建立等高線圖

繪圖 > 等高線圖 > 建立等高線圖

建立等高線圖

1. 在工作表中，按一下您要插入等高線圖的位置，然後按 Ctrl+5 鍵。空的等高線圖區域會隨即出現。

或者，請在「繪圖」標籤的「繪線」群組中，從「插入繪圖」清單中選取「等高線圖」。

按一下以複製此運算式

<region id="ID0E5Y1HB" actualWidth="295.90666666666664" actualHeight="286.79999999999995" top="115.20000000000002" left="38.400000000000006" xmlns="http://schemas.mathsoft.com/worksheet50">
  <plot background-type="white">
    <contourPlot>
      <axes>
        <xAxis rank="1" legend-position="PlotBoundaryBottom" start="-10" end="10">
          <axisLine position="ticknumberlock" positionticmark="0" legendWidth="0" />
          <axisGrid>
            <gridFrequency>11</gridFrequency>
            <gridLabels display="true" />
            <gridLines />
            <tickMarks display="true" />
          </axisGrid>
          <axisLabel />
          <markers />
          <xyDomain scale-type="linear" auto-scale="true">
            <startValue>
              <placeholder xmlns="http://schemas.mathsoft.com/math50" />
            </startValue>
            <endValue>
              <placeholder xmlns="http://schemas.mathsoft.com/math50" />
            </endValue>
          </xyDomain>
        </xAxis>
        <yAxis rank="1" legend-position="PlotBoundaryLeft" start="-10" end="10">
          <axisLine position="ticknumberlock" positionticmark="0" legendWidth="0" />
          <axisGrid>
            <gridFrequency>11</gridFrequency>
            <gridLabels display="true" />
            <gridLines />
            <tickMarks display="true" />
          </axisGrid>
          <axisLabel />
          <markers />
          <xyDomain scale-type="linear" auto-scale="true">
            <startValue>
              <placeholder xmlns="http://schemas.mathsoft.com/math50" />
            </startValue>
            <endValue>
              <placeholder xmlns="http://schemas.mathsoft.com/math50" />
            </endValue>
          </xyDomain>
        </yAxis>
        <zAxis rank="1" start="-10" end="10">
          <axisLine position="origin" positionticmark="5" legendWidth="0" />
          <axisGrid>
            <gridFrequency>11</gridFrequency>
            <gridLabels display="true" />
            <gridLines />
            <tickMarks display="true" />
          </axisGrid>
          <axisLabel />
          <markers />
          <zDomain scale-type="linear" auto-scale="true">
            <startValue>
              <placeholder xmlns="http://schemas.mathsoft.com/math50" />
            </startValue>
            <endValue>
              <placeholder xmlns="http://schemas.mathsoft.com/math50" />
            </endValue>
          </zDomain>
        </zAxis>
      </axes>
      <contour color="#FF000000" show-lables="false" resultRef="21" />
      <graph-size width="230.39999999999998" height="230.39999999999998" />
      <plotEquation>
        <math>
          <placeholder xmlns="http://schemas.mathsoft.com/math50" />
        </math>
        <math>
          <placeholder xmlns="http://schemas.mathsoft.com/math50" />
        </math>
      </plotEquation>
    </contourPlot>
  </plot>
</region>

