Function representation
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 of point coordinates ![f(x_1,x_2, ..., x_n)](/Images/godic/202501/14/fa9f2e86dc0c591d88ace9a15acc907e5238.png")
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](/Images/godic/202501/14/2259017055d78891621b4aa12878fd7c5238.png")
belong to the object, and the points with ![f(x_1,x_2, ..., x_n) < 0](/Images/godic/202501/14/413f3c047f4fc3593c42a25c42323abb5238.png")
are outside of the object. The point set with ![f(x_1,x_2, ..., x_n)=0](/Images/godic/202501/14/917065a2cbf6b4ff7a5e9fa81f1243855238.png")
is called an isosurface.