Loop detection in surface patch intersections

Sederberg, Thomas W.; Meyers, Ray J.

doi:10.1016/0167-8396(88)90029-5

Cited by 130 publications

(44 citation statements)

References 8 publications

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“…There exists a significant body of literature on the calculation of intersections of two parametric surfaces [1,6,18,23,30,76] (see also [17] for a more exhaustive bibliography). Recent developments include the possibility of handling intersection singularities [10,49].…”

Section: Intersection Of Curves and Surfacesmentioning

confidence: 99%

Computational Methods for Geometric Processing. Applications to Industry

Iglesias

Gálvez

Puig-Pey

2001

Computational Science — ICCS 2001

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Section: Intersection Of Curves and Surfacesmentioning

confidence: 99%

Computational Methods for Geometric Processing. Applications to Industry

Iglesias

Gálvez

Puig-Pey

2001

Computational Science — ICCS 2001

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“…It can be robustly and efficiently computed using a rational constraint solver [10,33]. The robustness is achieved by bounding the subdivided implicit surface I with the corresponding hyper-tangent cone [10], an extension of the bounding tangent cones for explicit plane curves and explicit surfaces [31,32]. Let us recall that the implicit 2-manifold I in R 5 {s,ŝ,t} is the locus of intersection points of the two deforming surfaces, over the whole time period.…”

Section: Detection Of Transition Eventsmentioning

confidence: 99%

Theoretically Based Robust Algorithms for Tracking Intersection Curves of Two Deforming Parametric Surfaces

Chen

Riesenfeld

Cohen

et al. 2006

Geometric Modeling and Processing - GMP 2006

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Abstract. This paper applies singularity theory of mappings of surfaces to 3-space and the generic transitions occurring in their deformations to develop algorithms for continuously and robustly tracking the intersection curves of two deforming parametric spline surfaces, when the deformation is represented as a family of generalized offset surfaces. The set of intersection curves of 2 deforming surfaces over all time is formulated as an implicit 2-manifold I in the augmented (by time domain) parametric space R 5 . Hyper-planes corresponding to some fixed time instants may touch I at some isolated transition points, which delineate transition events, i.e., the topological changes to the intersection curves. These transition points are the 0-dimensional solution to a rational system of 5 constraints in 5 variables, and can be computed efficiently and robustly with a rational constraint solver using subdivision and hyper-tangent bounding cones. The actual transition events are computed by contouring the local osculating paraboloids. Away from any transition points, the intersection curves do not change topology and evolve according to a simple evolution vector field that is constructed in the euclidean space in which the surfaces are embedded.

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“…Indeed, small intersections loops, which may be of vital importance for assessing the validity of a mechanical assembly, could be missed. Hence, a variety of conservative techniques have been proposed to ensure that no loop is missed [Sederberg88]. For surveys and representative research see [Patrikalakis93,Krishnan97].…”

Section: Intersectionsmentioning

confidence: 99%

Solid and Physical Modeling

Rossignac

2007

Wiley Encyclopedia of Electrical and Electronics Engineering

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The sections in this article are Introduction Topological Domain Geometric Domain and Representation Schemes Triangle Meshes Curved BReps Constructive Solid Geometry Parameters, Constraints, and Features Variational Geometry Morphological Transformations and Analysis Human‐Shape Interaction Conclusions

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Loop detection in surface patch intersections

Cited by 130 publications

References 8 publications

Computational Methods for Geometric Processing. Applications to Industry

Computational Methods for Geometric Processing. Applications to Industry

Theoretically Based Robust Algorithms for Tracking Intersection Curves of Two Deforming Parametric Surfaces

Solid and Physical Modeling

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