Matlab流體后處理中的奇淫巧術總結

主要參考\demos\volvec.m示例

1.等值面繪制

%% Isosurface of MRI Data
cla
load mri
D = squeeze(D);
[x, y, z, D] = subvolume(D, [nan nan nan nan nan 4]);
p = patch(isosurface(x,y,z,D, 5), 'FaceColor', 'red', 'EdgeColor', 'none');
patch(isocaps(x,y,z,D, 5), 'FaceColor', 'interp', 'EdgeColor', 'none');
isonormals(x,y,z,D,p);
view(3)
daspect([1 1 .4])
colormap(gray(100))
camva(9)
box on
camlight(40, 40)
camlight(-20,-10)
lighting gouraud

• isosurface(x,y,z,D, 5)

參數意義為，從由X,Y,Z構造的體積V數據中提取由isovalue指定的等值數據，返回結果為一個結構體，包含了等值面的頂點和面（頂點的次序），這些參數可以直接傳給patch命令畫出圖形來。

2.圓錐體流線圖繪制

cla
load wind
[cx, cy, cz] = meshgrid(linspace(71,134,10),linspace(18,59,10),3:4:15);
daspect([1 1 1])    % gca, 'DataAspectRatio' 屬性設置 
h = coneplot(x,y,z,u,v,w,cx,cy,cz,y,3);
set(h,'EdgeColor', 'none')
colormap(hsv)
box on
axis tight              % 使坐標系的最大值和最小值和你的數據范圍一致
camproj perspective
camva(35)               % Camera view angle.
campos([175 10 85])     % Camera position.
camtarget([105 40 0])   % Camera target. （三維圖形質心）
camlight left           % Create or set position of a light.
lighting gouraud        % 查看曲面單元時使用lighting gouraud 或 lighting phong

• h = coneplot(x,y,z,u,v,w,cx,cy,cz,y,3);

用圓錐體繪制三維流速圖，x,y,z,u,v,w是流速場分布，cx,cy,cz是圓錐體位置

3.繪制流線圖

cla
[sx, sy, sz] = meshgrid(80, 20:10:50, 0:5:15);
h = streamline(x,y,z,u,v,w,sx,sy,sz);
set(h, 'Color', 'cyan')
daspect([1 1 1])
box on
camproj perspective
camva(32)
axis tight
campos([175 10 85])
camtarget([105 40 0])
camlight left
lighting gouraud

• h = streamline(x,y,z,u,v,w,sx,sy,sz);

x,y,z,u,v,w是流速場分布，sx,sy,sz定義了流線起點。(有關如何定義流線起始點問題，請參考附錄B)

4.流管圖

cla
[sx, sy, sz] = meshgrid(80, [20 30 40], [5 10]);
daspect([1,1,1])
h = streamtube(x,y,z,u,v,w,sx,sy,sz);
set(h,'facecolor','cyan','edgecolor','none')
box on
camproj perspective
axis([70 138 17 60 2.5 16])
axis tight
camva(28)
campos([175 10 95])
camtarget([105 40 0])
camlight left
lighting gouraud  

• h = streamtube(x,y,z,u,v,w,sx,sy,sz);

  streamtube(X,Y,Z,U,V,W,STARTX,STARTY,STARTZ) draws stream
  tubes from vector data U,V,W. The arrays X,Y,Z define the
  coordinates for U,V,W and must be monotonic and 3D plaid (as if
  produced by MESHGRID). STARTX, STARTY, and STARTZ define the
  starting positions of the streamlines at the center of the
  tubes. The width of the tubes is proportional to the normalized divergence of the vector field. A vector of surface
  handles (one per start point) is returned in H.