2. 定義雙變數函數、一個矩陣或具有三個矩陣的向量：

3. 在 z 軸運算式佔位符號中，鍵入不包含其引數的函數名稱，然後按 Enter 鍵。等高線圖會隨即出現在繪圖區域中，並在 x 軸下方顯示色階。

按一下以複製此運算式

<region id="ID0E521HB" actualWidth="298.79666666666668" actualHeight="286.79999999999995" top="556.80000000000007" left="38.400000000000006" xmlns="http://schemas.mathsoft.com/worksheet50">
  <plot background-type="white">
    <contourPlot>
      <axes>
        <xAxis rank="1" legend-position="PlotBoundaryBottom" start="-10" end="10">
          <axisLine position="ticknumberlock" positionticmark="0" legendWidth="0" />
          <axisGrid>
            <gridFrequency>11</gridFrequency>
            <gridLabels display="true" />
            <gridLines />
            <tickMarks display="true" />
          </axisGrid>
          <axisLabel />
          <markers />
          <xyDomain scale-type="linear" auto-scale="true">
            <startValue>
              <placeholder xmlns="http://schemas.mathsoft.com/math50" />
            </startValue>
            <endValue>
              <placeholder xmlns="http://schemas.mathsoft.com/math50" />
            </endValue>
          </xyDomain>
        </xAxis>
        <yAxis rank="1" legend-position="PlotBoundaryLeft" start="-10" end="10">
          <axisLine position="ticknumberlock" positionticmark="0" legendWidth="0" />
          <axisGrid>
            <gridFrequency>11</gridFrequency>
            <gridLabels display="true" />
            <gridLines />
            <tickMarks display="true" />
          </axisGrid>
          <axisLabel />
          <markers />
          <xyDomain scale-type="linear" auto-scale="true">
            <startValue>
              <placeholder xmlns="http://schemas.mathsoft.com/math50" />
            </startValue>
            <endValue>
              <placeholder xmlns="http://schemas.mathsoft.com/math50" />
            </endValue>
          </xyDomain>
        </yAxis>
        <zAxis rank="1" start="20" end="180">
          <axisLine position="origin" positionticmark="5" legendWidth="0" />
          <axisGrid>
            <gridFrequency>9</gridFrequency>
            <gridLabels display="true" />
            <gridLines />
            <tickMarks display="true" />
          </axisGrid>
          <axisLabel />
          <markers />
          <zDomain scale-type="linear" auto-scale="true">
            <startValue>
              <placeholder xmlns="http://schemas.mathsoft.com/math50" />
            </startValue>
            <endValue>
              <placeholder xmlns="http://schemas.mathsoft.com/math50" />
            </endValue>
          </zDomain>
        </zAxis>
      </axes>
      <contour color="#FF000000" show-lables="false" resultRef="23" />
      <graph-size width="230.39999999999998" height="230.39999999999998" />
      <plotEquation>
        <math>
          <id labels="VARIABLE" xml:space="preserve" label-is-contextual="true" xmlns="http://schemas.mathsoft.com/math50">f</id>
        </math>
        <math>
          <placeholder xmlns="http://schemas.mathsoft.com/math50" />
        </math>
      </plotEquation>
    </contourPlot>
  </plot>
</region>

