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<title>Graphing — 3D Plots</title>
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<p style="Normal" margin-left="inherit" margin-right="inherit" text-indent="0" text-align="inherit" list-style-type="none" tabs="inherit">This worksheet shows you how to create a 3D plot from a function of two variables, and from a set of parametric functions. It also explains a little bit about how to format the look of these plots for maximum effect.</p>
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<p style="Normal" margin-left="inherit" margin-right="inherit" text-indent="inherit" text-align="inherit" list-style-type="inherit" tabs="inherit">Here are two 3D plots with special formatting:</p>
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<p style="Normal" margin-left="inherit" margin-right="inherit" text-indent="inherit" text-align="inherit" list-style-type="inherit" tabs="inherit">The 3D graph on the left shows the plot of a function of two variables, a paraboloid. The 3D graph on the right shows a parametric plot of a surface of revolution, specified by three functions to determine the x, y, and z coordinates.</p>
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<p style="Heading 2" margin-left="inherit" margin-right="inherit" text-indent="inherit" text-align="inherit" list-style-type="inherit" tabs="inherit">To Create a 3D QuickPlot from a Function</p>
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<p style="directions" margin-left="inherit" margin-right="inherit" text-indent="inherit" text-align="inherit" list-style-type="inherit" tabs="inherit">1. To define a two-variable function, </p>
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<ml:id xml:space="preserve">y</ml:id>
</ml:boundVars>
</ml:function>
<ml:apply>
<ml:plus></ml:plus>
<ml:apply>
<ml:pow></ml:pow>
<ml:id xml:space="preserve">x</ml:id>
<ml:real>2</ml:real>
</ml:apply>
<ml:apply>
<ml:mult style="auto-select"></ml:mult>
<ml:real>4</ml:real>
<ml:apply>
<ml:pow></ml:pow>
<ml:id xml:space="preserve">y</ml:id>
<ml:real>2</ml:real>
</ml:apply>
</ml:apply>
</ml:apply>
</ml:define>
</math>
<rendering item-idref="12"></rendering>
</region>
<region region-id="2182" left="6" top="698.25" width="209.25" height="36" align-x="16.5" align-y="708" 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="directions" margin-left="0" margin-right="0" text-indent="0" text-align="left" list-style-type="none" tabs="inherit">Click in a new region to insert a 3D graph<sp count="2"></sp>(<f family="Tahoma" charset="0">
<b>
<inlineAttr line-through="false">
<c val="#800080">surface plot</c>
</inlineAttr>
</b>
</f>) and enter the name of the function in this region by typing:</p>
</text>
</region>
<region region-id="2420" left="222" top="708" width="181.5" height="210" align-x="312" align-y="708" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag="">
<component hide-arguments="false" clsid-buddy="013500E0-1122-11DB-9380-000D56C6051A" item-idref="13" disable-calc="false">
<inputs>
<ml:id xml:space="preserve">H1</ml:id>
</inputs>
<outputs></outputs>
</component>
<rendering item-idref="14"></rendering>
</region>
<region region-id="2190" left="6" top="747" width="45.75" height="10.5" align-x="6" align-y="756" 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="false">
<p style="typing" margin-left="inherit" margin-right="inherit" text-indent="inherit" text-align="inherit" list-style-type="inherit" tabs="inherit">[Ctrl]2 H1</p>
</text>
</region>
<region region-id="2191" left="6" top="774.75" width="30.75" height="14.25" align-x="6" align-y="786" show-border="false" show-highlight="true" is-protected="true" z-order="0" background-color="inherit" tag="">
<text use-page-width="false" push-down="false" lock-width="false">
<p style="Normal" margin-left="inherit" margin-right="inherit" text-indent="0" text-align="inherit" list-style-type="none" tabs="inherit">Try it! </p>
</text>
</region>
<region region-id="2447" left="216" top="936.75" width="151.5" height="42.75" align-x="225" align-y="948" 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="inherit" margin-right="inherit" text-indent="inherit" text-align="inherit" list-style-type="inherit" tabs="inherit">
