
      </math>
      <rendering item-idref="38" />
    </region>
    <region region-id="827" left="6" top="2358.75" width="168" height="14.25" align-x="6" align-y="2370" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag="">
      <text use-page-width="false" push-down="false" lock-width="true">
        <p style="Normal" margin-left="0" margin-right="0" text-indent="inherit" text-align="left" list-style-type="inherit" tabs="inherit">Apply the transformation and display:</p>
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    <region region-id="825" left="36" top="2380.5" width="52.5" height="24" align-x="57" align-y="2400" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag="">
      <math optimize="false" disable-calc="false">
        <ml:define>
          <ml:id xml:space="preserve">T1</ml:id>
          <ml:apply>
            <ml:vectorize />
            <ml:apply>
              <ml:id xml:space="preserve">f</ml:id>
              <ml:id xml:space="preserve">C</ml:id>
            </ml:apply>
          </ml:apply>
        </ml:define>
      </math>
      <rendering item-idref="39" />
    </region>
    <region region-id="760" left="0" top="2412" width="6000" height="6" align-x="0" align-y="2412" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag="">
      <pageBreak />
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    <region region-id="829" left="6" top="2424.75" width="324" height="28.5" align-x="6" align-y="2436" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag="">
      <text use-page-width="false" push-down="false" lock-width="true">
        <p style="Normal" margin-left="0" margin-right="0" text-indent="inherit" text-align="left" list-style-type="inherit" tabs="inherit">Pixels are redistributed into the image matrix: a complicated expression, but it works.</p>
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    </region>
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      <math optimize="false" disable-calc="false">
        <ml:define>
          <ml:apply>
            <ml:indexer />
            <ml:id xml:space="preserve">U1</ml:id>
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              <ml:id xml:space="preserve">H</ml:id>
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            </ml:sequence>
          </ml:apply>
          <ml:real>0</ml:real>
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      </math>
      <rendering item-idref="40" />
    </region>
    <region region-id="833" left="132" top="2472.75" width="194.25" height="36" align-x="297.75" align-y="2484" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag="">
      <math optimize="false" disable-calc="false">
        <ml:define warning="WarnRedefinedUDScalar">
          <ml:apply>
            <ml:indexer />
            <ml:id xml:space="preserve">U1</ml:id>
            <ml:sequence>
              <ml:apply>
                <ml:id xml:space="preserve">rd</ml:id>
                <ml:apply>
                  <ml:minus />
                  <ml:apply>
                    <ml:div />
                    <ml:apply>
                      <ml:plus />
                      <ml:id xml:space="preserve">H</ml:id>
                      <ml:real>1</ml:real>
                    </ml:apply>
                    <ml:real>2</ml:real>
                  </ml:apply>
                  <ml:apply>
                    <ml:id xml:space="preserve">Im</ml:id>
                    <ml:apply>
                      <ml:indexer />
                      <ml:id xml:space="preserve">T1</ml:id>
                      <ml:id xml:space="preserve">r</ml:id>
                    </ml:apply>
                  </ml:apply>
                </ml:apply>
              </ml:apply>
              <ml:apply>
                <ml:id xml:space="preserve">rd</ml:id>
                <ml:apply>
                  <ml:id xml:space="preserve">Re</ml:id>
                  <ml:apply>
                    <ml:indexer />
                    <ml:id xml:space="preserve">T1</ml:id>
                    <ml:id xml:space="preserve">r</ml:id>
                  </ml:apply>
                </ml:apply>
              </ml:apply>
            </ml:sequence>
          </ml:apply>
          <ml:real>255</ml:real>
