**Function: **
surfarrows - plot a 3D surface (parametric or cartesian) with arrows from a vector field at points on the surface.

**Calling sequence:**

**surfarrows(fld,surf,s=a1..b1,t=a2..b2);**

**Parameters:**

**fld**
- the vector field, either a 3-component list or vector expression in the parameters
**s**
and
**t**
(specifying the vectors in terms of those parameters) or a function of three variables whose values are 3-component lists or vectors (specifying the vector field in terms of the spatial coordinates
,
and
).

**surf **
- the surface, either a 3-component list or vector expression in the parameters
**s**
and
**t**
(for a parametric representation of the surface) or a scalar expression in
**s**
and
**t**
(representing the
coordinate while
**s**
and
**t**
are the
and
coordinates respectively).

**s**
,
**t**
- names for the parameters.

**a1**
,
**b1**
,
**a2**
,
**b2**
- endpoints for the parameter intervals.
**a1**
and
**b1**
must be constants, while
**a2**
and
**b2**
may depend on the first parameter
**s**
.

Optional arguments:

**arrowgrid= [**
,
**]**
for arrows in an
by
grid, equally spaced in terms of the parameters of the surface (default is
**arrowgrid=[8,8]**
).

** scalefactor=**
to multiply arrow lengths by real constant
.

** arrowthickness=**
for thickness of the arrow shaft (
should be 0, 1, 2 or 3, default is the same as the
**thickness**
option if specified, or 3 if not).

**arrowcolour=**
to specify arrow colour (default is the same as the
**colour**
option if specified, or red if not). The alternate spelling
**arrowcolor**
is allowed.

other 3D surface plotting options.

**Description:**

This function creates a 3D plot data object which consists of a surface, plotted as with the command

**plot3d(surf, s=a1..b1, t=a2..b2)**
(including all options of the
**surfarrows**
command except
** **
**arrowgrid**
,
**scalefactor**
,
**arrowthickness**
and
**arrowcolour**
), plus arrows representing the vector field
**fld**
drawn at points on the surface.

Unless the option
**scaling=constrained**
("Projection, Constrained" on the plot menu or "1-1" on the context bar) is used, the shapes of the arrowheads may be distorted.

This function is part of the package
**surfarro**
in the Maple Advisor Database library, and must be loaded before use by the command
**with(surfarro);**
or
**with(surfarro,surfarrows);**
.

**Examples:**

`> `
**with(surfarro,surfarrows):**

Surface is a sphere represented parametrically, vectors are tangent to meridians.

`> `
**surf1:= [sin(t)*cos(s),sin(t)*sin(s),cos(t)];
F1:= diff(surf1,t);
surfarrows(F1, surf1, s = 0 .. 2*Pi, t = 0 .. Pi,
scalefactor=0.4, style=patch, scaling=constrained, orientation=[0,70]);**

surf1 := [sin(t) cos(s), sin(t) sin(s), cos(t)]

F1 := [cos(t) cos(s), cos(t) sin(s), -sin(t)]

Surface is a hemisphere represented in Cartesian coordinates, vectors are normal to surface. Note that the interval depends on .

`> `
**surf2:= sqrt(1-x^2-y^2);
F2:= [x,y,surf2];
surfarrows(F2,surf2, x = -1 .. 1, y = -0.999*sqrt(1-x^2) .. 0.999*sqrt(1-x^2), orientation = [90, 45],
scalefactor=1/3, style=patchcontour, scaling=constrained, arrowthickness = 2);**

2 2

surf2 := sqrt(1 - x - y )

2 2

F2 := [x, y, sqrt(1 - x - y )]

Parametric hemisphere, vector field is a function of , and coordinates (a dipole field in this case):

`> `
**F3:= (x,y,z) -> [3*x*z, 3*y*z, 2*z^2-x^2-y^2];
surfarrows(F3,surf1, s = 0 .. 2*Pi, t = 0 .. Pi/2,
arrowcolour=blue, scalefactor = 1/4, arrowgrid=[10,5], arrowthickness=1, scaling=constrained, style=patchnogrid, orientation=[0,60]);**

2 2 2

F3 := (x, y, z) -> [3 x z, 3 y z, 2 z - x - y ]

**See also:**
arrow3d
,
curvarrows
,
__plot3d__

**Maple Advisor Database**
R. Israel, 1998