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4. Nomenclature

‘AND, &’: These symbols are used for the binary operation known as Intersection. Only those parts of two sets that overlap will be preserved in the result. Equivalent notation found in other sources are ‘*, •, ∩’.

‘OR, +’: These symbols are used for the binary operation known as Union. The total set membership of both sets will become the resultant. An equivalent notation found in other sources is, ‘∪’.

‘NOT, ~’: These symbols are used for the unary operation known as Inverse, or Complement. The result of this operation will be an inverted geometry of the initial set. Where volume was before the operator was applied will become void, and vice versa for the previous void. An equivalent notation found in other texts is ‘X’.

‘-’: The CSG Difference, or Subtraction operator. When used as ‘A: B’, the set ‘A’ will have any overlap with set ‘B’ removed. This is not a simple Boolean operator, but actually a complex function of the form ‘A & ~B’. The order is not commutative.

‘:’: This is the notation used in this thesis for the Assembly operator. While this is not a Boolean operator, it can be considered to define a list of Boolean equations. Some references use ‘+’ for the assembly operator.

‘+*, &*, -*, ~*’: The regularized set operators that ensure closed regular sets. Other references use the notations, ‘∪*, ∩*, -*, c*’.

‘++, &+, -+, ~+’: The regularized set operators for open regular sets. Other references use the notation, ‘∪+, ∩+, -+, c+’.

‘;’: This operator is used in this thesis to append one set to another. For example ‘set1;set2’ will append the members of ‘set2’ to the end of ‘set1’. This operator would allow reuse of basis sets such as ‘set1’.