Using signature sequences to classify intersection curves of two quadrics
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Cited by (20)
Topological classification of the intersection curves of two quadrics using a set of discriminants
2023, Computer Aided Geometric DesignContact detection between a small ellipsoid and another quadric
2022, Computer Aided Geometric DesignCitation Excerpt :These methods have been extended to other quadric surfaces Brozos-Vázquez et al. (2018, 2019) and exploited for practical uses, such as the detection of position for Unmanned Aerial Vehicles Castro et al. (2019); Dapena et al. (2017). The analysis of the intersection of quadrics was initiated much earlier (see Levin (1979)) and continues to be an active research field (see González-Vega and Trocado (2021); Jia et al. (2020); Pazouki et al. (2012); Tu et al. (2009); Wang et al. (2003, 2004); Wilf and Manor (1993) and references therein). Quadric surfaces allow to approximate very accurately a large variety of shapes.
Enumerating the morphologies of non-degenerate Darboux cyclides
2019, Computer Aided Geometric DesignCitation Excerpt :Quadric pair canonical form Since the two canonical quadratic forms are projectively equivalent to the original two quadratic forms, Tu et al. (2009) show the following result. The terminology “morphology” in Tu et al. (2009) takes topology, real and imaginary components, types and numbers of singularities into account.
Classification of the relative positions between a small ellipsoid and an elliptic paraboloid
2019, Computer Aided Geometric DesignCitation Excerpt :Consequently, other more complicated relative positions that include multiple tangent points or intersections in curves with two connected components are excluded by this hypothesis. If the reader is interested just in the intersection curves of all the possible cases, we refer to Jia et al. (2016), Levin (1979), Tu et al. (2009), Wang et al. (2003). The “smallness” hypothesis can be phrased in terms of principal curvatures of the surfaces: the smallest principal curvature in the ellipsoid is greater than the largest principal curvature of the elliptic paraboloid (which is attained at the vertex point).
Continuous detection of the variations of the intersection curve of two moving quadrics in 3-dimensional projective space
2016, Journal of Symbolic ComputationCitation Excerpt :Hence quadrics have widely been used in CAD/CAM and industrial manufacture, where 3D shapes are frequently defined by piecewise quadrics (Wang, 2002; Yan et al., 2012). The intersection curve of two quadrics (QSIC) has attracted particular attention since it contributes to the boundary detection of 3D shapes defined by quadric patches in geometric modeling or industry design (Levin, 1979; Wang et al., 2003; Dupont et al., 2008a, 2008b, 2008c; Tu et al., 2009). Our work can be seen as a deeper extension of collision detection, which detect the variations in the algebraic property and topology (brief as ‘type’) of QSIC of two quadrics that are moving or deforming.
Continuous collision detection for composite quadric models
2014, Graphical Models