        </ml:define>
      </math>
      <rendering item-idref="41" />
    </region>
    <region region-id="900" left="54" top="2520" width="181.5" height="120" align-x="144" align-y="2520" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag="">
      <component hide-arguments="false" clsid-buddy="8442da2d-08d7-45ad-a4a6-f28bee6ae06a" item-idref="42" disable-calc="false">
        <inputs>
          <ml:apply>
            <ml:minus />
            <ml:real>255</ml:real>
            <ml:id xml:space="preserve">U1</ml:id>
          </ml:apply>
        </inputs>
        <outputs />
      </component>
      <rendering item-idref="43" />
    </region>
    <region region-id="836" left="6" top="2658.75" width="127.5" height="14.25" align-x="6" align-y="2670" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag="">
      <text use-page-width="false" push-down="false" lock-width="true">
        <p style="Normal" margin-left="0" margin-right="0" text-indent="inherit" text-align="left" list-style-type="inherit" tabs="inherit">Here are some other effects:</p>
      </text>
    </region>
    <region region-id="763" left="18" top="2694.75" width="33" height="14.25" align-x="18" align-y="2706" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag="">
      <text use-page-width="false" push-down="false" lock-width="true">
        <p style="Normal" margin-left="0" margin-right="0" text-indent="inherit" text-align="left" list-style-type="inherit" tabs="inherit">
          <b>Wave:</b>
        </p>
      </text>
      <indexes>
        <phrase>type, wave effect</phrase>
      </indexes>
    </region>
    <region region-id="764" left="78" top="2686.5" width="138" height="33.75" align-x="105.75" align-y="2706" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag="">
      <math optimize="false" disable-calc="false">
        <ml:define warning="WarnRedefinedBIUnit">
          <ml:function>
            <ml:id xml:space="preserve">g</ml:id>
            <ml:boundVars>
              <ml:id xml:space="preserve">z</ml:id>
            </ml:boundVars>
          </ml:function>
          <ml:apply>
            <ml:plus />
            <ml:id xml:space="preserve">z</ml:id>
            <ml:apply>
              <ml:mult style="default" />
              <ml:imag symbol="i">2</ml:imag>
              <ml:parens>
                <ml:apply>
                  <ml:id xml:space="preserve">sin</ml:id>
                  <ml:apply>
                    <ml:div />
                    <ml:apply>
                      <ml:id xml:space="preserve">Re</ml:id>
                      <ml:id xml:space="preserve">z</ml:id>
                    </ml:apply>
                    <ml:real>10</ml:real>
                  </ml:apply>
                </ml:apply>
              </ml:parens>
            </ml:apply>
          </ml:apply>
        </ml:define>
      </math>
      <rendering item-idref="44" />
    </region>
    <region region-id="765" left="228" top="2686.5" width="54.75" height="24" align-x="249" align-y="2706" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag="">
      <math optimize="false" disable-calc="false">
        <ml:define warning="WarnRedefinedUDScalar">
          <ml:id xml:space="preserve">T1</ml:id>
          <ml:apply>
            <ml:vectorize />
            <ml:apply>
              <ml:id xml:space="preserve">g</ml:id>
              <ml:id xml:space="preserve">C</ml:id>
            </ml:apply>
          </ml:apply>
        </ml:define>
      </math>
      <rendering item-idref="45" />
    </region>
    <region region-id="766" left="78" top="2730.75" width="58.5" height="17.25" align-x="120" align-y="2742" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag="">
      <math optimize="false" disable-calc="false">
        <ml:define warning="WarnRedefinedUDScalar">
          <ml:apply>
            <ml:indexer />
            <ml:id xml:space="preserve">U1</ml:id>
            <ml:sequence>
              <ml:id xml:space="preserve">m</ml:id>
              <ml:id xml:space="preserve">n</ml:id>
            </ml:sequence>
          </ml:apply>
          <ml:real>0</ml:real>
        </ml:define>
      </math>
      <rendering item-idref="46" />
    </region>
