Point Interpolation - Maple Help

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Student[Calculus1]

 PointInterpolation
 simplistic approximation of a function

 Calling Sequence PointInterpolation(f(x), x = a..b, opts) PointInterpolation(f(x), a..b, opts)

Parameters

 f(x) - algebraic expression in variable 'x' x - name; specify the independent variable a, b - algebraic expressions; specify the plot range opts - equation(s) of the form option=value where option is one of functionoptions, interpolation, interpolationoptions, numpoints, output, pointoptions, showfunction, showinterpolant, showpoints, view, or Student plot options; specify options for the plot

Description

 • The PointInterpolation(f(x), x=a..b) command plots the function f(x) and an approximation to f(x) obtained by sampling f(x) at a series of points and interpolating those points.
 • If no range a..b is provided, the range $-10..10$ is used.
 • If the independent variable can be uniquely determined from the expression, the parameter x need not be included in the calling sequence.
 • This routine demonstrates the failures that can result from attempting to graph an expression without finding further information about the function such as zeros, extreme points, inflection points, and asymptotes.
 • The opts argument can contain any of the Student plot options or any of the following equations that set plot options.
 functionoptions = list
 A list of options for the plot of the expression $f\left(x\right)$.  By default, the expression is plotted as a solid red line. For more information on plot options, see plot/options.
 interpolation = spline or linear
 Whether cubic spline or linear interpolation is used to approximate the function.  By default, the value is spline.
 interpolationoptions = list of values
 A list of options for the plot of the interpolation. By default, the interpolation is plotted as a solid blue line. For more information on plot options, see plot/options.
 numpoints = posint
 The number of points evenly spaced points that span the interval $\left(a,b\right)$.  By default, the value is 6.
 output = plot or animation
 This option controls the return value of the function.
 – output = plot specifies that a plot, which shows f(x), the points of interpolation, and the interpolant, is displayed.  This is the default.
 – output = animation specifies that an animation, where the first iteration shows f(x), the next adds the interpolation points, and the third adds the interpolant, is displayed.
 pointoptions = list
 A list of options for the plot of the interpolating points. By default, these points are plotted as blue circles. For more information on plot options, see plot/options.
 showfunction = true or false
 Whether the expression $f\left(x\right)$ is plotted.  By default, the value is true.
 showinterpolant = true or false
 Whether the interpolant is plotted.  By default, the value is true.
 showpoints = true or false
 Whether the interpolation points are marked.  By default, the value is true.
 view = [DEFAULT or numeric..numeric, DEFAULT or numeric..numeric]
 The view of the final plot.
 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.
 title = anything
 A title for the plot.
 The default title is constructed from the parameters and the command options. title = "" disables the default title. For more information about specifying a title, see plot/typesetting.

Examples

 > $\mathrm{with}\left(\mathrm{Student}\left[\mathrm{Calculus1}\right]\right):$
 > $\mathrm{PointInterpolation}\left(\mathrm{sin}\left(9x\right),x=0..\mathrm{\pi }\right)$

The command to create the plot from the Plotting Guide is

 > $\mathrm{PointInterpolation}\left(\frac{{x}^{2}-3x+1}{{x}^{2}-4x+3},x=-3..4\right)$

 See Also