Editing Implicit surface (section)

=== Metamorphoses  of implicit surfaces ===
A further simple method to generate new implicit surfaces is called ''metamorphosis'' or ''[[homotopy]]'' of implicit surfaces:

For two implicit surfaces <math>F_0(x,y,z)=0, F_1(x,y,z)=0</math> (in the diagram: a constant distance product surface and a torus) one defines new surfaces using the design parameter <math> \mu \in [0,1]</math>:
:<math>F_\mu (x,y,z)=\mu F_1(x,y,z)+(1-\mu)\,F_0(x,y,z)=0</math> 
In the diagram the design parameter is successively <math>\mu=0, \, 0.33, \, 0.66, \, 1</math> .

[[File:Approx-3tori.svg|240px|thumb|Approximation of three tori ([[parallel projection]])]]
[[File:Approx-3tori-pov.png|280px|thumb|[[POV-Ray]] image (central projection) of an approximation of three tori.]]