Comparaison des tracés 3D des fonctions à une ou deux variables

Tracés > Tracés 3D > Comparaison des tracés 3D des fonctions à une ou deux variables

Il est possible de tracer une fonction à une ou deux variables dans une zone de tracé 3D.

Cette rubrique compare les tracés de ces fonctions.

Tracez une fonction à une variable

Définissez et tracez la fonction à une variable f1(x) :

Le tracé 3D par défaut de f1(x) est sur la gauche et indique la trace d'une ligne. Le tracé de droite est le même tracé, mais pivoté pour vérifier que la courbe est bien une ligne.

Position des axes par défaut	Axes pivotés
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Position des axes par défaut

Axes pivotés

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      <traces>
        <trace3D resultRef="174" num-of-points="41">
          <traceStyle color="#FFED1D2F" automaticStyle="true">curve</traceStyle>
        </trace3D>
      </traces>
      <graph-size width="230.39999999999998" height="230.39999999999998" />
      <axes>
        <xAxis rank="1" start="-10" end="10">
          <axisLine />
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            <gridLabels display="true" />
            <gridLines />
            <tickMarks display="true" />
          </axisGrid>
          <axisLabel />
          <xyDomain auto-scale="true" allow-negative-values="true" scale-type="linear">
            <startValue />
            <endValue />
          </xyDomain>
        </xAxis>
        <yAxis rank="1" start="-1" end="1">
          <axisLine />
          <axisGrid>
            <gridFrequency>5</gridFrequency>
            <gridLabels display="true" />
            <gridLines />
            <tickMarks display="true" />
          </axisGrid>
          <axisLabel />
          <xyDomain auto-scale="true" allow-negative-values="true" scale-type="linear">
            <startValue />
            <endValue />
          </xyDomain>
        </yAxis>
        <zAxis rank="1" start="-10" end="10">
          <axisLine />
          <axisGrid>
            <gridFrequency>5</gridFrequency>
            <gridLabels display="true" />
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            <startValue />
            <endValue />
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        </zAxis>
      </axes>
      <plotEquations>
        <plotEquation>
          <math>
            <id labels="VARIABLE" xml:space="preserve" label-is-contextual="true" xmlns="http://schemas.mathsoft.com/math50">f1</id>
          </math>
          <math>
            <placeholder xmlns="http://schemas.mathsoft.com/math50" />
          </math>
        </plotEquation>
      </plotEquations>
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          <Cell>0</Cell>
          <Cell>0</Cell>
          <Cell>0</Cell>
          <Cell>0</Cell>
          <Cell>1</Cell>
          <Cell>0</Cell>
          <Cell>0</Cell>
          <Cell>0</Cell>
          <Cell>0</Cell>
          <Cell>1</Cell>
          <Cell>0</Cell>
          <Cell>0</Cell>
          <Cell>0</Cell>
          <Cell>0</Cell>
          <Cell>1</Cell>
        </Cells>
      </CameraTransformMatrix>
    </plot3D>
  </plot>
</region>

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      <traces>
        <trace3D resultRef="177" num-of-points="41">
          <traceStyle color="#FF2E3192" automaticStyle="true">curve</traceStyle>
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            <startValue />
            <endValue />
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        <yAxis rank="1" start="-1" end="1">
          <axisLine />
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            <gridFrequency>5</gridFrequency>
            <gridLabels display="true" />
            <gridLines />
            <tickMarks display="true" />
          </axisGrid>
          <axisLabel />
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            <startValue />
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          <axisLine />
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            <gridLabels display="true" />
            <gridLines />
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            <startValue />
            <endValue />
          </zDomain>
        </zAxis>
      </axes>
      <plotEquations>
        <plotEquation>
          <math>
            <id labels="VARIABLE" xml:space="preserve" label-is-contextual="true" xmlns="http://schemas.mathsoft.com/math50">f1</id>
          </math>
          <math>
            <placeholder xmlns="http://schemas.mathsoft.com/math50" />
          </math>
        </plotEquation>
      </plotEquations>
      <CameraTransformMatrix Columns="4" Rows="4">
        <Cells>
          <Cell>0.97392039271312958</Cell>
          <Cell>0.0042824428894279939</Cell>
          <Cell>0.22684957425660363</Cell>
          <Cell>0</Cell>
          <Cell>-0.070292004431413369</Cell>
          <Cell>0.95632519314437225</Cell>
          <Cell>0.28372726176804614</Cell>
          <Cell>0</Cell>
          <Cell>-0.21572691712096964</Cell>
          <Cell>-0.29227347748346583</Cell>
          <Cell>0.93168562916318742</Cell>
          <Cell>0</Cell>
          <Cell>0</Cell>
          <Cell>0</Cell>
          <Cell>0</Cell>
          <Cell>1</Cell>
        </Cells>
      </CameraTransformMatrix>
    </plot3D>
  </plot>
</region>

