Cassinian Oval

Note

This Mathematica notebook is from the WWW project A Visual Dictionary of Special Plane Curves. Copyright © 1995-2002 by Xah Lee. (http://xahlee.org/)

Graphics illustrating Cassinian Oval plotted as a surface.

Packages and Initializations

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

Needs["Graphics`ImplicitPlot`"]

Needs["Graphics`Shapes`"]	(* MathSource Item#: 0200-608 *)

$HistoryLength = 5;

Surface plot

Clear[m, b]; 
m = 2;
a = 1;
b = 0;
Plot3D[(Sqrt[(((x - a))^2) + (y^2)]) (Sqrt[(((x + a))^2) + (y^2)]) - 
        (b^2), {x, -m, m}, {y, -m, m}, 
      ViewPoint -> {0.858, -3.273, -0.026}, 
      PlotRange -> All, AspectRatio -> 1, 
      PlotPoints -> {1, 1} 60]

Clear[m, b];
m = 1.5;
a = 1;
b = 1;
ContourPlot[
      Sqrt[(x - a)^2 + y^2]*Sqrt[(x + a)^2 + y^2] - 
        b^2, {x, -m*1.2, m*1.2}, {y, -m, m}, 
      AspectRatio -> Automatic, PlotPoints -> {1, 1} 60]

Clear[m, b];
m = 1.5;
a = 1;
b = 1;
DensityPlot[
      Sqrt[(x - a)^2 + y^2]*Sqrt[(x + a)^2 + y^2] - b^2, {x, -m, 
        m}, {y, -m, m}, AspectRatio -> 1, PlotPoints -> {1, 1} 200, 
      Mesh -> False]