$plot::VectorField3d([v_1, v_2, v_3], x = `x_{min}`..`x_{max}`, y = `y_{min}`..`y_{max}`, z = `z_{min}`..`z_{max}`)$ represents a plot of the vector field defined by

with .

→ Examples

Calls:

plot::VectorField3d([v1, v2, v3], x = $`x_{min}`$ .. $`x_{max}`$ , y = $`y_{min}`$ .. $`y_{max}`$ , z = $`z_{min}`$ .. $`z_{max}`$ , <a = amin .. amax>, Options)

plot::VectorField3d(v1, v2, v3, x = $`x_{min}`$ .. $`x_{max}`$ , y = $`y_{min}`$ .. $`y_{max}`$ , z = $`z_{min}`$ .. $`z_{max}`$ , <a = amin .. amax>, Options)

Parameters:

v1, v2, v3:	the -, -, and -component of the vector field: arithmetical expressions in x, y, z and, possibly, the animation parameter a. v1, v2, v3 are equivalent to the attributes XFunction, YFunction, ZFunction.
x, y, z:	identifiers. x, y, z are equivalent to the attributes XName, YName, ZName.
$`x_{min}`$ .. $`x_{max}`$ , $`y_{min}`$ .. $`y_{max}`$ , $`z_{min}`$ .. $`z_{max}`$ :	real numerical values. $`x_{min}`$ .. $`x_{max}`$ , $`y_{min}`$ .. $`y_{max}`$ , $`z_{min}`$ .. $`z_{max}`$ are equivalent to the attributes XRange, YRange, ZRange, XMin, XMax, YMin, YMax, ZMin, ZMax.

Details:

A vector field is defined by a function . plot::VectorField3d displays a vector field by placing arrows at regular intervals with the arrow at pointing in the direction .
The length of the arrows depend on and the setting of the attribute ArrowLength: By default, arrow lengths are proportional to the magnitude of , but can be set to be of fixed length or to scale logarithmically.
The density of arrows placed can be controlled with the attributes XMesh, YMesh, ZMesh, and Mesh. See the examples below.

Example 1

We demonstrate a plot of the vector field :

field := plot::VectorField3d([1, sin(x) + cos(y), sin(z)],
x = 0..6, y = 0..2.5, z = 0..5,
Mesh = [7, 7, 7]):
plot(field):

MuPAD graphics

delete field:

Example 2

Like most other objects, plot::VectorField3d can be animated by supplying an extra parameter:

mycolor := (x, y, z, vx, vy, vz, a) -> [a, a*z, 1 - a]:
field := plot::VectorField3d([ a*y + (1-a)*x ,
                              -a*x + (1-a)*y,
                               a*sin(PI*z)],
                             x = -1..1, y = -1..1, z = 0..1,
                             LineColorFunction = mycolor,
                             Mesh = [7, 7, 7], a = 0..1):
text := plot::Text3d(a -> "a = ".stringlib::formatf(a, 2, 5),
                     [1, 0.7, 1.2], a = 0..1):
plot(field, text, Axes = Frame)

MuPAD graphics

delete field, text:

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R2012a Documentation → Symbolic Math Toolbox
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