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Solid modeling
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===Constructive solid geometry=== {{Main|Constructive Solid Geometry}} Constructive solid geometry (CSG) is a family of schemes for representing rigid solids as Boolean constructions or combinations of primitives via the regularized set operations discussed above. CSG and boundary representations are currently the most important representation schemes for solids. CSG representations take the form of ordered [[binary tree]]s where non-terminal [[Node (computer science)|nodes]] represent either rigid transformations ([[Orientation (mathematics)|orientation]] preserving [[Isometry|isometries]]) or regularized set operations. Terminal nodes are primitive leaves that represent closed regular sets. The semantics of CSG representations is clear. Each subtree represents a set resulting from applying the indicated transformations/regularized set operations on the set represented by the primitive leaves of the subtree. CSG representations are particularly useful for capturing design intent in the form of features corresponding to material addition or removal (bosses, holes, pockets etc.). The attractive properties of CSG include conciseness, guaranteed validity of solids, computationally convenient Boolean algebraic properties, and natural control of a solid's shape in terms of high level parameters defining the solid's primitives and their positions and orientations. The relatively simple data structure and elegant [[Recursion|recursive]] algorithms<ref name = "Recursivity">{{cite journal |doi=10.1002/malq.200310107 |title= Computable Operators on Regular Sets |author= Ziegler, M. |journal= Mathematical Logic Quarterly |year= 2004 |volume= 50 |issue= 45 |pages= 392β404 |publisher= Wiley|s2cid= 17579181 }}</ref> have further contributed to the popularity of CSG.
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