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Extrusion of 1D Implicit Profiles: Theory and First Application

This paper presents a new interpretation of the general definition of the binary blending operator of implicit modeling. Instead of considering the operator as a composition of potential functions or as a function defined in the combined primitives metric, we propose to consider it as an implicit curve extruded in an implicit extrusion field. An implicit extrusion field is a 2D space for which each coordinate is a potential field. The study of general concepts around implicit extrusion field allows us to introduce theoretical notion of free-form blending controlled point-by-point by the user. Through the use of functional interpolation functions, we propose modeling tools to create, sculpt or combine implicit primitives by extrusion of a profile in an implicit extrusion field.