Cartesian Equation

Author

Eric W. Weisstein
July 16, 2002

This notebook downloaded from http://mathworld.wolfram.com/notebooks/PlaneGeometry/CartesianEquation.nb.

For more information, see Eric's MathWorld entry http://mathworld.wolfram.com/CartesianEquation.html.

©2005 Wolfram Research, Inc. except for portions noted otherwise

Additional Authors

Firgures by Margherita Barile
July 2002

Initialization

<<Graphics`ContourPlot3D`;
<<Graphics`ImplicitPlot`;
<<SolidGeometry`;

Circle and Sphere

Show[GraphicsArray[{
ContourPlot[x^2+y^2-1, {x,-1,1},{y,-1,1},ContourShading->False,Contours->{0.}, Axes->True, 
DisplayFunction->Identity,FrameLabel->TraditionalForm/@{x,y}],
ContourPlot3D[x^2+y^2+z^2-1, {x,-1,1},{y,-1,1}, {z,-1,1}, Axes->True,DisplayFunction->Identity,
 AxesLabel->TraditionalForm/@{x,y,z}]
}]
]

Intersecting Surfaces

Show[GraphicsArray[{
Show[ContourPlot3D[#, {x,-5,5},{y,-5,5}, {z,-5,5}, DisplayFunction->Identity]&/@{x+y+z-1,3x-y+z-2},ViewPoint->{1,0,1}, Boxed->False],
Show[Graphics3D[{Sphere[{0,0,0},1],Sphere[{0,.5,.5},.5]}],DisplayFunction->Identity,
ViewPoint->{1,2,1}, Boxed->False],
Show[ContourPlot3D[#, {x,-1,1},{y,-1,1}, {z,-1,1}, DisplayFunction->Identity]&/@{x^2+y^2+z^2-1,-7x+y-10z+7},ViewPoint->{2,1,.5}, Boxed->False]
},GraphicsSpacing->-.2]]

To Parametric

Eliminate[{x==3t-1, y==4t+2, z==-5t+2},t]