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Proceedings of CAD'17, 2017, 278-282
Rounding, Filleting and Smoothing of Implicit Surfaces
Abstract. Modern developments in geometric modelling allow for using a variety of geometry representations in a wide range of applications. As new representations are introduced, one wants to adapt existing processing techniques and methods used with the other representations. One example of such techniques is filleting. It is well known how to perform rounding and filleting for parametric representations, but there is limited prior work for implicit surfaces and procedural volumetric objects. In this work, we discuss possible implementations of filleting, rounding and smoothing operations applied to objects defined in an implicit form by zero level-sets of continuous scalar fields (usually called implicit surfaces). This representation is useful to define a wide range of primitives and operations, including complex geometry such as procedural microstructures. It is possible to simply define these operations, if the scalar field corresponds to the distance to the surface of the object of interest. In practice, however, the distance property can be obtained analytically only for a very limited set of primitives and operations and is easily lost by some common operations in shape modelling, such as, for example, non-uniform scaling. In this work, we propose to use a numerical method to compute a signed distance field on the basis of an arbitrary continuous scalar field.
Keywords. Implicit Surfaces, Function Representation, Distance Function, Offsetting, Filleting