  矢量管的粗細和該點處散度有關

5.流線帶圖

cla
[sx, sy, sz] = meshgrid(80, [20 30 40], [5 10]);
daspect([1,1,1])
h = streamribbon(x,y,z,u,v,w,sx,sy,sz);
set(h,'facecolor','cyan','edgecolor','none')
box on
camproj perspective
axis([70 138 17 60 2.5 16])
axis tight
camva(28)
campos([175 10 85])
camtarget([105 40 0])
camlight left
lighting gouraud

• h = streamribbon(x,y,z,u,v,w,sx,sy,sz);

  streamribbon(X,Y,Z,U,V,W,STARTX,STARTY,STARTZ) draws stream
  ribbons from vector data U,V,W. The arrays X,Y,Z define the
  coordinates for U,V,W and must be monotonic and 3D plaid (as if
  produced by MESHGRID). STARTX, STARTY, and STARTZ define the
  starting positions of the streamlines at the center of the
  ribbons. The twist of the ribbons is proportional to the
  curl of the vector field. The width of the ribbons is
  calculated automatically.

附錄A.Accessing Subregions of Volume Data

The subvolume function provides a simple way to access subregions of a volume data set. subvolume enables you to select regions of interest based on limits rather than using the colon operator to index into the 3-D arrays that define volumes. Consider the following two approaches to creating the data for a subvolume — indexing with the colon operator and using subvolume.

Indexing with the Colon Operator

When you index the arrays, you work with values that specify the elements in each dimension of the array.

load wind
xsub = x(1:10,20:30,1:7);
ysub = y(1:10,20:30,1:7);
zsub = z(1:10,20:30,1:7);
usub = u(1:10,20:30,1:7);
vsub = v(1:10,20:30,1:7);
wsub = w(1:10,20:30,1:7);

Using the subvolume Function

subvolume enables you to use coordinate values that you can read from the axes. For example:

lims = [100.64 116.67 17.25 28.75 -0.02 6.86];
[xsub,ysub,zsub,usub,vsub,wsub] = subvolume(x,y,z,u,v,w,lims);

You can then use the subvolume data as inputs to any function requiring vector volume data.

附錄B.Specifying Starting Points for Stream Plots

Stream plots (stream lines, ribbons, tubes, and cones or arrows) illustrate the flow of a 3-D vector field. The MATLAB® stream-plotting functions (streamline, streamribbon, streamtube, coneplot, stream2, stream3) all require you to specify the point at which you want to begin each stream trace.

Determining the Starting Points

Generally, knowledge of your data's characteristics helps you select the starting points. Information such as the primary direction of flow and the range of the data coordinates helps you decide where to evaluate the data.

The streamslice function is useful for exploring your data. For example, these statements draw a slice through the vector field at a z value midway in the range.

load wind
zmax = max(z(:)); zmin = min(z(:));
streamslice(x,y,z,u,v,w,[],[],(zmax-zmin)/2)

This stream slice plot indicates that the flow is in the positive x-direction and also enables you to select starting points in both x and y. You could create similar plots that slice the volume in the x-z plane or the y-z plane to gain further insight into your data's range and orientation.

Specifying Arrays of Starting-Point Coordinates

To specify the starting point for one stream line, you need the x-, y-, and z-coordinates of the point. The meshgrid command provides a convenient way to create arrays of starting points. For example, you could select the following starting points from the wind data displayed in the previous stream slice.

[sx,sy,sz] = meshgrid(80,20:10:50,0:5:15);

This statement defines the starting points as all lying on x = 80, y ranging from 20 to 50, and z ranging from 0 to 15. You can use plot3 to display the locations.

plot3(sx(:),sy(:),sz(:),'*r');
axis(volumebounds(x,y,z,u,v,w))
grid on 
set(gca,'BoxStyle','full','Box','on')
daspect([2 2 1])

You do not need to use 3-D arrays, such as those returned by meshgrid, but the size of each array must be the same, and meshgrid provides a convenient way to generate arrays when you do not have an equal number of unique values in each coordinate. You can also define starting-point arrays as column vectors. For example, meshgrid returns 3-D arrays:

[sx,sy,sz] = meshgrid(80,20:10:50,0:5:15);
whos
  Name      Size             Bytes  Class     Attributes

  sx        4x1x4              128  double              
  sy        4x1x4              128  double              
  sz        4x1x4              128  double      

In addition, you could use 16-by-1 column vectors with the corresponding elements of the three arrays composing the coordinates of each starting point. (This is the equivalent of indexing the values returned by meshgrid as sx(😃, sy(😃, and sz(😃.)

For example, adding the stream lines to the starting points produces:

streamline(x,y,z,u,v,w,sx(:),sy(:),sz(:))