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Constructive solid geometnj [CSG] is the primary scheme used for representing solid objects in many contemporary solid modeling systems. A CSG representation is a binary tree whose nouterminal nodes represent Boolean operations and whose terminal nodes represent primitive solids. This paper deals with algorithtns that operate directly on CSG represctitations to solve two computationally difficult geometric problems-null-object detection [NOD] and same-object detection [SOD]. The paper also shows that CSG trees representing null objects may be reduced to null trees through the use of a nciv concept called primitive redundancy, and tluU, on average, tree reduction can be done cfficicttth/ by a new technique called spatial localization. Primitive redundancy and spatial localization enable a single complex instance of NOD to be converted into a nutnber of simpler siibproblems and lead to wore efficient algoiithms than those previously known.

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