Esempio: utilizzo di grafici polari per la rappresentazione grafica dei dati

Grafici > Grafici polari > Esempio: utilizzo di grafici polari per la rappresentazione grafica dei dati

1. Definire gli insiemi di dati seguenti:

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2. Utilizzare un Grafico XY per tracciare il grafico e rappresentare visivamente i dati:

<region id="ID0E3EFIB" top="902.4" left="38.4" width="571.981751848055" height="312" xmlns="http://schemas.mathsoft.com/worksheet50">
  <plot origin-positioning="true" background-type="white" show-axis-expressions="true">
    <xyPlot>
      <title class="- topic/title " wwtype:type="Paragraph" xmlns:wwtype="urn:WebWorks-Type-Schema" />
      <legend />
      <traces>
        <trace resultRef="15">
          <traceStyle color="#FF00008B" symbol="rectangle" line-weight="1" line-style="Solid">lines</traceStyle>
        </trace>
      </traces>
      <axes>
        <xAxis rank="1" legend-position="PlotBoundaryBottom" start="0" end="25">
          <axisLine position="bottom" positionticmark="-1" legendWidth="92.1466666666667" />
          <axisGrid>
            <gridFrequency>6</gridFrequency>
            <gridLabels display="true" />
            <gridLines />
            <tickMarks display="true" />
          </axisGrid>
          <axisLabel />
          <markers />
          <numberFormat>
            <general precision="3" show-trailing-zeros="false" radix="dec" zero-threshold="15" imaginary-value="i" exponential-threshold="3" />
          </numberFormat>
          <plotEquations>
            <plotEquation>
              <math>
                <id xml:space="preserve" xmlns="http://schemas.mathsoft.com/math50">range</id>
              </math>
              <math>
                <placeholder xmlns="http://schemas.mathsoft.com/math50" />
              </math>
            </plotEquation>
          </plotEquations>
          <xyDomain scale-type="linear" auto-scale="true">
            <startValue>
              <placeholder xmlns="http://schemas.mathsoft.com/math50" />
            </startValue>
            <secondTickValue resultRef="16">
              <real xmlns="http://schemas.mathsoft.com/math50">5</real>
            </secondTickValue>
            <endValue>
              <placeholder xmlns="http://schemas.mathsoft.com/math50" />
            </endValue>
          </xyDomain>
        </xAxis>
        <yAxis rank="1" legend-position="PlotBoundaryLeft" start="750" end="2050">
          <axisLine position="origin" positionticmark="0" legendWidth="88.55" />
          <axisGrid>
            <gridFrequency>14</gridFrequency>
            <gridLabels display="true" />
            <gridLines />
            <tickMarks display="true" />
          </axisGrid>
          <axisLabel />
          <markers />
          <numberFormat>
            <decimal precision="3" show-trailing-zeros="false" radix="dec" imaginary-value="i" />
          </numberFormat>
          <plotEquations>
            <plotEquation>
              <math>
                <id xml:space="preserve" xmlns="http://schemas.mathsoft.com/math50">force</id>
              </math>
              <math>
                <placeholder xmlns="http://schemas.mathsoft.com/math50" />
              </math>
            </plotEquation>
          </plotEquations>
          <xyDomain scale-type="linear" auto-scale="true">
            <startValue resultRef="17">
              <real xmlns="http://schemas.mathsoft.com/math50">750</real>
            </startValue>
            <endValue>
              <placeholder xmlns="http://schemas.mathsoft.com/math50" />
            </endValue>
          </xyDomain>
        </yAxis>
      </axes>
    </xyPlot>
  </plot>
</region>

Il grafico risulta simmetrico rispetto al tredicesimo punto dati.