<b>
<c val="#008080">Tip:</c>
</b> Any two-variable function of quadratic terms produces a paraboloid in a surface plot.</p>
</text>
</region>
<region region-id="2471" left="6" top="1020.75" width="349.5" height="71.25" align-x="6" align-y="1032" 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="inherit" margin-right="inherit" text-indent="inherit" text-align="inherit" list-style-type="inherit" tabs="inherit">This plot is a QuickPlot, meaning that you don't have to specify a range or spacing for the independent variables because Mathcad picks them automatically. To adjust the range used, double-click on the plot, and change the settings on the QuickPlot tab. The default is -5 to 5 for each independent variable with a spacing of 20 points across each range.</p>
</text>
</region>
<region region-id="2533" left="0" top="1104" width="6000" height="6" align-x="0" align-y="1104" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag="">
<pageBreak></pageBreak>
</region>
<region region-id="2205" left="6" top="1118.25" width="199.5" height="36" align-x="17.25" align-y="1128" 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="directions" margin-left="inherit" margin-right="inherit" text-indent="inherit" text-align="inherit" list-style-type="inherit" tabs="inherit">2. Insert a 3D graph region (<f family="Tahoma" charset="0">
<b>
<inlineAttr line-through="false">
<c val="#800080">bar plot)</c>
</inlineAttr>
</b>
</f> by clicking the following button on the <b>Graph</b> toolbar:</p>
</text>
</region>
<region region-id="2423" left="222" top="1118.25" width="36" height="12" align-x="229.5" align-y="1128" 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="directions" margin-left="inherit" margin-right="inherit" text-indent="inherit" text-align="inherit" list-style-type="inherit" tabs="inherit">See:</p>
</text>
</region>
<region region-id="2424" left="222" top="1140" width="181.5" height="210" align-x="312" align-y="1140" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag="">
<component hide-arguments="false" clsid-buddy="013500E0-1122-11DB-9380-000D56C6051A" item-idref="15" disable-calc="false">
<inputs>
<ml:id xml:space="preserve">H1</ml:id>
</inputs>
<outputs></outputs>
</component>
<rendering item-idref="16"></rendering>
</region>
<region region-id="2221" left="24" top="1164" width="16.5" height="16.5" align-x="24" align-y="1164" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag="">
<picture>
<png item-idref="17" display-width="15" display-height="15"></png>
</picture>
<rendering item-idref="18"></rendering>
</region>
<region region-id="2390" left="6" top="1190.25" width="195.75" height="36" align-x="12" align-y="1200" 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="directions" margin-left="inherit" margin-right="inherit" text-indent="inherit" text-align="inherit" list-style-type="inherit" tabs="inherit">Or, <f family="Tahoma" charset="0" size="10">
<inlineAttr font-weight="normal" line-through="false">
<c val="#800080">select </c>
</inlineAttr>
</f>
<f family="Tahoma" charset="0" size="10">
<b>
<c val="#800080">Graph &gt;</c>
</b>
</f>
<f family="Tahoma" charset="0" size="10">
<b>
<c val="#800080"> 3D Bar Plot </c>
</b>
</f>
<f family="Tahoma" charset="0" size="10">
<c val="#800080">
<inlineAttr font-weight="normal" line-through="false">from the</inlineAttr>
</c>
</f>
<f family="Tahoma" charset="0" size="10">
<b>
<c val="#800080"> Insert </c>
</b>
</f>
<f family="Tahoma" charset="0" size="10">
<inlineAttr font-weight="normal" line-through="false">
<c val="#800080">menu.</c>
</inlineAttr>
</f>
<f family="Tahoma" charset="0" size="10">
<b>
<c val="#800080">
<sp></sp>
</c>
</b>
</f>Then, enter the name of the function defined in the previous example, H1.</p>
</text>
</region>
<region region-id="2392" left="6" top="1254.75" width="30.75" height="14.25" align-x="6" align-y="1266" show-border="false" show-highlight="true" is-protected="true" z-order="0" background-color="inherit" tag="">
<text use-page-width="false" push-down="false" lock-width="false">
<p style="Normal" margin-left="inherit" margin-right="inherit" text-indent="0" text-align="inherit" list-style-type="none" tabs="inherit">Try it! </p>
