Sweeps are considered to be one of the basic representation schemes in solid modeling, and have numerous applications in very diverse fields ranging from engineering design and manufacturing to computer graphics. Despite their prevalence, many properties of the general sweeps are not well understood. Furthermore, boundary evaluation algorithms for 3-dimensional solid objects currently exist only for reasonably simple objects and motions. One of the main reasons for this state of affairs is the lack of a generic point membership test for sweeps. In this paper we describe a point membership classification (PMC) for sweeping solids of arbitrary complexity moving according to one parameter affine motions such that the initial and final configurations of the moving object do not intersect. Our PMC test is defined in terms of inverted trajectory tests against the original geometric representation of the generator object. This PMC test provides complete geometric information about the set swept by the 3-dimensional moving object, and can play a fundamental role in sweep boundary evaluation and trimming algorithms, as well in a number of practical applications such as contact analysis of higher pairs in design and manufacturing. Since our PMC is formulated in terms of intersections between inverted trajectories and the generator, it can be implemented for any geometric representation that supports curve-solid intersections.

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