Concept

Function representation

Summary
Function Representation (FRep or F-Rep) is used in solid modeling, volume modeling and computer graphics. FRep was introduced in "Function representation in geometric modeling: concepts, implementation and applications" as a uniform representation of multidimensional geometric objects (shapes). An object as a point set in multidimensional space is defined by a single continuous real-valued function f(X) of point coordinates X[x_1,x_2, ..., x_n] which is evaluated at the given point by a procedure traversing a tree structure with primitives in the leaves and operations in the nodes of the tree. The points with f(x_1,x_2, ..., x_n) \ge 0 belong to the object, and the points with f(x_1,x_2, ..., x_n) < 0 are outside of the object. The point set with f(x_1,x_2, ..., x_n)=0 is called an isosurface. Geometric domain The geometric domain of FRep in 3D space includes solids with non-manifold models and lower-dimensio
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