Implicit surface

Encyclopedia : I : IM : IMP : Implicit surface

In mathematics and computer graphics, an implicit surface is defined as an isosurface—a level set—of a function

[f\ :\ \mathbb^\rightarrow\mathbb.\,]

In other words, it is the set of points in the 3d-space that satisfy the equation

[f(x,y,z)=\mathrm.\,]

To find a parametrisation of the 'surface' (more precisely the solution set, since not all equations of this type define a surface, or indeed define any points at all) one has to treat this relation as giving an implicit function

Without loss of generality one may assume that the equation is of form

[g(x,y,z)=0,\,]

but it is often convenient to allow the arbitrary constant on the right side.

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