streamline

Plot streamlines from 2-D or 3-D vector data

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Syntax

streamline(X,Y,Z,U,V,W,startX,startY,startZ)

streamline(U,V,W,startX,startY,startZ)

streamline(X,Y,U,V,startX,startY)

streamline(U,V,startX,startY)

streamline(verts)

streamline(___,options)

streamline(ax,___)

lineobj = streamline(___)

Description

streamline(X,Y,Z,U,V,W,startX,startY,startZ) returns plotted streamlines for 3-D vector data. The inputs X, Y, and Z are vector data coordinates, U, V, and W are vector data, and startX, startY, and startZ are the starting positions of the streamlines.

streamline(U,V,W,startX,startY,startZ) uses the default coordinate data for U, V, and W. The (x,y,z) location for each element in U, V, and W is based on the column, row, and page index, respectively.

streamline(X,Y,U,V,startX,startY) returns plotted streamlines for 2-D vector data. The inputs X and Y are vector data coordinates, U and V are vector data, and startX and startY are the starting positions of the streamlines.

streamline(U,V,startX,startY) uses the default coordinate data for  U and V. The (x,y) location for each element in U and V is based on the column and row index, respectively.

streamline(verts) plots streamlines from vertices, specified as a cell array of vertex arrays (as returned by stream2, stream3, or streamslice).

streamline(___,options) plots streamlines using the specified options, defined as a one- or two-element vector with the form step or [step maxvert], where step is the step size in data units for interpolating the vector data and maxvert is the maximum number of vertices in a streamline. Use this argument with any of the input argument combinations from the previous syntaxes.

streamline(ax,___) plots streamlines into the specified axes, instead of into the current axes object (gca).

lineobj = streamline(___) returns a vector of one or more Line objects. Use lineobj to modify properties of the streamlines after creating them. For a list of properties, see Line Properties.

Examples

Compute 3-D Streamlines

Load the wind data set which contains measurements of air current over regions of North America.

• 3-D arrays x, y, and z represent the locations of air current measurements.

• 3-D arrays u, v, and w represent the velocity of the air current in 3-D vector fields.

Define the starting position of 16 hypothetical particles. In this case, the particles all start at x = 80 and have starting y positions ranging from 20 to 50 and starting z positions ranging from 0 to 15.

load wind
[startX,startY,startZ] = meshgrid(80,20:10:50,0:5:15);

Compute the 3-D streamline vertex data for a hypothetical particle placed into the air current at the collection of starting positions in startX, startY, and startZ.

verts = stream3(x,y,z,u,v,w,startX,startY,startZ);

Visualize the 3-D volume of vector fields with streamline. Return the line objects in the variable lineobj, so you can change their properties later.

lineobj = streamline(verts);
view(3)

To change aspects of a particular line, set properties on one of the returned line objects. For example, change the color of the tenth line to green and change its thickness to 3.

lineobj(10).Color = "g";
lineobj(10).LineWidth = 3;

Compute 2-D Streamlines

Load the wind data set, which contains measurements of air current over regions of North America.

• 3-D arrays x and y represent the locations of air current measurements.

• 3-D arrays u and v represent the velocity of the air current in 3-D vector fields.

Use the fifth page of the arrays. Define the starting position of four hypothetical particles. In this case, the four starting locations are (80, 20), (80, 30), (80, 40), and (80, 50).

load wind
x5 = x(:,:,5);
y5 = y(:,:,5);
u5 = u(:,:,5);
v5 = v(:,:,5);
[startX,startY] = meshgrid(80,20:10:50);

Compute the 2-D streamline vertex data for a hypothetical particle placed into the air current with stream2.

verts = stream2(x5,y5,u5,v5,startX,startY);

Visualize the 2-D matrix of vector fields by calling streamline. Return the line objects in the variable lineobj, so you can change their properties later.

lineobj = streamline(verts);

To change aspects of a particular line, set properties on one of the returned line objects. For example, change the color of the second line to magenta and change its style to dashed.

lineobj(2).Color = "m";
lineobj(2).LineStyle = "--";

Plot Streamlines from Vertices

Load the wind dataset and compute the vertices of streamlines that start at evenly spaced points on the plane x = 80. Then, plot the streamlines from the vertex data.

load wind
[startX,startY,startZ] = meshgrid(80,20:10:50,0:5:15);
verts = stream3(x,y,z,u,v,w,startX,startY,startZ);
streamline(verts)
axis tight
view(3);

Input Arguments

X — x-coordinates of vector data

2-D array | 3-D array

x-axis coordinates of vector data, specified as a 2-D or 3-D array that can be combined with Y (and optionally Z) to form a grid of coordinates. You can use the meshgrid function to create the arrays.

X must be the same size as Y, Z, U, V, and W.

Y — y-coordinates of vector data

2-D array | 3-D array

y-axis coordinates of vector data, specified as a 2-D or 3-D array that can be combined with X (and optionally Z) to form a grid of coordinates. You can use the meshgrid function to create the arrays.

Y must be the same size as X, Z, U, V, and W.

Z — z-coordinates of vector data

3-D array

z-axis coordinates of vector data, specified as a 3-D array that can be combined with X and Y to form a grid of coordinates. You can use the meshgrid function to create the arrays.

Z must be the same size as X, Y, U, V, and W.

U — x-components

2-D array | 3-D array

x-components of vector data, specified as a 2-D or 3-D array. U must be the same size as X, Y, Z, V, and W.

V — y-components

2-D array | 3-D array

y-components of vector data, specified as a 2-D or 3-D array. V must be the same size as X, Y, Z, U, and W.

W — z-components

3-D array

z-components of vector data, specified as a 3-D array. W must be the same size as X, Y, Z, U, and V.

startX — x-axis streamline starting positions

scalar | vector | matrix

x-axis streamline starting positions, specified as a vector or matrix. startX must be a scalar or be the same size as startY and startZ.

startY — y-axis streamline starting positions

scalar | vector | matrix

y-axis streamline starting positions, specified as a vector or matrix. startY must be a scalar or be the same size as startX and startZ.

startZ — z-axis streamline starting positions

scalar | vector | matrix

z-axis streamline starting positions, specified as a vector or matrix. startZ must be a scalar or be the same size as startX and startY.

verts — Streamline vertices

cell array

Streamline vertices, specified as a cell array (as returned by stream2, stream3, or streamslice). Each element of the cell array is a matrix of vertices for one line.

options — Streamline options

[0.1, 10000] (default) | one-element vector | two-element vector

Streamline options, specified as a one- or two-element vector with one of the following forms:

• step

• [step,maxvert]

step is the step size used to adjust the streamline resolution and determine the vertex locations for which streamline velocity is interpolated. maxvert is the maximum number of vertices calculated for a streamline before computation is complete.

The default step-size is 0.1, and the default maximum number of vertices is 10,000.

ax — Target axes

Axes object

Target axes, specified as an Axes object. If you do not specify the axes, then the streamline function uses the current axes.

Extended Capabilities

GPU Arrays

Accelerate code by running on a graphics processing unit (GPU) using Parallel Computing Toolbox™.

Usage notes and limitations:

• This function accepts GPU arrays, but does not run on a GPU.

For more information, see Run MATLAB Functions on a GPU (Parallel Computing Toolbox).

Distributed Arrays

Partition large arrays across the combined memory of your cluster using Parallel Computing Toolbox™.

Usage notes and limitations:

• This function operates on distributed arrays, but executes in the client MATLAB^®.

For more information, see Run MATLAB Functions with Distributed Arrays (Parallel Computing Toolbox).

Version History

Introduced before R2006a