</text>
</region>
<region region-id="2534" left="0" top="1488" width="6000" height="6" align-x="0" align-y="1488" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag="">
<pageBreak></pageBreak>
</region>
<region region-id="2521" left="6" top="1502.25" width="300" height="12" align-x="6" align-y="1512" 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="Heading 2" margin-left="inherit" margin-right="inherit" text-indent="inherit" text-align="inherit" list-style-type="inherit" tabs="inherit">To Create a 3D QuickPlot from Parametric Functions</p>
</text>
</region>
<region region-id="2550" left="6" top="1524.75" width="315.75" height="28.5" align-x="9" align-y="1536" 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="inherit" margin-right="inherit" text-indent="inherit" text-align="inherit" list-style-type="inherit" tabs="inherit">It is sometimes useful to define variables in terms of other variables or parameters. </p>
</text>
</region>
<region region-id="2522" left="6" top="1562.25" width="212.25" height="24" align-x="17.25" align-y="1572" 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="directions" margin-left="inherit" margin-right="inherit" text-indent="inherit" text-align="inherit" list-style-type="inherit" tabs="inherit">To define three two-variable functions, </p>
<p style="directions" margin-left="inherit" margin-right="inherit" text-indent="inherit" text-align="inherit" list-style-type="inherit" tabs="inherit">type:</p>
</text>
</region>
<region region-id="2523" left="222" top="1562.25" width="36" height="12" align-x="229.5" align-y="1572" 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="directions" margin-left="inherit" margin-right="inherit" text-indent="inherit" text-align="inherit" list-style-type="inherit" tabs="inherit">See:</p>
</text>
</region>
<region region-id="2524" left="264" top="1560.75" width="112.5" height="15.75" align-x="306.75" align-y="1572" 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">X</ml:id>
<ml:boundVars>
<ml:id xml:space="preserve">u</ml:id>
<ml:id xml:space="preserve">v</ml:id>
</ml:boundVars>
</ml:function>
<ml:apply>
<ml:mult style="default"></ml:mult>
<ml:apply>
<ml:id xml:space="preserve">sin</ml:id>
<ml:id xml:space="preserve">v</ml:id>
</ml:apply>
<ml:apply>
<ml:id xml:space="preserve">cos</ml:id>
<ml:id xml:space="preserve">u</ml:id>
</ml:apply>
</ml:apply>
</ml:define>
</math>
<rendering item-idref="19"></rendering>
</region>
<region region-id="2525" left="264" top="1584.75" width="108.75" height="15.75" align-x="306.75" align-y="1596" 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">Y</ml:id>
<ml:boundVars>
<ml:id xml:space="preserve">u</ml:id>
<ml:id xml:space="preserve">v</ml:id>
</ml:boundVars>
</ml:function>
<ml:apply>
<ml:mult style="default"></ml:mult>
<ml:apply>
<ml:id xml:space="preserve">sin</ml:id>
<ml:id xml:space="preserve">v</ml:id>
</ml:apply>
<ml:apply>
<ml:id xml:space="preserve">sin</ml:id>
<ml:id xml:space="preserve">u</ml:id>
</ml:apply>
</ml:apply>
</ml:define>
</math>
<rendering item-idref="20"></rendering>
</region>
<region region-id="2526" left="6" top="1599" width="123" height="31.5" align-x="6" align-y="1608" 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="typing" margin-left="inherit" margin-right="inherit" text-indent="inherit" text-align="inherit" list-style-type="inherit" tabs="inherit">X(u,v):sin(v)*cos(u)[Enter]</p>
<p style="typing" margin-left="inherit" margin-right="inherit" text-indent="inherit" text-align="inherit" list-style-type="inherit" tabs="inherit">Y(u,v):sin(v)*sin(u)[Enter]</p>
<p style="typing" margin-left="inherit" margin-right="inherit" text-indent="inherit" text-align="inherit" list-style-type="inherit" tabs="inherit">Z(u,v):cos(v)[Enter]</p>
</text>
</region>
<region region-id="2527" left="264" top="1608.75" width="82.5" height="15.75" align-x="305.25" align-y="1620" 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">Z</ml:id>
<ml:boundVars>
<ml:id xml:space="preserve">u</ml:id>
<ml:id xml:space="preserve">v</ml:id>
</ml:boundVars>
</ml:function>
<ml:apply>
<ml:id xml:space="preserve">cos</ml:id>
<ml:id xml:space="preserve">v</ml:id>
</ml:apply>
