Re: RE: Trace a function

• To: mathgroup at smc.vnet.net
• Subject: [mg34999] Re: [mg34990] RE: [mg34978] Trace a function
• From: Murray Eisenberg <murraye at attbi.com>
• Date: Wed, 19 Jun 2002 05:52:32 -0400 (EDT)
• Organization: Mathematics & Statistics, Univ. of Mass./Amherst
• References: <200206180648.CAA23362@smc.vnet.net>
• Sender: owner-wri-mathgroup at wolfram.com

```This is very useful!

Note the typo in the Animate cell: "gpoints" should be "pts" to be
consitent with the example GeneratePlotPoints cell.

David Park wrote:
>
> Declan,
>
> With a little work you can duplicate the graphical calculator trace plot
> function.
>
> Here are are a couple of routines and an example.
>
> Needs["Graphics`Animation`"]
> Needs["Graphics`Colors`"]
>
> This routine extracts the plot points from a plot statement. You use it just
> like you use a Plot statement.
>
> GeneratePlotPoints[f_, iter_, opts___?OptionQ] :=
>   Block[{g, pts, \$DisplayFunction = Identity},
>     g = First[Plot[f, iter, opts]];
>     First[Cases[g, Line[pts_] -> pts, Infinity]]
>     ]
>
> This generates the points for a sample curve. The points are the ones that
> Mathematica's adaptive plotting routine generated.
>
> pts = GeneratePlotPoints[x^2, {x, 0, 1}];
>
> We are going to generate an animation that will plot the line in black, a
> selected point in Red, and label the coordinates of the point at a user
> specified text position in the plot.
>
> trace[npoint_, pts_, textposition_] :=
>     Module[{x, y},
>       {x, y} = pts[[npoint]];
>       Show[Graphics[
>           {Line[pts],
>             AbsolutePointSize[5], Red,
>             Point[{x, y}],
>             Black,
>             Text[SequenceForm["x = ", NumberForm[x, 3], "\ny = ",
>                 NumberForm[y, 3]], textposition, {-1, 0}]}],
>         Frame -> True,
>         FrameLabel -> {"x", "y"},
>         ImageSize -> 500]];
>
> You could look a a specific point by evaluating trace with the point index,
> or better yet produce an animation.
>
> Animate[trace[n, pts, Scaled[{0.1, 0.9}]], {n, 1, Length[gpoints], 1}]
> SelectionMove[EvaluationNotebook[], All, GeneratedCell]
> FrontEndTokenExecute["OpenCloseGroup"]
> FrontEndTokenExecute["SelectionAnimate"]
>
> Use the up and down arrow keys to trace the point along the curve and see
> the coordinate values. (Using the up and down arrow keys are often the best
> method for viewing an animation.)
>
> David Park
>
> > From: Declan O'Reilly [mailto:declan at mcs.com]
> >
> >
> > Hi
> >     Is there a way to trace along the plot of a function similar to the
> > 'Trace' functionality on a graphing calculator.
> >
> > Thanks
> > Declan O'Reilly
> >
> >

--
Murray Eisenberg                     murray at math.umass.edu
Mathematics & Statistics Dept.
Lederle Graduate Research Tower      phone 413 549-1020 (H)
University of Massachusetts                413 545-2859 (W)
710 North Pleasant Street
Amherst, MA 01375

```

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