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An observation of Jupiter's tidal response is anticipated for the ongoing Juno spacecraft mission. We combine self-consistent, numerical models of Jupiter's equilibrium tidal response with observed Doppler shifts from the Juno gravity science experiment to test the sensitivity of the spacecraft to tides raised by the Galilean satellites and the Sun. The concentric Maclaurin spheroid (CMS) method finds the equilibrium shape and gravity field of a rotating, liquid planet with the tide raised by a satellite, expanded in Love numbers (knm). We present improvements to the CMS theory that eliminate an unphysical center-of-mass offset and study in detail the convergence behavior of the CMS approach. We demonstrate that the dependence of knm with orbital distance is important when considering the combined tidal response for Jupiter. Conversely, the details of the interior structure have a negligible influence on knm for models that match the zonal harmonics J2, J4, and J6, already measured to high precision by Juno. As the mission continues, improved coverage of Jupiter’s gravity field at different phases of Io’s orbit is expected to yield an observed value for the degree-two Love number (k22) and potentially select higher-degree knm. We present a test of the sensitivity of the Juno Doppler signal to the calculated knm, which suggests the detectability of k33, k42, and k31, in addition to k22. A mismatch of a robust Juno observation with the remarkably small range in calculated Io equilibrium, k22 = 0.58976 ± 0.0001, would indicate a heretofore uncharacterized dynamic contribution to the tides. [ABSTRACT FROM AUTHOR]

In anticipation of improved observational data for Jupiter’s gravitational field, from the Juno spacecraft, we predict the static tidal response for a variety of Jupiter interior models based on ab initio computer simulations of hydrogen–helium mixtures. We calculate hydrostatic-equilibrium gravity terms, using the non-perturbative concentric Maclaurin Spheroid method that eliminates lengthy expansions used in the theory of figures. Our method captures terms arising from the coupled tidal and rotational perturbations, which we find to be important for a rapidly rotating planet like Jupiter. Our predicted static tidal Love number, , is ∼10% larger than previous estimates. The value is, as expected, highly correlated with the zonal harmonic coefficient J2, and is thus nearly constant when plausible changes are made to the interior structure while holding J2 fixed at the observed value. We note that the predicted static k2 might change, due to Jupiter’s dynamical response to the Galilean moons, and find reasons to argue that the change may be detectable—although we do not present here a theory of dynamical tides for highly oblate Jovian planets. An accurate model of Jupiter’s tidal response will be essential for interpreting Juno observations and identifying tidal signals from effects of other interior dynamics of Jupiter’s gravitational field. [ABSTRACT FROM AUTHOR]

3D reconstruction of arbitrary free-formed objects is an important and challenging problem in computer vision. In this paper, we first discuss the importance of primitive selection in 3D reconstruction. Subsequently, a theorem, which reveals the perspective invariance of NURBS, is shown, making it a good choice as primitive in 3D reconstruction. Consequently, based on this theorem a new paradigm of free-formed line-like object reconstruction using NURBS as primitives is proposed. Furthermore, an approach for determining weights for 3D NURBS is presented, and the width effect of curved line-like objects is analyzed. Finally, experiments with line-like objects and machine part demonstrate the feasibility of our approach and prove the superiority of our approach over the point- or segment-based approaches as well as the B-spline-based reconstruction approach in terms of robustness and accuracy. [Copyright &y& Elsevier]