예제: 벡터 값 함수 도표화

도표 > 3D 도표 > 예제: 벡터 값 함수 도표화

예제: 벡터 값 함수 도표화

벡터 값 함수를 정의하여 3D 메시 도표를 생성하고 CreateMesh 함수를 사용하는 도표와 결과를 비교합니다.

벡터 값 함수 도표화

3D 공간에서 매개변수 평면을 정의하는 벡터 값 함수를 도표화합니다.

1. 두 매개변수의 벡터 값 함수를 정의합니다.

이 함수에서 u+v, v2 및 u*v는 각각 X 좌표, Y 좌표 및 Z 좌표를 나타냅니다.

2. Ctrl+3을 누르고 z축 식의 자리 표시자에 함수의 이름을 입력한 다음 그래프선 색상 및 평면 채우기를 변경합니다.

<region id="ID0EI3LIB" top="422.40000000000009" width="288" left="115.20000000000002" height="291.79999999999995" xmlns="http://schemas.mathsoft.com/worksheet50">
 <plot background-type="white">
 <plot3D>
 <traces>
 <trace3D resultRef="65" num-of-points="41" SurfaceFill="#FFDB9796">
 <traceStyle color="#FF932329">surface</traceStyle>
 </trace3D>
 </traces>
 <graph-size width="230.39999999999995" height="230.39999999999998" />
 <axes>
 <xAxis rank="1" start="-20" end="20">
 <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="0" end="100">
 <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="-100" end="100">
 <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 xml:space="preserve" xmlns="http://schemas.mathsoft.com/math50">g</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>

PTC Mathcad가 벡터 값 함수를 메시로 도표화합니다.

CreateMesh를 사용한 함수 도표화

1. 위 두 매개변수의 범위를 양의 값만 포함하도록 정의합니다.

2. CreateMesh를 사용하여 g 함수와 u 및 v 범위의 데이터 집합을 얻습니다.

<region id="ID0EMEMIB" top="1036.8000000000002" width="340.55000000000007" left="115.20000000000002" height="27.791200000000003" xmlns="http://schemas.mathsoft.com/worksheet50">
 <math resultRef="80">
 <define xmlns="http://schemas.mathsoft.com/math50">
 <id labels="VARIABLE" xml:space="preserve">M</id>
 <apply>
 <id labels="FUNCTION" xml:space="preserve" label-is-contextual="true">CreateMesh</id>
 <sequence>
 <id labels="VARIABLE" xml:space="preserve" label-is-contextual="true">g</id>
 <id labels="VARIABLE" xml:space="preserve" label-is-contextual="true">
 u<Subscript xmlns="clr-namespace:Ptc.Wpf;assembly=Ptc.Core">min</Subscript>
 </id>
 <id labels="VARIABLE" xml:space="preserve" label-is-contextual="true">
 u<Subscript xmlns="clr-namespace:Ptc.Wpf;assembly=Ptc.Core">max</Subscript>
 </id>
 <id labels="VARIABLE" xml:space="preserve" label-is-contextual="true">
 v<Subscript xmlns="clr-namespace:Ptc.Wpf;assembly=Ptc.Core">min</Subscript>
 </id>
 <id labels="VARIABLE" xml:space="preserve" label-is-contextual="true">
 v<Subscript xmlns="clr-namespace:Ptc.Wpf;assembly=Ptc.Core">max</Subscript>
 </id>
 <id labels="VARIABLE" xml:space="preserve" label-is-contextual="true">
 n<Subscript xmlns="clr-namespace:Ptc.Wpf;assembly=Ptc.Core">u</Subscript>
 </id>
 <id labels="VARIABLE" xml:space="preserve" label-is-contextual="true">
 n<Subscript xmlns="clr-namespace:Ptc.Wpf;assembly=Ptc.Core">v</Subscript>
 </id>
 </sequence>
 </apply>
 </define>
 </math>
</region>

3. Ctrl+3을 누르고 M을 도표화합니다.

<region id="ID0EOGMIB" top="1113.6000000000001" width="288" left="115.20000000000002" height="291.79999999999995" xmlns="http://schemas.mathsoft.com/worksheet50">
 <plot background-type="white">
 <plot3D>
 <traces>
 <trace3D resultRef="84" num-of-points="41" SurfaceFill="#FFE1ECD2">
 <traceStyle color="#FF068149">surface</traceStyle>
 </trace3D>
 </traces>
 <graph-size width="230.39999999999995" height="230.39999999999998" />
 <axes>
 <xAxis rank="1" start="0" end="20">
 <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="0" end="100">
 <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="0" end="100">
 <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 xml:space="preserve" xmlns="http://schemas.mathsoft.com/math50">M</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>

입력 변수의 차이로 인해 M 도표의 범위가 g 도표의 범위와 다릅니다. M은 1단계에서 정의한 범위에서 도표화되지만 g는 기본값인 (-10, 10) 범위에서 도표화됩니다.

4. g의 범위를 설정하려면 도표 위에 u 및 v에 대한 범위 변수를 정의합니다.

5. g를 다시 도표화합니다.