Le fait de tracer la fonction à une variable f1(x) dans une zone 3D est équivalent au fait de tracer une fonction à deux variables f2(u,v) où vous ne spécifiez qu'une variable, comme indiqué ci-dessous :

Position des axes par défaut	Axes pivotés
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Position des axes par défaut

Axes pivotés

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      <traces>
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          <traceStyle color="#FFED1D2F" automaticStyle="true">surface</traceStyle>
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          <axisLabel />
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            <startValue />
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        <yAxis rank="1" start="-1" end="1">
          <axisLine />
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            <gridFrequency>5</gridFrequency>
            <gridLabels display="true" />
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          <axisLabel />
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            <startValue />
            <endValue />
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        <zAxis rank="1" start="-10" end="10">
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            <gridLabels display="true" />
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            <startValue />
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          <Cell>0</Cell>
          <Cell>0</Cell>
          <Cell>0</Cell>
          <Cell>0</Cell>
          <Cell>1</Cell>
          <Cell>0</Cell>
          <Cell>0</Cell>
          <Cell>0</Cell>
          <Cell>0</Cell>
          <Cell>1</Cell>
          <Cell>0</Cell>
          <Cell>0</Cell>
          <Cell>0</Cell>
          <Cell>0</Cell>
          <Cell>1</Cell>
        </Cells>
      </CameraTransformMatrix>
    </plot3D>
  </plot>
</region>

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          <axisLine />
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            <gridLabels display="true" />
            <gridLines />
            <tickMarks display="true" />
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          <axisLabel />
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            <gridLabels display="true" />
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            <startValue />
            <endValue />
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      <plotEquations>
        <plotEquation>
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            <id labels="VARIABLE" xml:space="preserve" label-is-contextual="true" xmlns="http://schemas.mathsoft.com/math50">f2</id>
          </math>
          <math>
            <placeholder xmlns="http://schemas.mathsoft.com/math50" />
          </math>
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          <Cell>0.0042824428894279939</Cell>
          <Cell>0.22684957425660363</Cell>
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          <Cell>-0.070292004431413369</Cell>
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          <Cell>0</Cell>
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          <Cell>-0.29227347748346583</Cell>
          <Cell>0.93168562916318742</Cell>
          <Cell>0</Cell>
          <Cell>0</Cell>
          <Cell>0</Cell>
          <Cell>0</Cell>
          <Cell>1</Cell>
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Tracez une fonction à deux variables

Définissez une fonction à deux variables f3(x,y) en termes de fonction à une variable :

Le tracé 3D par défaut de f3(x,y) est sur la gauche et affiche un plan. Le tracé de droite est le même tracé, mais pivoté pour vérifier que la courbe est bien un plan.

Position des axes par défaut	Axes pivotés
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Position des axes par défaut

