compute the radius of curvature of a curve - Maple Help

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Student[VectorCalculus][RadiusOfCurvature] - compute the radius of curvature of a curve

Calling Sequence

RadiusOfCurvature(C, t, options)




free or position Vector; specify the components of the curve



(optional) name; specify the parameter of the curve



(optional) equation(s) of the form option=value where option is one of output, circleoptions, circles, curveoptions, range, or view



The RadiusOfCurvature(C, t) calling sequence computes the radius of curvature of the curve C.  This is defined to be 1/Curvature(C, t) when the curvature is not zero and infinity when the curvature is zero.


If t is not specified, the command tries to determine a suitable variable name from 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, this 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.


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


* output = plot returns a plot of the space curve and the circles. The number of circles is specified by the circles option. The RadiusOfCurvature command supports only three-dimensional Vector plots.


* output = animation returns an animation of the space curve and the circles. The number of circles of curvature is specified by the circles option.


circleoptions = list


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


circles = posint


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


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 [].


range = realcons..realcons


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


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.












To play the following animations in this help page, right-click (Control-click, on Macintosh) the plot to display the context menu.  Select Animation > Play.



The command to create the plot from the Plotting Guide is


See Also

realcons, Student[VectorCalculus], Student[VectorCalculus][Binormal], Student[VectorCalculus][Curvature], Student[VectorCalculus][GetCoordinates], Student[VectorCalculus][PrincipalNormal], Student[VectorCalculus][SetCoordinates], Student[VectorCalculus][SpaceCurve], Student[VectorCalculus][SpaceCurveTutor], Student[VectorCalculus][TangentVector], Student[VectorCalculus][TNBFrame], Student[VectorCalculus][Torsion], Student[VectorCalculus][Vector], VectorCalculus, VectorCalculus[RadiusOfCurvature]

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