3. Rappresentare graficamente gli stessi dati utilizzando un grafico polare.

<region id="ID0EGHFIB" top="1344" left="38.4" width="573.506054391782" height="360" xmlns="http://schemas.mathsoft.com/worksheet50">
  <plot origin-positioning="false" background-type="white" show-axis-expressions="true">
    <polarPlot>
      <title class="- topic/title " wwtype:type="Paragraph" xmlns:wwtype="urn:WebWorks-Type-Schema" />
      <legend />
      <traces>
        <trace resultRef="18">
          <traceStyle color="#FFFF0000" symbol="none" line-weight="2" line-style="Solid">lines</traceStyle>
        </trace>
      </traces>
      <axes>
        <angularAxis rank="1" legend-position="PlotBoundaryBottom" start="0" end="360">
          <axisLine position="origin" positionticmark="6" legendWidth="67.6633333333333" />
          <axisGrid>
            <gridFrequency>13</gridFrequency>
            <gridLabels display="true" />
            <gridLines />
            <tickMarks display="true" />
          </axisGrid>
          <axisLabel />
          <markers />
          <numberFormat>
            <general precision="3" show-trailing-zeros="false" radix="dec" zero-threshold="15" imaginary-value="i" exponential-threshold="3" />
          </numberFormat>
          <plotEquations>
            <plotEquation>
              <math>
                <id xml:space="preserve" xmlns="http://schemas.mathsoft.com/math50">range</id>
              </math>
            </plotEquation>
          </plotEquations>
          <angularDomain scale-type="linear" auto-scale="true">
            <startValue>
              <placeholder xmlns="http://schemas.mathsoft.com/math50" />
            </startValue>
            <secondTickValue resultRef="19">
              <real xmlns="http://schemas.mathsoft.com/math50">30</real>
            </secondTickValue>
            <endValue>
              <placeholder xmlns="http://schemas.mathsoft.com/math50" />
            </endValue>
          </angularDomain>
        </angularAxis>
        <radialAxis rank="1" legend-position="PlotBoundaryLeft" start="0" end="2000">
          <axisLine position="origin" positionticmark="2" legendWidth="88.55" />
          <axisGrid>
            <gridFrequency>5</gridFrequency>
            <gridLabels display="true" />
            <gridLines />
            <tickMarks display="true" />
          </axisGrid>
          <axisLabel />
          <markers />
          <numberFormat>
            <decimal precision="3" show-trailing-zeros="false" radix="dec" imaginary-value="i" />
          </numberFormat>
          <plotEquations>
            <plotEquation>
              <math>
                <id xml:space="preserve" xmlns="http://schemas.mathsoft.com/math50">force</id>
              </math>
              <math>
                <placeholder xmlns="http://schemas.mathsoft.com/math50" />
              </math>
            </plotEquation>
          </plotEquations>
          <radialDomain scale-type="linear" auto-scale="true">
            <startValue resultRef="20">
              <real xmlns="http://schemas.mathsoft.com/math50">0</real>
            </startValue>
            <secondTickValue resultRef="21">
              <real xmlns="http://schemas.mathsoft.com/math50">500</real>
            </secondTickValue>
            <endValue>
              <placeholder xmlns="http://schemas.mathsoft.com/math50" />
            </endValue>
          </radialDomain>
        </radialAxis>
      </axes>
    </polarPlot>
  </plot>
</region>

La simmetria non è visibile. È necessario normalizzare l'intervallo in modo che i dati vengano rappresentati su un singolo ciclo del grafico polare.

4. Convertire l'intervallo (rng) in angoli (angs) uniformemente distribuiti su un ciclo del grafico polare.

Gli angoli sono definiti in radianti. È possibile convertire i radianti in gradi inserendo l'unità di misura nel segnaposto.

5. Tracciare il grafico dei vettori modificati.

<region id="ID0EYNFIB" top="2688" left="38.4" width="573.908239073433" height="360" xmlns="http://schemas.mathsoft.com/worksheet50">
  <plot origin-positioning="false" background-type="white" show-axis-expressions="true">
    <polarPlot>
      <title class="- topic/title " wwtype:type="Paragraph" xmlns:wwtype="urn:WebWorks-Type-Schema" />
      <legend />
      <traces>
        <trace resultRef="24">
          <traceStyle color="#FF0000FF" symbol="none" line-weight="2" line-style="Solid">lines</traceStyle>
        </trace>
      </traces>
      <axes>
        <angularAxis rank="1" legend-position="PlotBoundaryBottom" start="0" end="360">
          <axisLine position="origin" positionticmark="6" legendWidth="71.5766666666667" />
          <axisGrid>
            <gridFrequency>13</gridFrequency>
            <gridLabels display="true" />
            <gridLines />
            <tickMarks display="true" />
          </axisGrid>
          <axisLabel />
          <markers />
          <numberFormat>
            <general precision="3" show-trailing-zeros="false" radix="dec" zero-threshold="15" imaginary-value="i" exponential-threshold="3" />
          </numberFormat>
          <plotEquations>
            <plotEquation>
              <math>
                <id xml:space="preserve" xmlns="http://schemas.mathsoft.com/math50">angles</id>
              </math>
            </plotEquation>
          </plotEquations>
          <angularDomain scale-type="linear" auto-scale="true">
            <startValue>
              <placeholder xmlns="http://schemas.mathsoft.com/math50" />
            </startValue>
            <endValue>
              <placeholder xmlns="http://schemas.mathsoft.com/math50" />
            </endValue>
          </angularDomain>
        </angularAxis>
        <radialAxis rank="1" legend-position="PlotBoundaryLeft" start="0" end="2000">
          <axisLine position="origin" positionticmark="2" legendWidth="88.55" />
          <axisGrid>
            <gridFrequency>5</gridFrequency>
            <gridLabels display="true" />
            <gridLines />
            <tickMarks display="true" />
          </axisGrid>
          <axisLabel />
          <markers />
          <numberFormat>
            <decimal precision="3" show-trailing-zeros="false" radix="dec" imaginary-value="i" />
          </numberFormat>
          <plotEquations>
            <plotEquation>
              <math>
                <id xml:space="preserve" xmlns="http://schemas.mathsoft.com/math50">force</id>
              </math>
              <math>
                <placeholder xmlns="http://schemas.mathsoft.com/math50" />
              </math>
            </plotEquation>
          </plotEquations>
          <radialDomain scale-type="linear" auto-scale="true">
            <startValue resultRef="25">
              <real xmlns="http://schemas.mathsoft.com/math50">0</real>
            </startValue>
            <secondTickValue resultRef="26">
              <real xmlns="http://schemas.mathsoft.com/math50">500</real>
            </secondTickValue>
            <endValue>
              <placeholder xmlns="http://schemas.mathsoft.com/math50" />
            </endValue>
          </radialDomain>
        </radialAxis>
      </axes>
    </polarPlot>
  </plot>
</region>

