Volumetric slice plot

`slice(V,sx,sy,sz)`

slice(X,Y,Z,V,sx,sy,sz)

slice(V,XI,YI,ZI)

slice(X,Y,Z,V,XI,YI,ZI)

slice(...,'* method*')

slice(axes_handle,...)

h = slice(...)

`slice`

displays orthogonal slice planes through
volumetric data.

`slice(V,sx,sy,sz)`

draws
slices along the *x*, *y*, *z* directions
in the volume `V`

at the points in the vectors `sx`

, `sy`

,
and `sz`

. `V`

is an *m*-by-*n*-by-*p* volume
array containing data values at the default location ```
X =
1:n
```

, `Y = 1:m`

, `Z =`

`1:p`

.
Each element in the vectors `sx`

, `sy`

,
and `sz`

defines a slice plane in the *x*-, *y*-,
or *z*-axis direction.

`slice(X,Y,Z,V,sx,sy,sz)`

draws slices of the volume `V`

. `X`

, `Y`

,
and `Z`

are three-dimensional arrays specifying the
coordinates for `V`

. `X`

, `Y`

,
and `Z`

must be monotonic and orthogonally spaced
(as if produced by the function `meshgrid`

). The
color at each point is determined by 3-D interpolation into the volume `V`

.

`slice(V,XI,YI,ZI)`

draws
data in the volume `V`

for the slices defined by `XI`

, `YI`

,
and `ZI`

. `XI`

, `YI`

,
and `ZI`

are matrices that define a surface, and
the volume is evaluated at the surface points. `XI`

, `YI`

,
and `ZI`

must all be the same size.

`slice(X,Y,Z,V,XI,YI,ZI)`

draws slices through the volume `V`

along the surface
defined by the arrays `XI`

, `YI`

, `ZI`

.

`slice(...,'`

specifies the interpolation method. * method*')

`'`

`method`

`'`

is `'linear'`

, `'cubic'`

,
or `'nearest'`

.`linear`

specifies trilinear interpolation (the default).`cubic`

specifies tricubic interpolation.`nearest`

specifies nearest-neighbor interpolation.

`slice(axes_handle,...)`

plots into the axes with the handle `axes_handle`

instead
of into the current axes object (`gca`

).
The axes `clim`

property is set to span the finite
values of `V`

.

`h = slice(...)`

returns
a vector of handles to surface graphics objects.

Visualize the function

$$v=x{e}^{\left(-{x}^{2}-{y}^{2}-{z}^{2}\right)}$$

over the range –2 ≤ x ≤ 2, –2 ≤y ≤2, – 2 ≤ z ≤2:

[x,y,z] = meshgrid(-2:.2:2,-2:.25:2,-2:.16:2); v = x.*exp(-x.^2-y.^2-z.^2); xslice = [-1.2,.8,2]; yslice = 2; zslice = [-2,0]; slice(x,y,z,v,xslice,yslice,zslice) colormap hsv

You can also create slices that are oriented in arbitrary planes. To do this,

Create a slice surface in the domain of the volume (

`surf`

,`linspace`

).Orient this surface with respect to the axes (

`rotate`

).Use this data to draw the slice plane within the volume.

For example, these statements slice the volume in the first
example with a rotated plane. Placing these commands
within a `for`

loop "passes" the plane
through the volume along the *z*-axis.

[x,y,z] = meshgrid(-2:.2:2,-2:.25:2,-2:.16:2); v = x.*exp(-x.^2-y.^2-z.^2); figure colormap hsv for k = -2:.05:2 hsp = surf(linspace(-2,2,20),linspace(-2,2,20),... zeros(20) + k); rotate(hsp,[1,-1,1],30) xd = hsp.XData; yd = hsp.YData; zd = hsp.ZData; delete(hsp) slice(x,y,z,v,[-2,2],2,-2) % Draw some volume boundaries hold on slice(x,y,z,v,xd,yd,zd) hold off view(-5,10) axis([-2.5 2.5 -2 2 -2 4]) drawnow end

The following picture illustrates three positions of the same slice surface as it passes through the volume.

You can slice the volume with any surface. This example probes the volume created in the previous example by passing a spherical slice surface through the volume.

[xsp,ysp,zsp] = sphere; slice(x,y,z,v,[-2,2],2,-2) colormap hsv for i = -3:.2:3 hsp = surface(xsp+i,ysp,zsp); rotate(hsp,[1 0 0],90) xd = hsp.XData; yd = hsp.YData; zd = hsp.ZData; delete(hsp) hold on hslicer = slice(x,y,z,v,xd,yd,zd); axis tight xlim([-3,3]) view(-10,35) drawnow delete(hslicer) hold off end

The following picture illustrates three positions of the spherical slice surface as it passes through the volume.

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