    <region region-id="767" left="168" top="2730.75" width="194.25" height="36" align-x="333.75" align-y="2742" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag="">
      <math optimize="false" disable-calc="false">
        <ml:define warning="WarnRedefinedUDScalar">
          <ml:apply>
            <ml:indexer />
            <ml:id xml:space="preserve">U1</ml:id>
            <ml:sequence>
              <ml:apply>
                <ml:id xml:space="preserve">rd</ml:id>
                <ml:apply>
                  <ml:minus />
                  <ml:apply>
                    <ml:div />
                    <ml:apply>
                      <ml:plus />
                      <ml:id xml:space="preserve">H</ml:id>
                      <ml:real>1</ml:real>
                    </ml:apply>
                    <ml:real>2</ml:real>
                  </ml:apply>
                  <ml:apply>
                    <ml:id xml:space="preserve">Im</ml:id>
                    <ml:apply>
                      <ml:indexer />
                      <ml:id xml:space="preserve">T1</ml:id>
                      <ml:id xml:space="preserve">r</ml:id>
                    </ml:apply>
                  </ml:apply>
                </ml:apply>
              </ml:apply>
              <ml:apply>
                <ml:id xml:space="preserve">rd</ml:id>
                <ml:apply>
                  <ml:id xml:space="preserve">Re</ml:id>
                  <ml:apply>
                    <ml:indexer />
                    <ml:id xml:space="preserve">T1</ml:id>
                    <ml:id xml:space="preserve">r</ml:id>
                  </ml:apply>
                </ml:apply>
              </ml:apply>
            </ml:sequence>
          </ml:apply>
          <ml:real>255</ml:real>
        </ml:define>
      </math>
      <rendering item-idref="47" />
    </region>
    <region region-id="899" left="54" top="2772" width="181.5" height="120" align-x="144" align-y="2772" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag="">
      <component hide-arguments="false" clsid-buddy="8442da2d-08d7-45ad-a4a6-f28bee6ae06a" item-idref="48" disable-calc="false">
        <inputs>
          <ml:apply>
            <ml:minus />
            <ml:real>255</ml:real>
            <ml:id xml:space="preserve">U1</ml:id>
          </ml:apply>
        </inputs>
        <outputs />
      </component>
      <rendering item-idref="49" />
    </region>
    <region region-id="769" left="0" top="2922" width="6000" height="6" align-x="0" align-y="2922" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag="">
      <pageBreak />
    </region>
    <region region-id="770" left="6" top="2946.75" width="51.75" height="14.25" align-x="6" align-y="2958" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag="">
      <text use-page-width="false" push-down="false" lock-width="true">
        <p style="Normal" margin-left="0" margin-right="0" text-indent="inherit" text-align="left" list-style-type="inherit" tabs="inherit">
          <b>Shrinking:</b>
        </p>
      </text>
      <indexes>
        <phrase>type, shrinking</phrase>
      </indexes>
    </region>
    <region region-id="771" left="66" top="2938.5" width="207.75" height="57" align-x="93.75" align-y="2958" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag="">
      <math optimize="false" disable-calc="false">
        <ml:define>
          <ml:function>
            <ml:id xml:space="preserve">h</ml:id>
            <ml:boundVars>
              <ml:id xml:space="preserve">z</ml:id>
            </ml:boundVars>
          </ml:function>
          <ml:apply>
            <ml:plus />
            <ml:apply>
              <ml:id xml:space="preserve">Re</ml:id>
              <ml:id xml:space="preserve">z</ml:id>
            </ml:apply>
            <ml:apply>
              <ml:mult style="default" />
              <ml:apply>
                <ml:id xml:space="preserve">Im</ml:id>
                <ml:id xml:space="preserve">z</ml:id>
              </ml:apply>
              <ml:apply>
                <ml:div />
                <ml:imag symbol="i">1</ml:imag>
                <ml:apply>
                  <ml:plus />
                  <ml:real>1</ml:real>
                  <ml:apply>
                    <ml:pow />
                    <ml:apply>