</ml:define>
</math>
<rendering item-idref="21"></rendering>
</region>
<region region-id="2528" left="228" top="1650" width="181.5" height="210" align-x="318" align-y="1650" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag="">
<component hide-arguments="false" clsid-buddy="013500E0-1122-11DB-9380-000D56C6051A" item-idref="22" disable-calc="false">
<inputs>
<ml:parens>
<ml:sequence>
<ml:id xml:space="preserve">X</ml:id>
<ml:id xml:space="preserve">Y</ml:id>
<ml:id xml:space="preserve">Z</ml:id>
</ml:sequence>
</ml:parens>
</inputs>
<outputs></outputs>
</component>
<rendering item-idref="23"></rendering>
</region>
<region region-id="2529" left="6" top="1646.25" width="209.25" height="36" align-x="16.5" align-y="1656" 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="directions" margin-left="0" margin-right="0" text-indent="0" text-align="left" list-style-type="none" tabs="inherit">Then, insert a 3D graph region (<f family="Tahoma" charset="0">
<b>
<inlineAttr line-through="false">
<c val="#800080">surface plot</c>
</inlineAttr>
</b>
</f>) and enter the name of the functions, surrounded by parentheses, in this region by typing:</p>
</text>
</region>
<region region-id="2530" left="6" top="1695" width="90" height="10.5" align-x="6" align-y="1704" 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="false">
<p style="typing" margin-left="inherit" margin-right="inherit" text-indent="inherit" text-align="inherit" list-style-type="inherit" tabs="inherit">[Ctrl]2 'X,Y,Z[Enter]</p>
</text>
</region>
<region region-id="2531" left="6" top="1722.75" width="27.75" height="14.25" align-x="6" align-y="1734" show-border="false" show-highlight="true" is-protected="true" z-order="0" background-color="inherit" tag="">
<text use-page-width="false" push-down="false" lock-width="false">
<p style="Normal" margin-left="inherit" margin-right="inherit" text-indent="0" text-align="inherit" list-style-type="none" tabs="inherit">Try it!</p>
</text>
</region>
<region region-id="2536" left="6" top="1980.75" width="333" height="57" align-x="6" align-y="1992" 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="inherit" margin-right="inherit" text-indent="inherit" text-align="inherit" list-style-type="inherit" tabs="inherit">In addition to functions of two variables and sets of parametric functions, you can also enter matrix names and sets of three paired vectors specifying X, Y, and Z coordinates.<sp count="2"></sp>See the <b>
<u>
<link href=".\..\..\Visualization\qwikdata.xmcd" title="Links to section" popup="false">Quicksheet on plotting data</link>
</u>
</b> for more examples.</p>
</text>
</region>
<region region-id="2265" left="0" top="2064" width="6000" height="6" align-x="0" align-y="2064" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag="">
<pageBreak></pageBreak>
</region>
<region region-id="2278" left="6" top="2078.25" width="241.5" height="12" align-x="6" align-y="2088" 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="Heading 2" margin-left="inherit" margin-right="inherit" text-indent="inherit" text-align="inherit" list-style-type="inherit" tabs="inherit">To Change the Appearance of a 3D Graph</p>
</text>
<indexes>
<phrase>3D graphs, formatting</phrase>
</indexes>
</region>
<region region-id="2279" left="6" top="2102.25" width="177.75" height="24" align-x="17.25" align-y="2112" 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="directions" margin-left="inherit" margin-right="inherit" text-indent="inherit" text-align="inherit" list-style-type="inherit" tabs="inherit">1. Double-click the 3D graph below to access the <b>3-</b>
<f family="Tahoma" charset="0">
<b>
<inlineAttr line-through="false">
<c val="#800080">D Plot Format </c>
</inlineAttr>
</b>
</f>
<f family="Tahoma" charset="0">
<inlineAttr font-weight="normal" line-through="false">
<c val="#800080">dialog box</c>
</inlineAttr>
</f>
<inlineAttr font-weight="normal">:</inlineAttr>
</p>
</text>
</region>
<region region-id="2543" left="210" top="2102.25" width="36" height="12" align-x="217.5" align-y="2112" 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="directions" margin-left="inherit" margin-right="inherit" text-indent="inherit" text-align="inherit" list-style-type="inherit" tabs="inherit">See:</p>
