利用Matlab绘制梯度图散度图旋度图
Posted ChenYuanshen
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1. 分别用mesh()和surf()绘制出函数xx.*exp(-xx.^2 - yy.^2)的例题曲面图。
例1(mesh):
x=linspace(-2, 2, 25);
y=linspace(-2, 2, 25);
[xx, yy]=meshgrid(x, y);
zz=xx.*exp(-xx.^2 - yy.^2);
mesh(xx, yy, zz);
colorbar;

例2(surf):
<pre name="code" class="plain">x=linspace(-2, 2, 25);
y=linspace(-2, 2, 25);
[xx, yy]=meshgrid(x, y);
zz=xx.*exp(-xx.^2 - yy.^2);
h=contour(zz, 12);
clabel(h);
;

2. 分别用mesh()和surf()绘制出函数sqrt(xx.^2 + yy.^2)的立体曲面图。
例3:
x=linspace(-2, 2, 25);
y=linspace(-2, 2, 25);
[xx, yy]=meshgrid(x, y);
zz=sqrt(xx.^2+ yy.^2);
mesh(xx, yy, zz);
colorbar;
例4:
x=linspace(-2, 2, 25);
y=linspace(-2, 2, 25);
[xx, yy]=meshgrid(x, y);
zz=sqrt(xx.^2+ yy.^2);
surf(xx, yy, zz);
colorbar;

3. 分别画出以上连个函数的等高线,并标注等高线值。
例5(conour):
x=linspace(-2, 2, 25);
y=linspace(-2, 2, 25);
[xx, yy]=meshgrid(x, y);
zz=xx.*exp(-xx.^2 - yy.^2);
h=contour(zz, 12);
clabel(h);

例6(conour):
x=linspace(-2, 2, 25);
y=linspace(-2, 2, 25);
[xx, yy]=meshgrid(x, y);
zz=sqrt(xx.^2 + yy.^2);
h=contour(zz, 12);
clabel(h);

4. 求以上两个函数的梯度,并在高等线图中以矢量箭头的形式显示各点的梯度。
例7(gradient):
x=linspace(-2, 2, 25);
y=linspace(-2, 2, 25);
[xx, yy]=meshgrid(x, y);
zz=xx.*exp(-xx.^2 - yy.^2);
h=contour(zz, 12);
clabel(h);
[dx, dy]=gradient(zz,.2,2);
hold on;
quiver(dx, dy);

例7(gradient):
x=linspace(-2, 2, 25);
y=linspace(-2, 2, 25);
[xx, yy]=meshgrid(x, y);
zz=sqrt(xx.^2 + yy.^2);
h=contour(zz, 12);
clabel(h);
[dx, dy]=gradient(zz,.2,2);
hold on;
quiver(dx, dy);

5. 求矢量场的散度。
例9(divergence):
[x, y, z] = meshgrid(-3:1:3);
u=3.*x.^2 + 2.*y.^2 + z.^2;
v=x.^2 + 3.*y.^2 + 2.*z.^2;
w=2.*x.^2 + 3.*y.^2 + z.^2;
div=divergence(x, y,z, u, v, w);
figure
for i=1:7
%figure
mesh(div(:,:,i));
hold on;
end

6. 求矢量场的旋度。
例10(curl):
[x, y, z] = meshgrid(-3:1:3);
u=3.*x.^2 + 2.*y.^2 + z.^2;
v=x.^2 + 3.*y.^2 + 2.*z.^2;
w=2.*x.^2 + 3.*y.^2 + z.^2;
[curlx, curly, curlz]=curl(x, y,z, u, v, w);
figure
for i=1:7
mesh(curlx(:,:,i));
hold on;
end
例11:
[x, y, z] = meshgrid(-3:1:3);
u=3.*x.^2 + 2.*y.^2 + z.^2;
v=x.^2 + 3.*y.^2 + 2.*z.^2;
w=2.*x.^2 + 3.*y.^2 + z.^2;
[curlx, curly, curlz]=curl(x, y,z, u, v, w);
figure
for i=1:7
mesh(curlx(:,:,i));
hold on;
end
figure
for i=1:7
mesh(curly(:,:,i));
hold on;
end

例12:
[x, y, z] = meshgrid(-3:1:3);
u=3.*x.^2 + 2.*y.^2 + z.^2;
v=x.^2 + 3.*y.^2 + 2.*z.^2;
w=2.*x.^2 + 3.*y.^2 + z.^2;
[curlx, curly, curlz]=curl(x, y,z, u, v, w);
figure
for i=1:7
mesh(curlx(:,:,i));
hold on;
end
figure
for i=1:7
mesh(curly(:,:,i));
hold on;
end
figure
for i=1:7
mesh(curlz(:,:,i));
hold on;
end

7. 总结:
函数 | 描述 |
linspace(a, b, n) | 在a,b之间取n个点 |
meshgrid() | 生成网格采样点 |
mesh() | 画出立体网状图 |
contour() | 画等高线 |
clabel() | 标注等高线值 |
gradient() | 求梯度 |
hold on | 保持图像 |
quiver() | 画矢量图箭头 |
divergence() | 求散度 |
figure | 显示图形 |
for i=1:7...end | 自动分成7个7*7矩阵的值 |
%figure | 7个图层单独显示 |
curl() | 求旋度 |
注:
1) type + 函数名 查看实现源码(type meshgrid )
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