Note

This Mathematica notebook is from the WWW project A Visual Dictionary of Special Plane Curves. Copyright © 1995-2000 by Xah Lee. (http://xahlee.org/)

Packages and Initializations

Needs["ParaPlot`"]
Needs["PlaneCurveFormulas`"]
Needs["PlaneCurveGenerator`"]

Needs["Graphics`ImplicitPlot`"]
(*MathSource Item:0200-529*)

Parallel

?Parallel

Sine and its parallel

Clear[d]; d = 3;
ParametricPlot[
        Evaluate[Parallel[{t, Sin[t]}, t, {-d, 0, d}]], {t, -2 Pi, 
          6 Pi}, PlotStyle -> {Hue[ .75], Hue[0], Hue[ .35, 1,  .7]}, 
        AspectRatio -> Automatic, 
        PlotRange -> {{-3, 16}, {-4.4, 4.4}}, 
        Axes -> False];

Plot[Sin[t], {t, -2 Pi, 6 Pi}, AspectRatio -> Automatic, 
        PlotStyle -> Hue[ .65], 
        PlotRange -> {{-3, 16}, {-4.4, 4.4}}, 
        Axes -> False, 
        Prolog -> {Hue[0,  .5, 1], 
            Table[Circle[{t, Sin[t]}, d], {t, -2 Pi, 6 Pi, 
                8 Pi/80}]}];

ParaPlot[{t, Sin[t]}, {t, -2 Pi, 6 Pi,  .25}, 
        ParallelCurveOffset -> {-d, d}, 
        NormalLineLength -> 2 d, 
        DotStyle -> {{{Hue[0, 0, 0], PointSize[ .009]}}}, 
        PlotRange -> {{-3, 16}, {-4.4, 4.4}}, 
        AspectRatio -> Automatic, Axes -> False];
Clear[d]

An animation of generating parallel curves of sine.

Clear[myList];
myList = Range[0, 3 π, ((3 π)/36)];
Do[
        ParaPlot[{t, Sin[t]}, {t, 0, 3 π}, Take[myList, i], 
          ParallelCurveOffset -> {- .2, 3}, 
          NormalLineLength -> 6, PlotDot -> False, 
          NormalLineStyle -> {Hue[ .17]}, AspectRatio -> Automatic, 
          PlotRange -> {{-2.5, 11.5}, {-2, 4}}]; , {i, 1, 
          Length[myList]}];
Clear[myList]