6. Per connettere l'ultimo punto dati al primo, utilizzare la funzione stack per aggiungere il primo punto dati alla fine dei due insiemi di dati.

7. Tracciare il grafico dei vettori modificati.

<region id="ID0EYRFIB" top="3532.8" left="38.4" width="573.940106635175" height="336" xmlns="http://schemas.mathsoft.com/worksheet50">
  <plot origin-positioning="false" background-type="white" show-axis-expressions="true">
    <polarPlot>
      <title class="- topic/title " wwtype:type="Paragraph" xmlns:wwtype="urn:WebWorks-Type-Schema" />
      <legend />
      <traces>
        <trace resultRef="27">
          <traceStyle color="#FF008000" symbol="none" line-weight="2" line-style="Solid">lines</traceStyle>
        </trace>
      </traces>
      <axes>
        <angularAxis rank="1" legend-position="PlotBoundaryBottom" start="0" end="360">
          <axisLine position="origin" positionticmark="6" legendWidth="71.5766666666667" />
          <axisGrid>
            <gridFrequency>13</gridFrequency>
            <gridLabels display="true" />
            <gridLines />
            <tickMarks display="true" />
          </axisGrid>
          <axisLabel />
          <markers />
          <numberFormat>
            <general precision="3" show-trailing-zeros="false" radix="dec" zero-threshold="15" imaginary-value="i" exponential-threshold="3" />
          </numberFormat>
          <plotEquations>
            <plotEquation>
              <math>
                <id xml:space="preserve" xmlns="http://schemas.mathsoft.com/math50">angles</id>
              </math>
            </plotEquation>
          </plotEquations>
          <angularDomain scale-type="linear" auto-scale="true">
            <startValue>
              <placeholder xmlns="http://schemas.mathsoft.com/math50" />
            </startValue>
            <endValue>
              <placeholder xmlns="http://schemas.mathsoft.com/math50" />
            </endValue>
          </angularDomain>
        </angularAxis>
        <radialAxis rank="1" legend-position="PlotBoundaryLeft" start="0" end="2000">
          <axisLine position="origin" positionticmark="2" legendWidth="88.55" />
          <axisGrid>
            <gridFrequency>5</gridFrequency>
            <gridLabels display="true" />
            <gridLines />
            <tickMarks display="true" />
          </axisGrid>
          <axisLabel />
          <markers />
          <numberFormat>
            <decimal precision="3" show-trailing-zeros="false" radix="dec" imaginary-value="i" />
          </numberFormat>
          <plotEquations>
            <plotEquation>
              <math>
                <id xml:space="preserve" xmlns="http://schemas.mathsoft.com/math50">force</id>
              </math>
              <math>
                <placeholder xmlns="http://schemas.mathsoft.com/math50" />
              </math>
            </plotEquation>
          </plotEquations>
          <radialDomain scale-type="linear" auto-scale="true">
            <startValue resultRef="28">
              <real xmlns="http://schemas.mathsoft.com/math50">0</real>
            </startValue>
            <secondTickValue resultRef="29">
              <real xmlns="http://schemas.mathsoft.com/math50">500</real>
            </secondTickValue>
            <endValue>
              <placeholder xmlns="http://schemas.mathsoft.com/math50" />
            </endValue>
          </radialDomain>
        </radialAxis>
      </axes>
    </polarPlot>
  </plot>
</region>

Ora l'insieme di dati è rappresentato su un singolo ciclo e tutti i punti sono collegati. Si noti che in PTC Mathcad gli angoli vengono visualizzati in senso antiorario.

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Parti di un grafico polare

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