**Function: **
curvarrows - plot a 2D or 3D curve (parametric or cartesian) with arrows from a vector field at points on the curve.

**Calling sequence:**

**curvarrows(fld,curv,t=a..b);**

**Parameters:**

**fld**
- the vector field, either a
-component list or vector expression in the parameter
**t**
(specifying the vectors in terms of the parameter) or a function of
variables whose values are
-component lists or vectors (specifying the vector field in terms of Cartesian coordinates), where
is 2 or 3.

**curv **
- the curve, either a
-component list or vector expression in the parameter
**t**
(for a parametric representation of the curve) or a scalar expression in
**t**
(representing the
coordinate while
**t**
is the
coordinate).

**t**
- name for the parameter.

**a**
,
**b**
- real constants, endpoints for the parameter interval.

Optional arguments:

**arrownum= **
for
arrows along the curve, equally spaced in terms of the parameter (default is
**arrownum=10**
)

** 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 2D or 3D curve plotting options

**Description:**

This function creates a 2D or 3D plot data object which consists of a curve specified by
**curv**
for
**t = a .. b**
(including all options of the
**curvarrows**
command except
** **
**arrownum**
,
**scalefactor**
,
**arrowthickness**
and
**arrowcolour**
), plus arrows representing the vector field
**fld**
drawn at points on the curve.

The curve is drawn using
**plot**
(in either the parametric or Cartesian form) for the 2D case, or
**spacecurve**
for the 3D case.

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,curvarrows);**

**Examples:**

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

Curve is a circle represented parametrically, vectors are tangent.

`> `
**curv1:= [cos(t),sin(t)];
F1:= diff(curv1,t);
curvarrows(F1, curv1, t = 0 .. 2*Pi, arrowcolour=blue,
scalefactor=1/2, arrowthickness=1, scaling=constrained);**

curv1 := [cos(t), sin(t)]

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

Curve is a semicircle represented in Cartesian coordinates, vectors are normal.

`> `
**curv2:= sqrt(1-x^2);
F2:= [x,curv2];
curvarrows(F2,curv2, x = -1 .. 1,
scalefactor=1/3, scaling=constrained);**

2

curv2 := sqrt(1 - x )

2

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

Parametric 3D curve, vector field is a function of , and coordinates. Note that 6 arrows appear because the arrows at the beginning and end of the parameter interval coincide.

`> `
**curv3:= [cos(t), sin(t), 1];
F3:= (x,y,z) -> [x, y, z];
curvarrows(F3,curv3, t = 0 .. 2*Pi,
arrowcolour=blue, scalefactor = 1/4, arrownum = 7, scaling=constrained);**

curv3 := [cos(t), sin(t), 1]

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

**See also: **
arrow2d,
** **
arrow3d
,
surfarrows,
__plot__
,
__plot[parametric]__
,
__spacecurve__

**Maple Advisor Database**
R. Israel 1998