                      <ml:id xml:space="preserve">Re</ml:id>
                      <ml:apply>
                        <ml:div />
                        <ml:apply>
                          <ml:minus />
                          <ml:id xml:space="preserve">z</ml:id>
                          <ml:apply>
                            <ml:mult style="default" />
                            <ml:real>.5</ml:real>
                            <ml:id xml:space="preserve">W</ml:id>
                          </ml:apply>
                        </ml:apply>
                        <ml:real>50</ml:real>
                      </ml:apply>
                    </ml:apply>
                    <ml:real>2</ml:real>
                  </ml:apply>
                </ml:apply>
              </ml:apply>
            </ml:apply>
          </ml:apply>
        </ml:define>
      </math>
      <rendering item-idref="50" />
    </region>
    <region region-id="772" left="288" top="2944.5" width="54.75" height="24" align-x="309" align-y="2964" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag="">
      <math optimize="false" disable-calc="false">
        <ml:define warning="WarnRedefinedUDScalar">
          <ml:id xml:space="preserve">T1</ml:id>
          <ml:apply>
            <ml:vectorize />
            <ml:apply>
              <ml:id xml:space="preserve">h</ml:id>
              <ml:id xml:space="preserve">C</ml:id>
            </ml:apply>
          </ml:apply>
        </ml:define>
      </math>
      <rendering item-idref="51" />
    </region>
    <region region-id="773" left="66" top="3006.75" width="58.5" height="17.25" align-x="108" align-y="3018" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag="">
      <math optimize="false" disable-calc="false">
        <ml:define warning="WarnRedefinedUDScalar">
          <ml:apply>
            <ml:indexer />
            <ml:id xml:space="preserve">U1</ml:id>
            <ml:sequence>
              <ml:id xml:space="preserve">m</ml:id>
              <ml:id xml:space="preserve">n</ml:id>
            </ml:sequence>
          </ml:apply>
          <ml:real>0</ml:real>
        </ml:define>
      </math>
      <rendering item-idref="52" />
    </region>
    <region region-id="774" left="156" top="3006.75" width="194.25" height="36" align-x="321.75" align-y="3018" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag="">
      <math optimize="false" disable-calc="false">
        <ml:define warning="WarnRedefinedUDScalar">
          <ml:apply>
            <ml:indexer />
            <ml:id xml:space="preserve">U1</ml:id>
            <ml:sequence>
              <ml:apply>
                <ml:id xml:space="preserve">rd</ml:id>
                <ml:apply>
                  <ml:minus />
                  <ml:apply>
                    <ml:div />
                    <ml:apply>
                      <ml:plus />
                      <ml:id xml:space="preserve">H</ml:id>
                      <ml:real>1</ml:real>
                    </ml:apply>
                    <ml:real>2</ml:real>
                  </ml:apply>
                  <ml:apply>
                    <ml:id xml:space="preserve">Im</ml:id>
                    <ml:apply>
                      <ml:indexer />
                      <ml:id xml:space="preserve">T1</ml:id>
                      <ml:id xml:space="preserve">r</ml:id>
                    </ml:apply>
                  </ml:apply>
                </ml:apply>
              </ml:apply>
              <ml:apply>
                <ml:id xml:space="preserve">rd</ml:id>
                <ml:apply>
                  <ml:id xml:space="preserve">Re</ml:id>
                  <ml:apply>
                    <ml:indexer />
                    <ml:id xml:space="preserve">T1</ml:id>
                    <ml:id xml:space="preserve">r</ml:id>
                  </ml:apply>
                </ml:apply>
              </ml:apply>
            </ml:sequence>
          </ml:apply>
          <ml:real>255</ml:real>
        </ml:define>
      </math>
      <rendering item-idref="53" />
    </region>
    <region region-id="898" left="54" top="3054" width="181.5" height="120" align-x="144" align-y="3054" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag="">
