Polar Interpolation Research Articles

FlexScale: Modeling and Characterization of Flexible Scaled Sheets

We present a computational approach for modeling the mechanical behavior of flexible scaled sheet materials---3D-printed hard scales embedded in a soft substrate. Balancing strength and flexibility, these structured materials find applications in protective gear, soft robotics, and 3D-printed fashion. To unlock their full potential, however, we must unravel the complex relation between scale pattern and mechanical properties. To address this problem, we propose a contact-aware homogenization approach that distills native-level simulation data into a novel macromechanical model. This macro-model combines piecewise-quadratic uniaxial fits with polar interpolation using circular harmonics, allowing for efficient simulation of large-scale patterns. We apply our approach to explore the space of isohedral scale patterns, revealing a diverse range of anisotropic and nonlinear material behaviors. Through an extensive set of experiments, we show that our models reproduce various scale-level effects while offering good qualitative agreement with physical prototypes on the macro-level.

A comprehensive study on natural characteristics and dynamic responses of a dual-rotor system with inter-shaft bearing under non-random uncertainty

Aeroengines are usually designed with a dual-rotor configuration for the rotating part. A dual-rotor system has coupling characteristics introduced by an inter-shaft bearing, and the rotating direction of the rotors has critical influences on the performance. It becomes more complicated when the inevitable uncertainties of the dual-frequency excited dynamical system are considered. This paper delivers a comprehensive study of the natural characteristics and dynamic responses of a dual-rotor system with an inter-shaft bearing considering the non-random parametric uncertainties under co- and counter-rotating conditions. To this end, the finite element modeling and the deterministic solutions of a dual-rotor system are established. Then, the polynomial surrogate function is constructed for the desired natural characteristics and dynamic responses under non-random uncertainty. The polar interpolation technique is implemented to compute uncertain shaft orbits, overcoming difficulties in the traditional frequency-sense measure. Intensive case studies for different interval uncertain parameters are carried out and the results are comparatively discussed. It is found that the mass unbalance uncertainties only affect the respective modes excited by the rotor where the unbalance is located. The shaft stiffness has global uncertainty effects on the Campbell diagram, mode shapes, time history, shaft orbit and responses. Uncertainties in the inter-shaft bearing stiffness and speed ratio generally influence higher-order modes. The results of the present work gain insights into the modal characteristics and dynamical behaviors of the dual-rotor system under complex parametric uncertainties.

3D Curve Generation Using Spherical Polar Piecewise Interpolation in CAD and CAM

In this paper a newly 3D path planning approach and curve generation for design and manufacturing efficiency is considered. The 3D path is generated by a combination of piecewise interpolating curves - along a given number of via-points - created via a spherical coordinate system specified by the polar angles, radial distances and the associated azimuthal angles. Each piecewise interpolating curve is constructed using Hermite polar interpolation in the projective polar plane and the rotating azimuthal plane. To verify the proposed approach, numerical simulations for the generation of a helix design, a 4 and 6 leaf design and a trajectory planning of a picking robot arm are conducted.

Optimal transport-based polar interpolation of directional fields

We propose an algorithm that interpolates between vector and frame fields on triangulated surfaces, designed to complement field design methods in geometry processing and simulation. Our algorithm is based on apolarconstruction, leveraging a conservation law from the Hopf-Poincaré theorem to match singular points using ideas from optimal transport; the remaining detail of the field is interpolated using straightforward machinery. Our model is designed with topology in mind, sliding singular points along the surface rather than having them appear and disappear, and it caters to all surface topologies, including boundary and generator loops.

Integrating Motion Compensation With Polar Format Interpolation for Enhanced Highly Squinted Airborne SAR Imagery

Spatial-variant motion compensation (MOCO) is critical for high resolution and highly squinted airborne synthetic aperture radar (SAR) imaging. Conventional imaging strategies generally perform systematic imaging algorithm and motion compensation algorithm in a separate way, the residual azimuth-variant motion error usually causes defocusing in the image. It is difficult for existing post-filtering strategies to realize high precision and high efficiency imaging simultaneously. To solve this problem, a novel parametric polar format algorithm (PPFA) is proposed in this paper. The polar format interpolation kernel is redefined and improved by inducing motion error parameter, so the proposed algorithm can realize fast imaging and precise spatial-variant motion compensation at the same time. The proposed algorithm has advantage of high processing efficiency as polar format algorithm (PFA) and effectively improves the focusing precision. Extensive comparisons with conventional algorithms illustrate the superiority of the proposed algorithm in both precision and efficiency.

Continuous basis compressive time‐delay estimation in overlapped echoes

High-accuracy time-delay estimation is basically noted in several research areas. L1-minimisation is a compressive sensing (CS) approach which solves this problem with high resolution and accuracy in the case of spars signals. Band excluded orthogonal matching pursuit is another CS method which uses a greedy algorithm to retrieve time delays and has lower complexity compared with the L1-minimisation method; however, it is only applicable when the signals are well spaced or orthogonal. Moreover, both approaches are established on a discrete basis which inherently limits their accuracy for the constraint on the sampling rate of the system. To mitigate these challenges in this study, the authors first incorporate the L1-minimisation method in a greedy algorithm to achieve a high resolution in the discrete grid. In the next step, to overcome the limitation caused by the sampling rate and refine the obtained time delays, the algorithm is combined with a complex continuous basis pursuit (CCBP) by using a polar interpolation. Their simulation and experiment results show that the proposed combination of L1-minimisation-CCBP can recover time delays in very closely spaced echoes not only with high accuracy but also with low computational time and sampling rate.

