Editing Implicit surface (section)

=== Constant distance product surface ===
A Cassini oval can be defined as the point set for which the product of the distances to two given points is constant (in contrast, for an ellipse the ''sum'' is constant). In a similar way implicit surfaces can be defined by a constant distance product to several fixed points.

In the diagram ''metamorphoses'' the upper left surface is generated by this rule: With

: <math>
\begin{align}
F(x,y,z) = {} &  \sqrt{(x-1)^2+y^2+z^2}\cdot \sqrt{(x+1)^2+y^2+z^2} \\
& \quad \cdot \sqrt{x^2+(y-1)^2+z^2}\cdot\sqrt{x^2+(y+1)^2+z^2}
\end{align}
</math>

the constant distance product surface  <math>F(x,y,z)-1.1=0</math> is displayed.
[[File:Metamorphose-torus-4ppfl.svg|400px|thumb|Metamorphoses between two implicit surfaces: a torus and a constant distance product surface.]]