Shaping geometric objects by cumulative translational sweeps
IBM Journal of Research and Development
Sweeping of three-dimensional objects
Computer-Aided Design
Representations for Rigid Solids: Theory, Methods, and Systems
ACM Computing Surveys (CSUR)
Function Representation for Sweeping by a Moving Solid
IEEE Transactions on Visualization and Computer Graphics
Fast swept volume approximation of complex polyhedral models
SM '03 Proceedings of the eighth ACM symposium on Solid modeling and applications
Generalized sweep templates for implicit modeling
GRAPHITE '05 Proceedings of the 3rd international conference on Computer graphics and interactive techniques in Australasia and South East Asia
Boundary of the volume swept by a free-form solid in screw motion
Computer-Aided Design
Set Membership Classification: A Unified Approach to Geometric Intersection Problems
IEEE Transactions on Computers
Approximating 3D general sweep boundary using depth-buffer
ICCSA'03 Proceedings of the 2003 international conference on Computational science and its applications: PartIII
A New Approach to Point Membership Classification in B-rep Solids
Proceedings of the 13th IMA International Conference on Mathematics of Surfaces XIII
2009 SIAM/ACM Joint Conference on Geometric and Physical Modeling
A comparison of sampling strategies for computing general sweeps
Computer-Aided Design
Conservative swept volume boundary approximation
Proceedings of the 14th ACM Symposium on Solid and Physical Modeling
High accuracy NC milling simulation using composite adaptively sampled distance fields
Computer-Aided Design
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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.