預設的等高線數為十。

4. 若要變更等高線數，請編輯 z 軸刻度線上限。

按一下以複製此運算式

<region id="ID0EI51HB" actualWidth="298.79666666666668" actualHeight="286.79999999999995" top="960.00000000000011" left="38.400000000000006" xmlns="http://schemas.mathsoft.com/worksheet50">
  <plot background-type="white">
    <contourPlot>
      <axes>
        <xAxis rank="1" legend-position="PlotBoundaryBottom" start="-10" end="10">
          <axisLine position="ticknumberlock" positionticmark="0" legendWidth="0" />
          <axisGrid>
            <gridFrequency>11</gridFrequency>
            <gridLabels display="true" />
            <gridLines />
            <tickMarks display="true" />
          </axisGrid>
          <axisLabel />
          <markers />
          <xyDomain scale-type="linear" auto-scale="true">
            <startValue>
              <placeholder xmlns="http://schemas.mathsoft.com/math50" />
            </startValue>
            <endValue>
              <placeholder xmlns="http://schemas.mathsoft.com/math50" />
            </endValue>
          </xyDomain>
        </xAxis>
        <yAxis rank="1" legend-position="PlotBoundaryLeft" start="-10" end="10">
          <axisLine position="ticknumberlock" positionticmark="0" legendWidth="0" />
          <axisGrid>
            <gridFrequency>11</gridFrequency>
            <gridLabels display="true" />
            <gridLines />
            <tickMarks display="true" />
          </axisGrid>
          <axisLabel />
          <markers />
          <xyDomain scale-type="linear" auto-scale="true">
            <startValue>
              <placeholder xmlns="http://schemas.mathsoft.com/math50" />
            </startValue>
            <endValue>
              <placeholder xmlns="http://schemas.mathsoft.com/math50" />
            </endValue>
          </xyDomain>
        </yAxis>
        <zAxis rank="1" start="20" end="90">
          <axisLine position="origin" positionticmark="5" legendWidth="0" />
          <axisGrid>
            <gridFrequency>11</gridFrequency>
            <gridLabels display="true" />
            <gridLines />
            <tickMarks display="true" />
          </axisGrid>
          <axisLabel />
          <markers />
          <zDomain scale-type="linear" auto-scale="true">
            <startValue>
              <placeholder xmlns="http://schemas.mathsoft.com/math50" />
            </startValue>
            <endValue resultRef="24">
              <real xmlns="http://schemas.mathsoft.com/math50">90</real>
            </endValue>
          </zDomain>
        </zAxis>
      </axes>
      <contour color="#FF000000" show-lables="false" resultRef="25" />
      <graph-size width="230.39999999999998" height="230.39999999999998" />
      <plotEquation>
        <math>
          <id labels="VARIABLE" xml:space="preserve" label-is-contextual="true" xmlns="http://schemas.mathsoft.com/math50">f</id>
        </math>
        <math>
          <placeholder xmlns="http://schemas.mathsoft.com/math50" />
        </math>
      </plotEquation>
    </contourPlot>
  </plot>
</region>

系統會自動設定刻度線間隔，並據以變更等高線數。

5. 若要取得特定的等高線數 (如三條)，請如下設定刻度線值：

a. 設定刻度線上限 ULTM

b. 設定刻度線下限 LLTM

c. 設定刻度線間隔 ITM，讓下列方程式計算結果為三：

d. 繪圖現在會顯示三條等高線

按一下以複製此運算式

<region id="ID0E6G2HB" actualWidth="298.79666666666668" actualHeight="286.79999999999995" top="1747.2000000000003" left="38.400000000000006" xmlns="http://schemas.mathsoft.com/worksheet50">
  <plot background-type="white">
    <contourPlot>
      <axes>
        <xAxis rank="1" legend-position="PlotBoundaryBottom" start="-10" end="10">
          <axisLine position="ticknumberlock" positionticmark="0" legendWidth="0" />
          <axisGrid>
            <gridFrequency>11</gridFrequency>
            <gridLabels display="true" />
            <gridLines />
            <tickMarks display="true" />
          </axisGrid>
          <axisLabel />
          <markers />
          <xyDomain scale-type="linear" auto-scale="true">
            <startValue>
              <placeholder xmlns="http://schemas.mathsoft.com/math50" />
            </startValue>
            <endValue>
              <placeholder xmlns="http://schemas.mathsoft.com/math50" />
            </endValue>
          </xyDomain>
        </xAxis>
        <yAxis rank="1" legend-position="PlotBoundaryLeft" start="-10" end="10">
          <axisLine position="ticknumberlock" positionticmark="0" legendWidth="0" />
          <axisGrid>
            <gridFrequency>11</gridFrequency>
            <gridLabels display="true" />
            <gridLines />
            <tickMarks display="true" />
          </axisGrid>
          <axisLabel />
          <markers />
          <xyDomain scale-type="linear" auto-scale="true">
            <startValue>
              <placeholder xmlns="http://schemas.mathsoft.com/math50" />
            </startValue>
            <endValue>
              <placeholder xmlns="http://schemas.mathsoft.com/math50" />
            </endValue>
          </xyDomain>
        </yAxis>
        <zAxis rank="1" start="0" end="90">
          <axisLine position="origin" positionticmark="5" legendWidth="0" />
          <axisGrid>
            <gridFrequency>4</gridFrequency>
            <gridLabels display="true" />
            <gridLines />
            <tickMarks display="true" />
          </axisGrid>
          <axisLabel />
          <markers />
          <zDomain scale-type="linear" auto-scale="true">
            <startValue resultRef="30">
              <real xmlns="http://schemas.mathsoft.com/math50">0</real>
            </startValue>
            <secondTickValue resultRef="31">
              <real xmlns="http://schemas.mathsoft.com/math50">30</real>
            </secondTickValue>
            <endValue resultRef="32">
              <real xmlns="http://schemas.mathsoft.com/math50">90</real>
            </endValue>
          </zDomain>
        </zAxis>
      </axes>
      <contour color="#FF000000" show-lables="false" resultRef="33" />
      <graph-size width="230.39999999999998" height="230.39999999999998" />
      <plotEquation>
        <math>
          <id labels="VARIABLE" xml:space="preserve" label-is-contextual="true" xmlns="http://schemas.mathsoft.com/math50">f</id>
        </math>
        <math>
          <placeholder xmlns="http://schemas.mathsoft.com/math50" />
        </math>
      </plotEquation>
    </contourPlot>
  </plot>
</region>