      <component hide-arguments="false" clsid-buddy="8442da2d-08d7-45ad-a4a6-f28bee6ae06a" item-idref="54" disable-calc="false">
        <inputs>
          <ml:apply>
            <ml:minus />
            <ml:real>255</ml:real>
            <ml:id xml:space="preserve">U1</ml:id>
          </ml:apply>
        </inputs>
        <outputs />
      </component>
      <rendering item-idref="55" />
    </region>
    <region region-id="837" left="6" top="3198.75" width="43.5" height="14.25" align-x="6" align-y="3210" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag="">
      <text use-page-width="false" push-down="false" lock-width="true">
        <p style="Normal" margin-left="0" margin-right="0" text-indent="inherit" text-align="left" list-style-type="inherit" tabs="inherit">
          <b>Curving:</b>
        </p>
      </text>
      <indexes>
        <phrase>type, curving</phrase>
      </indexes>
    </region>
    <region region-id="778" left="72" top="3190.5" width="186" height="33.75" align-x="100.5" align-y="3210" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag="">
      <math optimize="false" disable-calc="false">
        <ml:define>
          <ml:function>
            <ml:id xml:space="preserve">p</ml:id>
            <ml:boundVars>
              <ml:id xml:space="preserve">z</ml:id>
            </ml:boundVars>
          </ml:function>
          <ml:apply>
            <ml:mult style="default" />
            <ml:apply>
              <ml:id xml:space="preserve">exp</ml:id>
              <ml:apply>
                <ml:mult style="default" />
                <ml:imag symbol="i">1</ml:imag>
                <ml:parens>
                  <ml:apply>
                    <ml:minus />
                    <ml:real>.5</ml:real>
                    <ml:parens>
                      <ml:apply>
                        <ml:mult style="default" />
                        <ml:apply>
                          <ml:mult style="default" />
                          <ml:real>2</ml:real>
                          <ml:id xml:space="preserve">π</ml:id>
                        </ml:apply>
                        <ml:apply>
                          <ml:div />
                          <ml:id xml:space="preserve">z</ml:id>
                          <ml:apply>
                            <ml:mult style="default" />
                            <ml:real>4</ml:real>
                            <ml:id xml:space="preserve">W</ml:id>
                          </ml:apply>
                        </ml:apply>
                      </ml:apply>
                    </ml:parens>
                  </ml:apply>
                </ml:parens>
              </ml:apply>
            </ml:apply>
            <ml:real>100</ml:real>
          </ml:apply>
        </ml:define>
      </math>
      <rendering item-idref="56" />
    </region>
    <region region-id="779" left="276" top="3190.5" width="55.5" height="24" align-x="297" align-y="3210" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag="">
      <math optimize="false" disable-calc="false">
        <ml:define warning="WarnRedefinedUDScalar">
          <ml:id xml:space="preserve">T1</ml:id>
          <ml:apply>
            <ml:vectorize />
            <ml:apply>
              <ml:id xml:space="preserve">p</ml:id>
              <ml:id xml:space="preserve">C</ml:id>
            </ml:apply>
          </ml:apply>
        </ml:define>
      </math>
      <rendering item-idref="57" />
    </region>
    <region region-id="780" left="72" top="3234.75" width="58.5" height="17.25" align-x="114" align-y="3246" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag="">
      <math optimize="false" disable-calc="false">
        <ml:define warning="WarnRedefinedUDScalar">
          <ml:apply>
            <ml:indexer />
            <ml:id xml:space="preserve">U1</ml:id>
            <ml:sequence>
              <ml:id xml:space="preserve">m</ml:id>
              <ml:id xml:space="preserve">n</ml:id>
            </ml:sequence>
          </ml:apply>
          <ml:real>0</ml:real>
        </ml:define>
      </math>
      <rendering item-idref="58" />
    </region>
    <region region-id="781" left="162" top="3234.75" width="194.25" height="36" align-x="327.75" align-y="3246" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag="">