A Novel Motion Compensation Approach for Airborne Spotlight SAR of High-Resolution and High-Squint Mode

This letter proposes a new motion compensation approach for high-squint and high-resolution airborne spotlight synthetic aperture radar (SAR) integrated with polar format algorithm (PFA). The motion error is coarsely compensated by means of measuring systems. In PFA, the expressions of the line-of-sight polar interpolation are first explicitly revealed, and the nonsystematic range cell migration (NsRCM) induced by residual motion error is also corrected, which paves the way for autofocus application. After the NsRCM correction, the enhanced total least square estimator-based phase adjustment by contrast enhancement (PACE) algorithm is considered to account for the residual phase errors extended to the range-dependent case. The processing results of airborne SAR real data are presented to demonstrate the validity of the proposed algorithm.

Compressive Parameter Estimation for Sparse Translation-Invariant Signals Using Polar Interpolation

We propose new compressive parameter estimation algorithms that make use of polar interpolation to improve the estimator precision. Our work extends previous approaches involving polar interpolation for compressive parameter estimation in two aspects: (i) we extend the formulation from real non-negative amplitude parameters to arbitrary complex ones, and (ii) we allow for mismatch between the manifold described by the parameters and its polar approximation. To quantify the improvements afforded by the proposed extensions, we evaluate six algorithms for estimation of parameters in sparse translation-invariant signals, exemplified with the time delay estimation problem. The evaluation is based on three performance metrics: estimator precision, sampling rate and computational complexity. We use compressive sensing with all the algorithms to lower the necessary sampling rate and show that it is still possible to attain good estimation precision and keep the computational complexity low. Our numerical experiments show that the proposed algorithms outperform existing approaches that either leverage polynomial interpolation or are based on a conversion to a frequency-estimation problem followed by a super-resolution algorithm. The algorithms studied here provide various tradeoffs between computational complexity, estimation precision, and necessary sampling rate. The work shows that compressive sensing for the class of sparse translation-invariant signals allows for a decrease in sampling rate and that the use of polar interpolation increases the estimation precision.

The Application of the Principle of Chirp Scaling in Processing Stepped Chirps in Spotlight SAR

A new approach to process stepped chirps in spotlight synthetic aperture radar is presented in this letter, which is based on exploiting the principle of chirp scaling (PCS). In particular, PCS is integrated into the polar format algorithm (PFA), obtaining a more efficient solution compared with the existing polar interpolation technique. The main contribution of this letter is the implementation of azimuth scaling, in which the bandwidth synthesis is embedded. The algorithm is developed dedicatedly for dealing with stepped chirps. The signal processing flow is investigated in detail, in which no interpolations but only fast Fourier transform and complex multiplications are involved. Point-target simulation has validated the new approach and indicated that it is more efficient than the classic interpolation-based one. The achieved computational gain measured in execution time is around 25%-30%.

A fast iterative physical optics (FIPO) algorithm based on non‐uniform polar grid interpolation

AbstractIn this paper, a novel fast iterative physical optics (FIPO) algorithm is proposed for analysis of scattering from electrically large objects involving multiple reflections such as the case for open‐ended cavities. At each iteration, the physical optics current induced on the surface of the scatterer produces a correction to the incident field, which in turn induces a correction to the physical optics current. The FIPO algorithm relies on fast field evaluation, which is achieved via domain decomposition of the scatterer surface and comprises two steps repeated for each subdomain. First, computation of the field is produced by currents residing within a subdomain over a sparse set of points surrounding the scatterer. Second, phase removal, interpolation, phase restoration, and aggregation of the field of the subdomain are integrated into the total field on the surface. The proposed approach can be extended to fast iterative solution of problems discretized via the method of moments. © 2002 Wiley Periodicals, Inc. Microwave Opt Technol Lett 35: 240–244, 2002; Published online in Wiley InterScience (www.interscience.wiley.com). DOI 10.1002/mop.10568

On the modifier chirp z transform for synthetic aperture radar systems

A modified chirp z-transform (MCZT) algorithm which has been proposed by W. Lawton (IEEE Trans. Acoust., Speech, Signal Processing, vol.ASSP-36, p.931-3, June 1988) to replace the conventional polar format interpolation in synthetic aperture radar (SAR) systems is discussed. The key assumption used in the MCZT approach is that the spatial-frequency samples can be obtained on a concentric squares (CS) grid. The CS grid is briefly reviewed. The conventional approach to processing CS grid data is described. The MCZT is discussed, and its disadvantages are emphasized. >

Comments and corrections on the use of polar sampling theorems in CT

In two recent papers, an exact polar interpolation formula was used to reconstruct computer tomography (CT) imagery by a procedure known as direct Fourier transform inversion. The resulting imagery compared favorably to CT imagery reconstructed by filtered convolution back projection. Strictly speaking, however, the interpolation formula was inappropriately used since it is valid only for an odd number of azimuthal samples while in CT one uses an even number of samples. When the number of samples N is large (say > 200 as in CT) the error is not noticeable and the appropriateness of the formula has no practical significance. However, when N is small, a large error can result. We derive, in this paper, exact azimuthal interpolation formulas for N even and arbitrary N.