</text>
</region>
<region region-id="2286" left="6" top="2148" width="181.5" height="210" align-x="96" align-y="2148" show-border="false" show-highlight="true" is-protected="true" z-order="0" background-color="#ffffce" tag="">
<component hide-arguments="false" clsid-buddy="013500E0-1122-11DB-9380-000D56C6051A" item-idref="24" disable-calc="false">
<inputs>
<ml:id xml:space="preserve">H1</ml:id>
</inputs>
<outputs></outputs>
</component>
<rendering item-idref="25"></rendering>
</region>
<region region-id="2599" left="216" top="2148" width="307.5" height="229.5" align-x="216" align-y="2148" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag="">
<picture>
<png item-idref="26" display-width="306" display-height="228"></png>
</picture>
<rendering item-idref="27"></rendering>
</region>
<region region-id="2452" left="6" top="2408.25" width="180" height="24" align-x="12.75" align-y="2418" 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="directions" margin-left="0" margin-right="0" text-indent="0" text-align="left" list-style-type="none" tabs="inherit">On the <f family="Tahoma" charset="0">
<b>
<inlineAttr line-through="false">
<c val="#800080">Appearance</c>
</inlineAttr>
</b>
</f> page, select "Fill Surface" and "Colormap" and click OK.</p>
</text>
<indexes>
<phrase>colormap</phrase>
</indexes>
</region>
<region region-id="2441" left="222" top="2408.25" width="36" height="12" align-x="222" align-y="2418" 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="directions" margin-left="inherit" margin-right="inherit" text-indent="inherit" text-align="inherit" list-style-type="inherit" tabs="inherit">See:</p>
</text>
</region>
<region region-id="2440" left="222" top="2436" width="181.5" height="210" align-x="312" align-y="2436" show-border="false" show-highlight="true" is-protected="true" z-order="0" background-color="#ffffce" tag="">
<component hide-arguments="false" clsid-buddy="013500E0-1122-11DB-9380-000D56C6051A" item-idref="28" disable-calc="false">
<inputs>
<ml:id xml:space="preserve">H1</ml:id>
</inputs>
<outputs></outputs>
</component>
<rendering item-idref="29"></rendering>
</region>
<region region-id="2453" left="6" top="2444.25" width="198" height="48" align-x="17.25" align-y="2454" 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="directions" margin-left="inherit" margin-right="inherit" text-indent="inherit" text-align="inherit" list-style-type="inherit" tabs="inherit">Click on the plot itself, hold down the mouse button, and move the mouse around. Notice that this changes the view you have of the plot.</p>
</text>
</region>
<region region-id="2454" left="6" top="2504.25" width="195" height="36" align-x="21.75" align-y="2514" 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="directions" margin-left="inherit" margin-right="inherit" text-indent="inherit" text-align="inherit" list-style-type="inherit" tabs="inherit">Double-click on the plot again. On the <f family="Tahoma" charset="0">
<b>
<inlineAttr line-through="false">
<c val="#800080">General</c>
</inlineAttr>
</b>
</f> page, set the Rotation, Tilt, and Twist as follows:</p>
</text>
</region>
<region region-id="2455" left="6" top="2553" width="53.25" height="31.5" align-x="24.75" align-y="2562" 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="false">
<p style="typing" margin-left="inherit" margin-right="inherit" text-indent="inherit" text-align="inherit" list-style-type="inherit" tabs="inherit">Rotation: 0</p>
<p style="typing" margin-left="inherit" margin-right="inherit" text-indent="inherit" text-align="inherit" list-style-type="inherit" tabs="inherit">Tilt: 35</p>
<p style="typing" margin-left="inherit" margin-right="inherit" text-indent="inherit" text-align="inherit" list-style-type="inherit" tabs="inherit">Twist: -10</p>
</text>
</region>
<region region-id="2456" left="6" top="2600.25" width="180.75" height="12" align-x="15" align-y="2610" 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="directions" margin-left="inherit" margin-right="inherit" text-indent="inherit" text-align="inherit" list-style-type="inherit" tabs="inherit">The graph appears as it does to the right.</p>
</text>
