Boolean operations.

Regularized set of operations is used on the standard primitives with additional checks to prevent lower dimension objects in special cases. Such operations are regularized union, denoted ; regularized intersection, denoted and regularized difference, denoted . Degeneration of shapes into lower dimensions (Fig. 1) must be prevented to follow the manifold representation.

  
Figure 1: Example of non-regularized intersection in 2D space

Regularized operations are combined together to form tree of operations on primitives. Additional tests for redundancy in CSG tree can also be performed.