P.-A. Fayolle, A. Pasko, N. Mirenkov (Japan), C. Rosenberger, and C. Toinard (France)

Function Representation, R-functions, constuctive model ing, genetic algorithms, modeling automation.

An algorithm is described for recovering a constructive tree representation of a solid from a segmented point-set. The term point-set refers here to a ﬁnite set of points on or near the surface of the solid. Constructive geometry refers to the construction of complex solids by recursively applying set operations to simple primitives. It can be implemented on a computer by using a tree data structure with geomet ric primitives (planes, spheres and others) in the leaves and set-operations in the internal nodes. This tree data struc ture is called a constructive tree. A constructive tree can be syntactically translated into representations of solids by real-valued functions with the theory of R-functions. The recovered constructive tree is a correct representation of the point-set if the solid deﬁned by the corresponding function matches the solid deﬁned by the point-set. The search for a constructive tree is performed by a genetic algorithm. The formulation of the problem, the genetic algorithm and its parameters are discussed here.

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