RBF Implicit Representation of Geometrical Entities
In this chapter the implicit surface method based on RBF is explained and demonstrated. The classical method that consists of the definition of a scalar valued function in the 3D space that is null at on-surface points and positive (negative) at off-surface points that are positioned outside (inside) the surface is firstly introduced. The projection onto the surface is achieved by computing the gradient of the implicit function. The second one is a novel method that consists of the creation of a projection field (vector valued RBF) defined on the surface and at off-surface points that is zero at on-surface points whereas it is equal to the vector moving to the surface at off-surface points. The effectiveness of both methods is demonstrated with practical examples.
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