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# interpstreamspeed

Interpolate stream-line vertices from flow speed

## Syntax

interpstreamspeed(X,Y,Z,U,V,W,vertices)
interpstreamspeed(U,V,W,vertices)
interpstreamspeed(X,Y,Z,speed,vertices)
interpstreamspeed(speed,vertices)
interpstreamspeed(X,Y,U,V,vertices)
interpstreamspeed(U,V,vertices)
interpstreamspeed(X,Y,speed,vertices)
interpstreamspeed(speed,vertices)
interpstreamspeed(...,sf)
vertsout = interpstreamspeed(...)

## Description

interpstreamspeed(X,Y,Z,U,V,W,vertices) interpolates streamline vertices based on the magnitude of the vector data U, V, W.

The arrays X, Y, and Z, which define the coordinates for U, V, and W, must be monotonic, but do not need to be uniformly spaced. X, Y, and Z must have the same number of elements, as if produced by meshgrid.

interpstreamspeed(U,V,W,vertices) assumes X, Y, and Z are determined by the expression

`[X Y Z] = meshgrid(1:n,1:m,1:p) `

where [m n p] = size(U).

interpstreamspeed(X,Y,Z,speed,vertices) uses the 3-D array speed for the speed of the vector field.

interpstreamspeed(speed,vertices) assumes X, Y, and Z are determined by the expression

`[X Y Z] = meshgrid(1:n,1:m,1:p) `

where [m n p]=size(speed).

interpstreamspeed(X,Y,U,V,vertices) interpolates streamline vertices based on the magnitude of the vector data U, V.

The arrays X and Y, which define the coordinates for U and V, must be monotonic, but do not need to be uniformly spaced. X and Y must have the same number of elements, as if produced by meshgrid.

interpstreamspeed(U,V,vertices) assumes X and Y are determined by the expression

`[X Y] = meshgrid(1:n,1:m) `

where [M N]=size(U).

interpstreamspeed(X,Y,speed,vertices) uses the 2-D array speed for the speed of the vector field.

interpstreamspeed(speed,vertices) assumes X and Y are determined by the expression

`[X Y] = meshgrid(1:n,1:m)`

where [M,N]= size(speed).

interpstreamspeed(...,sf) uses sf to scale the magnitude of the vector data and therefore controls the number of interpolated vertices. For example, if sf is 3, then interpstreamspeed creates only one-third of the vertices.

vertsout = interpstreamspeed(...) returns a cell array of vertex arrays.

## Examples

This example draws streamlines using the vertices returned by interpstreamspeed. Dot markers indicate the location of each vertex. This example enables you to visualize the relative speeds of the flow data. Streamlines having widely spaced vertices indicate faster flow; those with closely spaced vertices indicate slower flow.

```load wind
[sx sy sz] = meshgrid(80,20:1:55,5);
verts = stream3(x,y,z,u,v,w,sx,sy,sz);
iverts = interpstreamspeed(x,y,z,u,v,w,verts,.2);
sl = streamline(iverts);
set(sl,'Marker','.')
axis tight; view(2); daspect([1 1 1])```

This example plots streamlines whose vertex spacing indicates the value of the gradient along the streamline.

```figure
z = membrane(6,30);
pcolor(z)
hold on
[verts averts] = streamslice(u,v);
iverts = interpstreamspeed(u,v,verts,15);
sl = streamline(iverts);
set(sl,'Marker','.')