Interactive Gallery of Dynamically-Generated 3D Level Surfaces
(Equations in 3D)

Elliptic Paraboloid: x^2+2y^2-z = 0 Compare this surface plot to the 3D Level Curve surface plot of the same elliptic paraboloid that places bounds only on x and y. Here, the bounds are on x, y, and z. In this graph, limiting the bound on z enables the shape of the elliptic cross section to be shown as the ridge at the top.
Ellipsoid: x^2+y^2/4+z^2/9 = 1  Note that all cross sections parallel to a coordinate plane are ellipses.
Double Cone: 3x^2+2y^2-z^2 = 0
Hyperboloid of One Sheet: x^2+y^2/4-z^2/9 = 1  
Hyperboloid of Two Sheets: x^2-y^2/4-z^2/9 = -1
A quartic: (x^2-1)^2+(y^2-1)^2+(z^2-1)^2 = 1.5
A cubic with holes: x^3+y^3+z^3-x-y-z = 0
Simple Cubic: x^2*y+y^2*z+z^2*x = 0  
Cayley Cubic: 4*(x^2+y^2+z^2)+16*x*y*z = 1

 

 

 

       

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United States Patent Numbers 7,432,926, 7,595,801, & 7,889,199.
Other Patent Pending.
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