</region>
<region region-id="2308" left="0" top="2676" width="6000" height="6" align-x="0" align-y="2676" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag="">
<pageBreak></pageBreak>
</region>
<region region-id="2323" left="6" top="2690.25" width="189.75" height="24" align-x="17.25" align-y="2700" 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="directions" margin-left="inherit" margin-right="inherit" text-indent="inherit" text-align="inherit" list-style-type="inherit" tabs="inherit">2. Double-click the 3D graph below to access the <f family="Tahoma" charset="0">
<b>
<inlineAttr line-through="false">
<c val="#800080">3-D Plot Format dialog box</c>
</inlineAttr>
</b>
</f>. </p>
</text>
</region>
<region region-id="2439" left="222" top="2690.25" width="36" height="12" align-x="229.5" align-y="2700" 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="directions" margin-left="inherit" margin-right="inherit" text-indent="inherit" text-align="inherit" list-style-type="inherit" tabs="inherit">See:</p>
</text>
</region>
<region region-id="2438" left="222" top="2712" width="181.5" height="210" align-x="312" align-y="2712" show-border="false" show-highlight="true" is-protected="true" z-order="0" background-color="#ffffce" tag="">
<component hide-arguments="false" clsid-buddy="013500E0-1122-11DB-9380-000D56C6051A" item-idref="30" disable-calc="false">
<inputs>
<ml:parens>
<ml:sequence>
<ml:id xml:space="preserve">X</ml:id>
<ml:id xml:space="preserve">Y</ml:id>
<ml:id xml:space="preserve">Z</ml:id>
</ml:sequence>
</ml:parens>
</inputs>
<outputs></outputs>
</component>
<rendering item-idref="31"></rendering>
</region>
<region region-id="2336" left="6" top="2726.25" width="201" height="72" align-x="12.75" align-y="2736" 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="directions" margin-left="inherit" margin-right="inherit" text-indent="inherit" text-align="inherit" list-style-type="inherit" tabs="inherit">On the <f family="Tahoma" charset="0">
<b>
<inlineAttr line-through="false">
<c val="#800080">Appearance page</c>
</inlineAttr>
</b>
</f>, select "Fill Surface" and "Solid Color" in the first column. </p>
<p style="directions" margin-left="inherit" margin-right="inherit" text-indent="inherit" text-align="inherit" list-style-type="inherit" tabs="inherit">Click the color box to the right of the Solid Color selection. Select the following color from the palette and click OK twice to close the dialogs:</p>
</text>
<indexes>
<phrase>fill surface</phrase>
<phrase>solidcolor</phrase>
</indexes>
</region>
<region region-id="2345" left="24" top="2808" width="20.25" height="18" align-x="24" align-y="2808" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag="">
<picture>
<png item-idref="32" display-width="18.75" display-height="16.5"></png>
</picture>
<rendering item-idref="33"></rendering>
</region>
<region region-id="2346" left="6" top="2838" width="181.5" height="210" align-x="96" align-y="2838" show-border="false" show-highlight="true" is-protected="true" z-order="0" background-color="#ffffce" tag="">
<component hide-arguments="false" clsid-buddy="013500E0-1122-11DB-9380-000D56C6051A" item-idref="34" disable-calc="false">
<inputs>
<ml:parens>
<ml:sequence>
<ml:id xml:space="preserve">X</ml:id>
<ml:id xml:space="preserve">Y</ml:id>
<ml:id xml:space="preserve">Z</ml:id>
</ml:sequence>
</ml:parens>
</inputs>
<outputs></outputs>
</component>
<rendering item-idref="35"></rendering>
</region>
<region region-id="2442" left="222" top="2936.25" width="36" height="12" align-x="222" align-y="2946" 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="directions" margin-left="inherit" margin-right="inherit" text-indent="inherit" text-align="inherit" list-style-type="inherit" tabs="inherit">See:</p>
</text>
</region>
<region region-id="2443" left="222" top="2958" width="181.5" height="210" align-x="312" align-y="2958" show-border="false" show-highlight="true" is-protected="true" z-order="0" background-color="#ffffce" tag="">
<component hide-arguments="false" clsid-buddy="013500E0-1122-11DB-9380-000D56C6051A" item-idref="36" disable-calc="false">
<inputs>
<ml:parens>
<ml:sequence>
<ml:id xml:space="preserve">X</ml:id>