Axes pivotés

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  <plot background-type="white">
    <plot3D>
      <traces>
        <trace3D resultRef="190" num-of-points="41">
          <traceStyle color="#FFED1D2F" automaticStyle="true">surface</traceStyle>
        </trace3D>
      </traces>
      <graph-size width="230.39999999999998" height="230.39999999999998" />
      <axes>
        <xAxis rank="1" start="-10" end="10">
          <axisLine />
          <axisGrid>
            <gridFrequency>5</gridFrequency>
            <gridLabels display="true" />
            <gridLines />
            <tickMarks display="true" />
          </axisGrid>
          <axisLabel />
          <xyDomain auto-scale="true" allow-negative-values="true" scale-type="linear">
            <startValue />
            <endValue />
          </xyDomain>
        </xAxis>
        <yAxis rank="1" start="-10" end="10">
          <axisLine />
          <axisGrid>
            <gridFrequency>5</gridFrequency>
            <gridLabels display="true" />
            <gridLines />
            <tickMarks display="true" />
          </axisGrid>
          <axisLabel />
          <xyDomain auto-scale="true" allow-negative-values="true" scale-type="linear">
            <startValue />
            <endValue />
          </xyDomain>
        </yAxis>
        <zAxis rank="1" start="-10" end="10">
          <axisLine />
          <axisGrid>
            <gridFrequency>5</gridFrequency>
            <gridLabels display="true" />
            <gridLines />
            <tickMarks display="true" />
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          <axisLabel />
          <zDomain auto-scale="true" allow-negative-values="true" scale-type="linear">
            <startValue />
            <endValue />
          </zDomain>
        </zAxis>
      </axes>
      <plotEquations>
        <plotEquation>
          <math>
            <id labels="VARIABLE" xml:space="preserve" label-is-contextual="true" xmlns="http://schemas.mathsoft.com/math50">f3</id>
          </math>
          <math>
            <placeholder xmlns="http://schemas.mathsoft.com/math50" />
          </math>
        </plotEquation>
      </plotEquations>
      <CameraTransformMatrix Columns="4" Rows="4">
        <Cells>
          <Cell>1</Cell>
          <Cell>0</Cell>
          <Cell>0</Cell>
          <Cell>0</Cell>
          <Cell>0</Cell>
          <Cell>1</Cell>
          <Cell>0</Cell>
          <Cell>0</Cell>
          <Cell>0</Cell>
          <Cell>0</Cell>
          <Cell>1</Cell>
          <Cell>0</Cell>
          <Cell>0</Cell>
          <Cell>0</Cell>
          <Cell>0</Cell>
          <Cell>1</Cell>
        </Cells>
      </CameraTransformMatrix>
    </plot3D>
  </plot>
</region>

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  <plot background-type="white">
    <plot3D>
      <traces>
        <trace3D resultRef="193" num-of-points="41">
          <traceStyle color="#FF2E3192" automaticStyle="true">surface</traceStyle>
        </trace3D>
      </traces>
      <graph-size width="230.39999999999998" height="230.39999999999998" />
      <axes>
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          <axisLine />
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            <gridFrequency>5</gridFrequency>
            <gridLabels display="true" />
            <gridLines />
            <tickMarks display="true" />
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          <axisLabel />
          <xyDomain auto-scale="true" allow-negative-values="true" scale-type="linear">
            <startValue />
            <endValue />
          </xyDomain>
        </xAxis>
        <yAxis rank="1" start="-10" end="10">
          <axisLine />
          <axisGrid>
            <gridFrequency>5</gridFrequency>
            <gridLabels display="true" />
            <gridLines />
            <tickMarks display="true" />
          </axisGrid>
          <axisLabel />
          <xyDomain auto-scale="true" allow-negative-values="true" scale-type="linear">
            <startValue />
            <endValue />
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        </yAxis>
        <zAxis rank="1" start="-10" end="10">
          <axisLine />
          <axisGrid>
            <gridFrequency>5</gridFrequency>
            <gridLabels display="true" />
            <gridLines />
            <tickMarks display="true" />
          </axisGrid>
          <axisLabel />
          <zDomain auto-scale="true" allow-negative-values="true" scale-type="linear">
            <startValue />
            <endValue />
          </zDomain>
        </zAxis>
      </axes>
      <plotEquations>
        <plotEquation>
          <math>
            <id labels="VARIABLE" xml:space="preserve" label-is-contextual="true" xmlns="http://schemas.mathsoft.com/math50">f3</id>
          </math>
          <math>
            <placeholder xmlns="http://schemas.mathsoft.com/math50" />
          </math>
        </plotEquation>
      </plotEquations>
      <CameraTransformMatrix Columns="4" Rows="4">
        <Cells>
          <Cell>0.97392039271312958</Cell>
          <Cell>0.0042824428894279939</Cell>
          <Cell>0.22684957425660363</Cell>
          <Cell>0</Cell>
          <Cell>-0.070292004431413369</Cell>
          <Cell>0.95632519314437225</Cell>
          <Cell>0.28372726176804614</Cell>
          <Cell>0</Cell>
          <Cell>-0.21572691712096964</Cell>
          <Cell>-0.29227347748346583</Cell>
          <Cell>0.93168562916318742</Cell>
          <Cell>0</Cell>
          <Cell>0</Cell>
          <Cell>0</Cell>
          <Cell>0</Cell>
          <Cell>1</Cell>
        </Cells>
      </CameraTransformMatrix>
    </plot3D>
  </plot>
</region>