<region id="ID0EJNMIB" top="1612.8000000000002" width="288" left="96.000000000000014" height="291.79999999999995" xmlns="http://schemas.mathsoft.com/worksheet50">
 <plot background-type="white">
 <plot3D>
 <traces>
 <trace3D resultRef="95" num-of-points="41" SurfaceFill="#FFE1ECD2">
 <traceStyle color="#FF068149">surface</traceStyle>
 </trace3D>
 </traces>
 <graph-size width="230.39999999999995" height="230.39999999999998" />
 <axes>
 <xAxis rank="1" start="0" end="20">
 <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="0" end="100">
 <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="0" end="100">
 <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>
 <apply xmlns="http://schemas.mathsoft.com/math50">
 <id xml:space="preserve">g</id>
 <sequence>
 <id xml:space="preserve">u</id>
 <id xml:space="preserve">v</id>
 </sequence>
 </apply>
 </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>

벡터 값 함수를 도표화할 때에는 도표 위에 범위 변수를 정의하여 범위를 설정해야 합니다.

두 도표 비교

1. 범위 min 및 max에 대한 새 값을 정의합니다.

2. 구간 수를 정의하고 M을 다시 계산합니다.

<region id="ID0EVUMIB" top="2208.0000000000005" width="340.55000000000007" left="57.600000000000009" height="27.791200000000003" xmlns="http://schemas.mathsoft.com/worksheet50">
 <math resultRef="110">
 <define xmlns="http://schemas.mathsoft.com/math50">
 <id labels="VARIABLE" xml:space="preserve">M</id>
 <apply>
 <id labels="FUNCTION" xml:space="preserve" label-is-contextual="true">CreateMesh</id>
 <sequence>
 <id labels="VARIABLE" xml:space="preserve" label-is-contextual="true">g</id>
 <id labels="VARIABLE" xml:space="preserve" label-is-contextual="true">
 u<Subscript xmlns="clr-namespace:Ptc.Wpf;assembly=Ptc.Core">min</Subscript>
 </id>
 <id labels="VARIABLE" xml:space="preserve" label-is-contextual="true">
 u<Subscript xmlns="clr-namespace:Ptc.Wpf;assembly=Ptc.Core">max</Subscript>
 </id>
 <id labels="VARIABLE" xml:space="preserve" label-is-contextual="true">
 v<Subscript xmlns="clr-namespace:Ptc.Wpf;assembly=Ptc.Core">min</Subscript>
 </id>
 <id labels="VARIABLE" xml:space="preserve" label-is-contextual="true">
 v<Subscript xmlns="clr-namespace:Ptc.Wpf;assembly=Ptc.Core">max</Subscript>
 </id>
 <id labels="VARIABLE" xml:space="preserve" label-is-contextual="true">
 n<Subscript xmlns="clr-namespace:Ptc.Wpf;assembly=Ptc.Core">u</Subscript>
 </id>
 <id labels="VARIABLE" xml:space="preserve" label-is-contextual="true">
 n<Subscript xmlns="clr-namespace:Ptc.Wpf;assembly=Ptc.Core">v</Subscript>
 </id>
 </sequence>
 </apply>
 </define>
 </math>
</region>

3. u 및 v의 범위를 다시 계산합니다.

4. M 및 g를 도표화합니다.

<region id="ID0E21MIB" top="2438.4000000000005" width="288" left="38.400000000000006" height="291.79999999999995" xmlns="http://schemas.mathsoft.com/worksheet50">
 <plot background-type="white">
 <plot3D>
 <traces>
 <trace3D resultRef="120" num-of-points="41" SurfaceFill="#FFC3D9A5">
 <traceStyle color="#FF068149">surface</traceStyle>
 </trace3D>
 </traces>
 <graph-size width="230.39999999999995" height="230.39999999999998" />
 <axes>
 <xAxis rank="1" start="-60" end="20">
 <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="2000" end="6500">
 <axisLine />
 <axisGrid>
 <gridFrequency>6</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="-7500" end="-1500">
 <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 xml:space="preserve" xmlns="http://schemas.mathsoft.com/math50">M</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>

<region id="ID0EE2MIB" top="2438.4000000000005" width="288" left="326.40000000000003" height="291.79999999999995" xmlns="http://schemas.mathsoft.com/worksheet50">
 <plot background-type="white">
 <plot3D>
 <traces>
 <trace3D resultRef="123" num-of-points="41" SurfaceFill="#FFC3D9A5">
 <traceStyle color="#FF068149">surface</traceStyle>
 </trace3D>
 </traces>
 <graph-size width="230.39999999999995" height="230.39999999999998" />
 <axes>
 <xAxis rank="1" start="-60" end="20">
 <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="2000" end="6500">
 <axisLine />
 <axisGrid>
 <gridFrequency>6</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="-7500" end="-1500">
 <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>
 <apply xmlns="http://schemas.mathsoft.com/math50">
 <id xml:space="preserve">g</id>
 <sequence>
 <id xml:space="preserve">u</id>
 <id xml:space="preserve">v</id>
 </sequence>
 </apply>
 </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>

두 경우 모두 동일한 노드가 도표화되므로 두 도표가 정확하게 같습니다.