Classifying points for sweeping solids

Many diverse engineering problems can be modeled with solid sweeping in a conceptually simple and intuitive way, and sweeps are considered to be one of the basic representation schemes in solid modeling. However, many properties of sweeps as well as their ''informational completeness'' are not well understood, which is the primary reason why computational support for solid sweeping remains scarce. We propose a generic point membership classification (PMC) for sweeping solids of arbitrary complexity moving according to one parameter affine motions. The only restrictive assumption that we make in this paper is that the initial and final configurations of the moving object do not intersect during the sweep. Our PMC test is defined in terms of inverted trajectory tests against the original geometric representation of the generator object, which implies that this test can be implemented in any geometric representation that supports curve-solid intersections. Importantly, this PMC test provides complete geometric information about the set swept by 3-dimensional objects in general motions. At the same time, it establishes the foundations for developing a new generation of computational tools for sweep boundary evaluation and trimming, as well as a number of practical applications such as shape synthesis, contact analysis and path planning.