# stream3

Compute 3-D streamline data

## Syntax

## Description

computes 3-D streamline data using the specified options, defined as a one- or two-element
vector with the form `XYZ`

= stream3(___,`options`

)`step`

or `[step maxvert]`

, where
`step`

is the step size 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.

## 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;
```

### Specify Step Size for 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);
```

Decrease the streamline resolution by increasing the step size from the default of 0.1 to 3.

step = 3;

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,step);

Visualize the 3-D volume of vector fields with `streamline`

. The larger step size results in a lower resolution streamline.

streamline(verts) view(3)

### Specify Maximum Number of Vertices for 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);
```

Increase the streamline resolution by decreasing the step size from the default of 0.1 to 0.01.

step = 0.01;

Set the maximum number of vertices so that computation ends after the first 1,000 vertices are calculated.

maxvert = 1000;

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,[step maxvert]);

Visualize the 3-D volume of vector fields with `streamline`

. Show the full range of data values by setting the axis limits. The streamlines end after 1,000 vertices are calculated, so the streamlines stop before showing the full range of data.

streamline(verts) xlim([75 135]) ylim([15 65]) zlim([0 15]) view(3)

## Input Arguments

`X`

— *x*-axis coordinates of vector data

3-D array

*x*-axis coordinates of vector data, specified as a 3-D array. It
must be monotonic, but does not need to be uniformly spaced. `X`

must
be the same size as `Y`

, `Z`

, `U`

,
`V`

, and `W`

.

You can use the `meshgrid`

function to create
`X`

.

`Y`

— *y*-axis coordinates of vector data

3-D array

*y*-axis coordinates of vector data, specified as a 3-D array. It
must be monotonic, but does not need to be uniformly spaced. `Y`

must
be the same size as `X`

, `Z`

, `U`

,
`V`

, and `W`

.

You can use the `meshgrid`

function to create
`Y`

.

`Z`

— *z*-axis coordinates of vector data

3-D array

*z*-axis coordinates of vector data, specified as a 3-D array. It
must be monotonic, but does not need to be uniformly spaced. `Z`

must
be the same size as `X`

, `Y`

, `U`

,
`V`

, and `W`

.

You can use the `meshgrid`

function to create
`Z`

.

`U`

— *x*-components of vector data

3-D array

*x*-components of vector data, specified as a 3-D array.
`U`

must be the same size as `X`

,
`Y`

, `Z`

, `V`

, and
`W`

.

`V`

— *y*-components of vector data

3-D array

*y*-components of vector data, specified as a 3-D array.
`V`

must be the same size as `X`

,
`Y`

, `Z`

, `U`

, and
`W`

.

`W`

— *z*-components of vector data

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`

.

`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 in a streamline is `10,000`

.

## 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**

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