6. 若要顯示等高線值，請在「繪圖」標籤的「樣式」群組中，按一下「等高線值」。

按一下以複製此運算式

<region id="ID0E3I2HB" actualWidth="298.79666666666668" actualHeight="286.79999999999995" top="2092.8" left="38.400000000000006" xmlns="http://schemas.mathsoft.com/worksheet50">
  <plot background-type="white">
    <contourPlot>
      <axes>
        <xAxis rank="1" legend-position="PlotBoundaryBottom" start="-10" end="10">
          <axisLine position="ticknumberlock" positionticmark="0" legendWidth="0" />
          <axisGrid>
            <gridFrequency>11</gridFrequency>
            <gridLabels display="true" />
            <gridLines />
            <tickMarks display="true" />
          </axisGrid>
          <axisLabel />
          <markers />
          <xyDomain scale-type="linear" auto-scale="true">
            <startValue>
              <placeholder xmlns="http://schemas.mathsoft.com/math50" />
            </startValue>
            <endValue>
              <placeholder xmlns="http://schemas.mathsoft.com/math50" />
            </endValue>
          </xyDomain>
        </xAxis>
        <yAxis rank="1" legend-position="PlotBoundaryLeft" start="-10" end="10">
          <axisLine position="ticknumberlock" positionticmark="0" legendWidth="0" />
          <axisGrid>
            <gridFrequency>11</gridFrequency>
            <gridLabels display="true" />
            <gridLines />
            <tickMarks display="true" />
          </axisGrid>
          <axisLabel />
          <markers />
          <xyDomain scale-type="linear" auto-scale="true">
            <startValue>
              <placeholder xmlns="http://schemas.mathsoft.com/math50" />
            </startValue>
            <endValue>
              <placeholder xmlns="http://schemas.mathsoft.com/math50" />
            </endValue>
          </xyDomain>
        </yAxis>
        <zAxis rank="1" start="0" end="90">
          <axisLine position="origin" positionticmark="5" legendWidth="0" />
          <axisGrid>
            <gridFrequency>4</gridFrequency>
            <gridLabels display="true" />
            <gridLines />
            <tickMarks display="true" />
          </axisGrid>
          <axisLabel />
          <markers />
          <zDomain scale-type="linear" auto-scale="true">
            <startValue resultRef="34">
              <real xmlns="http://schemas.mathsoft.com/math50">0</real>
            </startValue>
            <secondTickValue resultRef="35">
              <real xmlns="http://schemas.mathsoft.com/math50">30</real>
            </secondTickValue>
            <endValue resultRef="36">
              <real xmlns="http://schemas.mathsoft.com/math50">90</real>
            </endValue>
          </zDomain>
        </zAxis>
      </axes>
      <contour color="#FF000000" resultRef="37" />
      <graph-size width="230.39999999999998" height="230.39999999999998" />
      <plotEquation>
        <math>
          <id labels="VARIABLE" xml:space="preserve" label-is-contextual="true" xmlns="http://schemas.mathsoft.com/math50">f</id>
        </math>
        <math>
          <placeholder xmlns="http://schemas.mathsoft.com/math50" />
        </math>
      </plotEquation>
    </contourPlot>
  </plot>
</region>

