Re: How to find the equidistance curves of a curve defined by Interpolation function?
- To: mathgroup at smc.vnet.net
- Subject: [mg27895] Re: How to find the equidistance curves of a curve defined by Interpolation function?
- From: "Allan Hayes" <hay at haystack.demon.co.uk>
- Date: Fri, 23 Mar 2001 04:31:14 -0500 (EST)
- References: <99chna$8d4@smc.vnet.net>
- Sender: owner-wri-mathgroup at wolfram.com
liwen
unitnormal[v_,t_] := Reverse[#/Sqrt[# .#]&[D[v,t]]]{-1,1};
equidistant[v_, d_, t_] := (v + d*unitnormal[v,t])
Example:
v = {7*Cos[t], 3*Sin[t]};
ParametricPlot[Evaluate[{v, equidistant[v, 3, t]}],
{t, 0, 2*Pi}, AspectRatio -> Automatic,
Compiled -> False];
We can get a good idea of how this comes about by using an animation:
(close the group with the pictures in it and then use menu > Cell > Animate
Selected Graphics).
K = 25;
Do[ParametricPlot[Evaluate[{v, equidistant[v, 3, t]}],
{t, 0, k}, AspectRatio -> Automatic,
Compiled -> False, PlotRange -> {{-9, 9}, {-5, 5}},
Epilog -> Line[{v, equidistant[v, 3, t]} /. t -> k]],
{k, Pi/K, 2*Pi, (Pi + 1)/K}];
--
Allan
---------------------
Allan Hayes
Mathematica Training and Consulting
Leicester UK
www.haystack.demon.co.uk
hay at haystack.demon.co.uk
Voice: +44 (0)116 271 4198
Fax: +44 (0)870 164 0565
"liwen liwen" <gzgear at yahoo.com> wrote in message
news:99chna$8d4 at smc.vnet.net...
> Dear friends,
>
> How are you! I want to know how to find the
> equidistance curves of a curve defined by
> Interpolation function, for example,
> when the equidistance is 2, the equidistance curve of
> a circle with a radium of 5 is a circle with a radium
> of 3, now I want to
> find the equidistance curves of an Interpolation curve
> defined by the following data:
>
> data1={{0,0},{1,1},{2,3},{5,8},{7,12}};
> cur=Interpolation[data1];
>
> The equidistance curves of the curve defined above has
> two curves. How can I find them?
>
>
> Thank you very much!
>
> Liwen 3/21/2001
>
> e-mail: gzgear at yahoo.com
>
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