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 []. Note: Vectors are plotted using plots[arrow].

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 []. Note: Vectors are plotted using plots[arrow].

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 []. Note: Vectors are plotted using plots[arrow].

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.

$\mathrm{with}\left(\mathrm{Student}\left[\mathrm{VectorCalculus}\right]\right)\:$

$\mathrm{TNBFrame}\left(⟨\cos \left(t\right)\,\sin \left(t\right)\,t⟩\,t\right)$

$\left[\begin{array}{c}-\frac{\sqrt{2}\sin \left(t\right)}{2}\\ \frac{\sqrt{2}\cos \left(t\right)}{2}\\ \frac{\sqrt{2}}{2}\end{array}\right],\left[\begin{array}{c}-\cos \left(t\right)\\ -\sin \left(t\right)\\ 0\end{array}\right],\left[\begin{array}{c}\frac{\sqrt{2}\sin \left(t\right)}{2}\\ -\frac{\sqrt{2}\cos \left(t\right)}{2}\\ \frac{\sqrt{2}}{2}\end{array}\right]$

$\mathrm{TNBFrame}\left(\mathrm{PositionVector}\left(\left[\cos \left(t\right)\,\sin \left(t\right)\right]\right)\right)$

$\left[\begin{array}{c}-\sin \left(t\right)\\ \cos \left(t\right)\end{array}\right],\left[\begin{array}{c}-\cos \left(t\right)\\ -\sin \left(t\right)\end{array}\right]$

$\mathrm{TNBFrame}\left(⟨\cos \left(t\right)\,\sin \left(t\right)\,\frac{t}{3}⟩\,\mathrm{range}=0..2\mathrm{\pi }\,\mathrm{output}=\mathrm{animation}\,\mathrm{scaling}=\mathrm{constrained}\,\mathrm{axes}=\mathrm{frame}\,\mathrm{frames}=15\right)$

$\mathrm{SetCoordinates}\left(\mathrm{cylindrical}\left[r,t,z\right]\right)$

${\mathrm{cylindrical}}_{r,t,z}$

$\mathrm{TNBFrame}\left(⟨1\,t\,t⟩\right)$

$\left[\begin{array}{c}\frac{-\frac{\cos \left(t\right)\cos \left(\sin \left(t\right)\right)\sqrt{2}\sin \left(t\right)}{2}+\frac{{\cos \left(t\right)}^2\sin \left(\sin \left(t\right)\right)\sqrt{2}}{2}}{\sqrt{{\cos \left(t\right)}^2{\sin \left(\sin \left(t\right)\right)}^2+{\cos \left(t\right)}^2{\cos \left(\sin \left(t\right)\right)}^2}}\\ \frac{\frac{{\cos \left(t\right)}^2\cos \left(\sin \left(t\right)\right)\sqrt{2}}{2}+\frac{\cos \left(t\right)\sin \left(\sin \left(t\right)\right)\sqrt{2}\sin \left(t\right)}{2}}{\sqrt{{\cos \left(t\right)}^2{\sin \left(\sin \left(t\right)\right)}^2+{\cos \left(t\right)}^2{\cos \left(\sin \left(t\right)\right)}^2}}\\ \frac{\sqrt{2}}{2}\end{array}\right],\left[\begin{array}{c}\frac{-{\cos \left(t\right)}^2\cos \left(\sin \left(t\right)\right)-\cos \left(t\right)\sin \left(\sin \left(t\right)\right)\sin \left(t\right)}{\sqrt{{\cos \left(t\right)}^2{\sin \left(\sin \left(t\right)\right)}^2+{\cos \left(t\right)}^2{\cos \left(\sin \left(t\right)\right)}^2}}\\ \frac{-\cos \left(t\right)\cos \left(\sin \left(t\right)\right)\sin \left(t\right)+{\cos \left(t\right)}^2\sin \left(\sin \left(t\right)\right)}{\sqrt{{\cos \left(t\right)}^2{\sin \left(\sin \left(t\right)\right)}^2+{\cos \left(t\right)}^2{\cos \left(\sin \left(t\right)\right)}^2}}\\ 0\end{array}\right],\left[\begin{array}{c}\frac{\frac{\cos \left(t\right)\cos \left(\sin \left(t\right)\right)\sqrt{2}\sin \left(t\right)}{2}-\frac{{\cos \left(t\right)}^2\sin \left(\sin \left(t\right)\right)\sqrt{2}}{2}}{\sqrt{{\cos \left(t\right)}^2{\sin \left(\sin \left(t\right)\right)}^2+{\cos \left(t\right)}^2{\cos \left(\sin \left(t\right)\right)}^2}}\\ \frac{-\frac{{\cos \left(t\right)}^2\cos \left(\sin \left(t\right)\right)\sqrt{2}}{2}-\frac{\cos \left(t\right)\sin \left(\sin \left(t\right)\right)\sqrt{2}\sin \left(t\right)}{2}}{\sqrt{{\cos \left(t\right)}^2{\sin \left(\sin \left(t\right)\right)}^2+{\cos \left(t\right)}^2{\cos \left(\sin \left(t\right)\right)}^2}}\\ \frac{\sqrt{2}}{2}\end{array}\right]$

$\mathrm{SetCoordinates}\left(\mathrm{cartesian}\right)$

$\mathrm{cartesian}$

$\mathrm{TNBFrame}\left(⟨\cos \left(t\right)\,\sin \left(t\right)\,t⟩\,\mathrm{output}=\mathrm{plot}\,\mathrm{binormal}=\mathrm{false}\,\mathrm{scaling}=\mathrm{constrained}\,\mathrm{normaloptions}=\left[\mathrm{orientation}=\left[240\,130\right]\right]\right)$