Пример. Использование полярных графиков для отображения данных

Графики > Полярные графики > Пример. Использование полярных графиков для отображения данных

1. Определите следующие наборы данных:

Щелкните для копирования этого выражения

2. Постройте график XY для визуализации данных:

<region id="ID0E6NFIB" 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>

На графике видна симметрия с центром в 13-й точке данных.

3. Постройте полярный график для этих же данных:

<region id="ID0EJQFIB" 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>

Симметрия пропала. Чтобы отобразить данные в пределах одного цикла полярного графика, необходимо нормализовать диапазон.

4. Преобразуйте значения диапазона (rng) в значения углов (angs), равномерно распределенные в пределах одного цикла полярного графика.

Углы определены в радианах. Радианы можно преобразовать в градусы, вставив единицу измерения в местозаполнитель.

5. Постройте график по измененным векторам:

<region id="ID0E2WFIB" 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. Чтобы соединить последнюю точку данных с первой, используйте функцию stack, чтобы добавить первую точку данных в конец каждого набора данных.

7. Постройте график по измененным векторам:

<region id="ID0E21FIB" 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>

Теперь график набора данных построен в пределах одного цикла, и все точки соединены. Обратите внимание, что в PTC Mathcad углы отображаются против часовой стрелки.

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