Le fait de tracer la fonction à une variable f3(x,y) dans une zone 3D est équivalent au fait de tracer une fonction à deux variables f4(u,v) où vous spécifiez deux variables, comme indiqué ci-dessous :

Position des axes par défaut	Axes pivotés
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Position des axes par défaut

Axes pivotés

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    <plot3D>
      <traces>
        <trace3D resultRef="198" num-of-points="41">
          <traceStyle color="#FFED1D2F" automaticStyle="true">surface</traceStyle>
        </trace3D>
      </traces>
      <graph-size width="230.39999999999998" height="230.39999999999998" />
      <axes>
        <xAxis rank="1" start="-10" end="10">
          <axisLine />
          <axisGrid>
            <gridFrequency>5</gridFrequency>
            <gridLabels display="true" />
            <gridLines />
            <tickMarks display="true" />
          </axisGrid>
          <axisLabel />
          <xyDomain auto-scale="true" allow-negative-values="true" scale-type="linear">
            <startValue />
            <endValue />
          </xyDomain>
        </xAxis>
        <yAxis rank="1" start="-10" end="10">
          <axisLine />
          <axisGrid>
            <gridFrequency>5</gridFrequency>
            <gridLabels display="true" />
            <gridLines />
            <tickMarks display="true" />
          </axisGrid>
          <axisLabel />
          <xyDomain auto-scale="true" allow-negative-values="true" scale-type="linear">
            <startValue />
            <endValue />
          </xyDomain>
        </yAxis>
        <zAxis rank="1" start="-10" end="10">
          <axisLine />
          <axisGrid>
            <gridFrequency>5</gridFrequency>
            <gridLabels display="true" />
            <gridLines />
            <tickMarks display="true" />
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          <axisLabel />
          <zDomain auto-scale="true" allow-negative-values="true" scale-type="linear">
            <startValue />
            <endValue />
          </zDomain>
        </zAxis>
      </axes>
      <plotEquations>
        <plotEquation>
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            <id labels="VARIABLE" xml:space="preserve" label-is-contextual="true" xmlns="http://schemas.mathsoft.com/math50">f4</id>
          </math>
          <math>
            <placeholder xmlns="http://schemas.mathsoft.com/math50" />
          </math>
        </plotEquation>
      </plotEquations>
      <CameraTransformMatrix Columns="4" Rows="4">
        <Cells>
          <Cell>1</Cell>
          <Cell>0</Cell>
          <Cell>0</Cell>
          <Cell>0</Cell>
          <Cell>0</Cell>
          <Cell>1</Cell>
          <Cell>0</Cell>
          <Cell>0</Cell>
          <Cell>0</Cell>
          <Cell>0</Cell>
          <Cell>1</Cell>
          <Cell>0</Cell>
          <Cell>0</Cell>
          <Cell>0</Cell>
          <Cell>0</Cell>
          <Cell>1</Cell>
        </Cells>
      </CameraTransformMatrix>
    </plot3D>
  </plot>
</region>

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        <yAxis rank="1" start="-10" end="10">
          <axisLine />
          <axisGrid>
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            <gridLabels display="true" />
            <gridLines />
            <tickMarks display="true" />
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          <axisLabel />
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        </yAxis>
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            <gridLabels display="true" />
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            <startValue />
            <endValue />
          </zDomain>
        </zAxis>
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      <plotEquations>
        <plotEquation>
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            <id labels="VARIABLE" xml:space="preserve" label-is-contextual="true" xmlns="http://schemas.mathsoft.com/math50">f4</id>
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          <math>
            <placeholder xmlns="http://schemas.mathsoft.com/math50" />
          </math>
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      </plotEquations>
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          <Cell>0.97392039271312958</Cell>
          <Cell>0.0042824428894279939</Cell>
          <Cell>0.22684957425660363</Cell>
          <Cell>0</Cell>
          <Cell>-0.070292004431413369</Cell>
          <Cell>0.95632519314437225</Cell>
          <Cell>0.28372726176804614</Cell>
          <Cell>0</Cell>
          <Cell>-0.21572691712096964</Cell>
          <Cell>-0.29227347748346583</Cell>
          <Cell>0.93168562916318742</Cell>
          <Cell>0</Cell>
          <Cell>0</Cell>
          <Cell>0</Cell>
          <Cell>0</Cell>
          <Cell>1</Cell>
        </Cells>
      </CameraTransformMatrix>
    </plot3D>
  </plot>
</region>

Rubriques associées

A propos des tracés 3D

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