<ml:id xml:space="preserve">Y</ml:id>
<ml:id xml:space="preserve">Z</ml:id>
</ml:sequence>
</ml:parens>
</inputs>
<outputs></outputs>
</component>
<rendering item-idref="37"></rendering>
</region>
<region region-id="2347" left="6" top="3068.25" width="198" height="36" align-x="17.25" align-y="3078" 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="directions" margin-left="inherit" margin-right="inherit" text-indent="inherit" text-align="inherit" list-style-type="inherit" tabs="inherit">Right-click on the plot and select <f family="Tahoma" charset="0">
<b>
<inlineAttr line-through="false">
<c val="#800080">Lighting</c>
</inlineAttr>
</b>
</f> from the menu. Under "Light Scheme," choose "Scheme 1." </p>
</text>
<indexes>
<phrase>lighting</phrase>
</indexes>
</region>
<region region-id="2370" left="0" top="3180" width="6000" height="6" align-x="0" align-y="3180" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag="">
<pageBreak></pageBreak>
</region>
<region region-id="2374" left="6" top="3188.25" width="195" height="48" align-x="21.75" align-y="3198" 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="directions" margin-left="inherit" margin-right="inherit" text-indent="inherit" text-align="inherit" list-style-type="inherit" tabs="inherit">Double-click on the plot again. On the <f family="Tahoma" charset="0">
<b>
<inlineAttr line-through="false">
<c val="#800080">Advanced</c>
</inlineAttr>
</b>
</f> page, set %Transparency to 50%. On the <f family="Tahoma" charset="0">
<b>
<inlineAttr line-through="false">
<c val="#800080">General</c>
</inlineAttr>
</b>
</f> page, set the Rotation, Tilt, and Twist as follows:</p>
</text>
<indexes>
<phrase>transparency</phrase>
</indexes>
</region>
<region region-id="2444" left="222" top="3188.25" width="36" height="12" align-x="222" align-y="3198" 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="directions" margin-left="inherit" margin-right="inherit" text-indent="inherit" text-align="inherit" list-style-type="inherit" tabs="inherit">See:</p>
</text>
</region>
<region region-id="2445" left="222" top="3210" width="181.5" height="210" align-x="312" align-y="3210" show-border="false" show-highlight="true" is-protected="true" z-order="0" background-color="#ffffce" tag="">
<component hide-arguments="false" clsid-buddy="013500E0-1122-11DB-9380-000D56C6051A" item-idref="38" disable-calc="false">
<inputs>
<ml:parens>
<ml:sequence>
<ml:id xml:space="preserve">X</ml:id>
<ml:id xml:space="preserve">Y</ml:id>
<ml:id xml:space="preserve">Z</ml:id>
</ml:sequence>
</ml:parens>
</inputs>
<outputs></outputs>
</component>
<rendering item-idref="39"></rendering>
</region>
<region region-id="2375" left="6" top="3249" width="59.25" height="31.5" align-x="6" align-y="3258" 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="false">
<p style="typing" margin-left="inherit" margin-right="inherit" text-indent="inherit" text-align="inherit" list-style-type="inherit" tabs="inherit">Rotation: 40</p>
<p style="typing" margin-left="inherit" margin-right="inherit" text-indent="inherit" text-align="inherit" list-style-type="inherit" tabs="inherit">Tilt: 20</p>
<p style="typing" margin-left="inherit" margin-right="inherit" text-indent="inherit" text-align="inherit" list-style-type="inherit" tabs="inherit">Twist: 320</p>
</text>
</region>
<region region-id="2457" left="6" top="3444.75" width="326.25" height="28.5" align-x="12.75" align-y="3456" 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="inherit" margin-right="inherit" text-indent="inherit" text-align="inherit" list-style-type="inherit" tabs="inherit">Continue to try different options to see how you can transform the look of a 3D graph. See <b>
<u>
<link href=".\..\Features\feat_05.xmcd" title="Links to section" popup="false">Formatting 3D Plots</link>
</u>
</b> for more information.</p>
</text>
</region>
<region region-id="2600" left="6" top="3498" width="426.75" height="5.25" align-x="6" align-y="3498" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag="">
<picture>
<png item-idref="40" display-width="425.25" display-height="3.75"></png>
</picture>
<rendering item-idref="41"></rendering>
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