Example: Parametric Curves in 2D Plots

Plots > Polar Plots > Example: Parametric Curves in 2D Plots

Plot the points of a curve whose coordinates are functions of one or more parameters.

One Parameter

1. Use the sin function to define the functions x and y in terms of parameter a:

2. Plot y against x. For parametric curves, 500 points are plotted over a range determined by an algorithm. When you change the number of plotted points, the range is changed accordingly.

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    <xyPlot>
      <title class="- topic/title " wwtype:type="Paragraph" xmlns:wwtype="urn:WebWorks-Type-Schema" />
      <legend />
      <traces>
        <trace num-of-points="500" resultRef="5">
          <traceStyle color="#FFFF0000" symbol="none" line-weight="1" line-style="Solid">lines</traceStyle>
        </trace>
      </traces>
      <axes>
        <xAxis rank="1" legend-position="PlotBoundaryBottom">
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          <numberFormat>
            <decimal precision="3" show-trailing-zeros="false" radix="dec" imaginary-value="i" />
          </numberFormat>
          <plotEquations>
            <plotEquation>
              <math>
                <apply xmlns="http://schemas.mathsoft.com/math50">
                  <id>x</id>
                  <id>a</id>
                </apply>
              </math>
              <math>
                <placeholder xmlns="http://schemas.mathsoft.com/math50" />
              </math>
            </plotEquation>
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        </xAxis>
        <yAxis rank="1" legend-position="PlotBoundaryLeft">
          <axisLine position="ticknumberlock" positionticmark="5" legendWidth="83.1266666666667" />
          <axisGrid>
            <gridFrequency>11</gridFrequency>
            <gridLabels display="true" />
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            <tickMarks display="true" />
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          <axisLabel />
          <markers />
          <numberFormat>
            <decimal precision="3" show-trailing-zeros="false" radix="dec" imaginary-value="i" />
          </numberFormat>
          <plotEquations>
            <plotEquation>
              <math>
                <apply xmlns="http://schemas.mathsoft.com/math50">
                  <id>y</id>
                  <id>a</id>
                </apply>
              </math>
              <math>
                <placeholder xmlns="http://schemas.mathsoft.com/math50" />
              </math>
            </plotEquation>
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        </yAxis>
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Two Parameters

1. Set the number of data points.

2. Define the angle and the radius at each data point.

3. Define the parametrized coordinate vectors.

4. Use the augment function to record the above values in a matrix so that you can reuse them or write them to an external file for other applications.

5. Use the stack function to add titles to matrix.

6. Plot y against x. You can change the plotted points by modifying the definition of the range variable i.

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                <id xmlns="http://schemas.mathsoft.com/math50">x</id>
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                <placeholder xmlns="http://schemas.mathsoft.com/math50" />
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            <endValue resultRef="8">
              <real xmlns="http://schemas.mathsoft.com/math50">3</real>
            </endValue>
          </xyDomain>
        </xAxis>
        <yAxis rank="1" legend-position="PlotBoundaryLeft">
          <axisLine position="ticknumberlock" positionticmark="1" legendWidth="60.74" />
          <axisGrid>
            <gridFrequency>13</gridFrequency>
            <gridLabels display="true" />
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          <axisLabel />
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          <numberFormat>
            <decimal precision="3" show-trailing-zeros="false" radix="dec" imaginary-value="i" />
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                <id xmlns="http://schemas.mathsoft.com/math50">y</id>
              </math>
              <math>
                <placeholder xmlns="http://schemas.mathsoft.com/math50" />
              </math>
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7. Show the above curve as a polar plot (non-parametric).

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          <axisLabel />
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        <radialAxis rank="1" legend-position="PlotBoundaryLeft">
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          <axisLabel />
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            <decimal precision="3" show-trailing-zeros="false" radix="dec" imaginary-value="i" />
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