      <math optimize="false" disable-calc="false">
        <ml:define warning="WarnRedefinedUDScalar">
          <ml:apply>
            <ml:indexer />
            <ml:id xml:space="preserve">U1</ml:id>
            <ml:sequence>
              <ml:apply>
                <ml:id xml:space="preserve">rd</ml:id>
                <ml:apply>
                  <ml:minus />
                  <ml:apply>
                    <ml:div />
                    <ml:apply>
                      <ml:plus />
                      <ml:id xml:space="preserve">H</ml:id>
                      <ml:real>1</ml:real>
                    </ml:apply>
                    <ml:real>2</ml:real>
                  </ml:apply>
                  <ml:apply>
                    <ml:id xml:space="preserve">Im</ml:id>
                    <ml:apply>
                      <ml:indexer />
                      <ml:id xml:space="preserve">T1</ml:id>
                      <ml:id xml:space="preserve">r</ml:id>
                    </ml:apply>
                  </ml:apply>
                </ml:apply>
              </ml:apply>
              <ml:apply>
                <ml:id xml:space="preserve">rd</ml:id>
                <ml:apply>
                  <ml:id xml:space="preserve">Re</ml:id>
                  <ml:apply>
                    <ml:indexer />
                    <ml:id xml:space="preserve">T1</ml:id>
                    <ml:id xml:space="preserve">r</ml:id>
                  </ml:apply>
                </ml:apply>
              </ml:apply>
            </ml:sequence>
          </ml:apply>
          <ml:real>255</ml:real>
        </ml:define>
      </math>
      <rendering item-idref="59" />
    </region>
    <region region-id="897" left="54" top="3288" width="181.5" height="139.5" align-x="144" align-y="3288" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag="">
      <component hide-arguments="false" clsid-buddy="8442da2d-08d7-45ad-a4a6-f28bee6ae06a" item-idref="60" disable-calc="false">
        <inputs>
          <ml:apply>
            <ml:minus />
            <ml:real>255</ml:real>
            <ml:id xml:space="preserve">U1</ml:id>
          </ml:apply>
        </inputs>
        <outputs />
      </component>
      <rendering item-idref="61" />
    </region>
    <region region-id="838" left="6" top="3450.75" width="42.75" height="14.25" align-x="6" align-y="3462" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag="">
      <text use-page-width="false" push-down="false" lock-width="true">
        <p style="Normal" margin-left="0" margin-right="0" text-indent="inherit" text-align="left" list-style-type="inherit" tabs="inherit">
          <b>Twisted:</b>
        </p>
      </text>
      <indexes>
        <phrase>type, twisted</phrase>
      </indexes>
    </region>
    <region region-id="784" left="72" top="3442.5" width="190.5" height="33.75" align-x="97.5" align-y="3462" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag="">
      <math optimize="false" disable-calc="false">
        <ml:define>
          <ml:function>
            <ml:id xml:space="preserve">t</ml:id>
            <ml:boundVars>
              <ml:id xml:space="preserve">z</ml:id>
            </ml:boundVars>
          </ml:function>
          <ml:apply>
            <ml:plus />
            <ml:apply>
              <ml:id xml:space="preserve">Re</ml:id>
              <ml:id xml:space="preserve">z</ml:id>
            </ml:apply>
            <ml:apply>
              <ml:mult style="default" />
              <ml:apply>
                <ml:mult style="default" />
                <ml:imag symbol="i">1</ml:imag>
                <ml:apply>
                  <ml:id xml:space="preserve">Im</ml:id>
                  <ml:id xml:space="preserve">z</ml:id>
                </ml:apply>
              </ml:apply>
              <ml:apply>
                <ml:id xml:space="preserve">sin</ml:id>
                <ml:apply>
                  <ml:mult style="default" />
                  <ml:apply>
                    <ml:mult style="default" />
                    <ml:apply>
                      <ml:div />
                      <ml:apply>
                        <ml:id xml:space="preserve">Re</ml:id>
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