若要隱藏等高線值，請再按一下「等高線值」。

7. 若要將繪圖的顏色配置變更為「地形」，請在「繪圖」標籤的「樣式」群組中，按一下「顏色配置」，然後從清單中選取該選項。

按一下以複製此運算式

<region id="ID0EFL2HB" actualWidth="298.79666666666668" actualHeight="286.79999999999995" top="2611.2000000000003" left="57.600000000000009" xmlns="http://schemas.mathsoft.com/worksheet50">
  <plot background-type="white">
    <contourPlot>
      <axes>
        <xAxis rank="1" legend-position="PlotBoundaryBottom" start="-10" end="10">
          <axisLine position="ticknumberlock" positionticmark="0" legendWidth="0" />
          <axisGrid>
            <gridFrequency>11</gridFrequency>
            <gridLabels display="true" />
            <gridLines />
            <tickMarks display="true" />
          </axisGrid>
          <axisLabel />
          <markers />
          <xyDomain scale-type="linear" auto-scale="true">
            <startValue>
              <placeholder xmlns="http://schemas.mathsoft.com/math50" />
            </startValue>
            <endValue>
              <placeholder xmlns="http://schemas.mathsoft.com/math50" />
            </endValue>
          </xyDomain>
        </xAxis>
        <yAxis rank="1" legend-position="PlotBoundaryLeft" start="-10" end="10">
          <axisLine position="ticknumberlock" positionticmark="0" legendWidth="0" />
          <axisGrid>
            <gridFrequency>11</gridFrequency>
            <gridLabels display="true" />
            <gridLines />
            <tickMarks display="true" />
          </axisGrid>
          <axisLabel />
          <markers />
          <xyDomain scale-type="linear" auto-scale="true">
            <startValue>
              <placeholder xmlns="http://schemas.mathsoft.com/math50" />
            </startValue>
            <endValue>
              <placeholder xmlns="http://schemas.mathsoft.com/math50" />
            </endValue>
          </xyDomain>
        </yAxis>
        <zAxis rank="1" start="0" end="90">
          <axisLine position="origin" positionticmark="5" legendWidth="0" />
          <axisGrid>
            <gridFrequency>4</gridFrequency>
            <gridLabels display="true" />
            <gridLines />
            <tickMarks display="true" />
          </axisGrid>
          <axisLabel />
          <markers />
          <zDomain scale-type="linear" auto-scale="true">
            <startValue resultRef="38">
              <real xmlns="http://schemas.mathsoft.com/math50">0</real>
            </startValue>
            <secondTickValue resultRef="39">
              <real xmlns="http://schemas.mathsoft.com/math50">30</real>
            </secondTickValue>
            <endValue resultRef="40">
              <real xmlns="http://schemas.mathsoft.com/math50">90</real>
            </endValue>
          </zDomain>
        </zAxis>
      </axes>
      <contour color="#FF000000" resultRef="41" color-scheme="topographical" />
      <graph-size width="230.39999999999998" height="230.39999999999998" />
      <plotEquation>
        <math>
          <id labels="VARIABLE" xml:space="preserve" label-is-contextual="true" xmlns="http://schemas.mathsoft.com/math50">f</id>
        </math>
        <math>
          <placeholder xmlns="http://schemas.mathsoft.com/math50" />
        </math>
      </plotEquation>
    </contourPlot>
  </plot>
</region>

您可以使用 CreateMesh 控制 x 軸與 y 軸值域，而不需要繪製函數再格式化繪圖。此外，CreateMesh 可讓您控制等高線圖的格點大小，並將函數對映至卡式座標。

相關主題

關於等高線圖元件

CreateSpace 與 CreateMesh

這是否有幫助?