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If geometries are represented as level sets, Boolean operations can be expressed as simple operations on the corresponding LS functions [89,110]. If one considers the sets
,
, and
and the corresponding boundaries
,
, and
, which are represented by the LS functions
,
, and
, the LS counterparts of Boolean operations are listed in the following.
Union: 







(4.10) 
Intersection: 







(4.11) 
Complement: 







(4.12) 
Relative complement: 







(4.13) 
Here the convention is used that the LS function
is negative for all
.
Boolean operations are very useful for more general topography simulations, if consecutive process steps, like etching and/or deposition processes, should be simulated or several materials are involved.
Subsections
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Otmar Ertl: Numerical Methods for Topography Simulation