The TNBFrame(C, t, out) calling sequence computes the tangent-normal-binormal frame of the curve C, that is, the unit tangent, normal, and binormal Vectors.  The computed objects are returned in an expression sequence.

If t is not specified, the command tries to determine a suitable variable name by using the components of C.  To do this, it checks all of the indeterminates of type name in the components of C and removes the ones that are determined to be constants.

If the resulting set has a single entry, the single entry is the variable name.  If it has more than one entry, an error is raised.

The options arguments primarily control plot options.

output = value, plot, or animation

This option controls the return value of the command. The output is always returned in the order: tangent, normal, binormal.

* output = value returns the value of the binormal. Plot options are ignored if output = value.  This is the default value.

* output = plot returns a plot of the space curve and the TNB frames. The number of TNB frames is specified by the frames option.

* output = animation returns an animation of the space curve and the TNB frames. The number of binormal frames is specified by the frames option.

binormal = truefalse

Controls whether the binormal vector is included in the output or plot. The default value is true.

binormaloptions = list

A list of plot options for plotting the binormal portion of the TNB frame. For more information on plotting options, see plot/options. The default value is [].

curveoptions = list

A list of plot options for plotting the space curve. For more information on plotting options, see plot/options. The default value is [].

frames = posint

Specifies how many TNB frames are to be plotted or animated. The default value is 5.

normal = truefalse

Controls whether the normal vector is included in the output or plot. The default value is true.

normaloptions = list

A list of plot options for plotting the normal portion of the TNB frame. For more information on plotting options, see plot/options. The default value is [].

range = realcons..realcons

The range of the independent variable. The default value is 0..5.

tangent = truefalse

Controls whether the tangent vector is included in the output or plot. The default value is true.

tangentoptions = list

A list of plot options for plotting the tangent portion of the TNB frame. For more information on plotting options, see plot/options. The default value is [].

view = [realcons..realcons, realcons..realcons, realcons..realcons]

Specify the plot view. For more information, see plot3d/options.

caption = anything

A caption for the plot.

The default caption is constructed from the parameters and the command options. caption = "" disables the default caption. For more information about specifying a caption , see plot/typesetting.