The not-a-knot piecewise interpolatory cubic polynomial

Behforooz, G.

doi:10.1016/0096-3003(92)90096-j

Cited by 7 publications

(3 citation statements)

References 7 publications

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“…Its second derivatives have continuous variation. Continuous third derivative is also obtainable with respect to some round-off error (Behforooz, 1992). CR spline approximation is the third type of the Hermite interpolation method, and it benefits from a balanced flatness.…”

Section: Thrust Profile Approximationmentioning

confidence: 99%

Trajectory optimization of space vehicle in rendezvous proximity operation with evolutionary feasibility conserving techniques

Shirazi

Ceberio

Lozano

2023

Engineering Applications of Artificial Intelligence

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Section: Thrust Profile Approximationmentioning

confidence: 99%

Trajectory optimization of space vehicle in rendezvous proximity operation with evolutionary feasibility conserving techniques

Shirazi

Ceberio

Lozano

2023

Engineering Applications of Artificial Intelligence

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“…

is the exposure quality corresponding to the exposure time t . Different from the conventional cubic spline interpolation method, the boundary condition of the spline curve in this paper is the Not-A-Knot [ 23 ]:

where

indicates the third derivative of the curve at point

.…”

Section: Proposed Algorithmmentioning

confidence: 99%

An Automatic Exposure Method of Plane Array Remote Sensing Image Based on Two-Dimensional Entropy

Gao

Zheng

et al. 2021

Sensors

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The improper setting of exposure time for the space camera will cause serious image quality degradation (overexposure or underexposure) in the imaging process. In order to solve the problem of insufficient utilization of the camera’s dynamic range to obtain high-quality original images, an automatic exposure method for plane array remote sensing images based on two-dimensional entropy is proposed. First, a two-dimensional entropy-based image exposure quality evaluation model is proposed. The two-dimensional entropy matrix of the image is partitioned to distinguish the saturated areas (region of overexposure and underexposure) and the unsaturated areas (region of propitious exposure) from the original image. The ratio of the saturated area is used as an evaluating indicator of image exposure quality, which is more sensitive to the brightness, edges, information volume, and signal-to-noise ratio of the image. Then, the cubic spline interpolation method is applied to fit the exposure quality curve to efficiently improve the camera’s exposure accuracy. A series of experiments have been carried out for different targets in different environments using the existing imaging system to verify the superiority and robustness of the proposed method. Compared with the conventional automatic exposure method, the signal-to-noise ratio of the image obtained by the proposed algorithm is increased by at least 1.6730 dB, and the number of saturated pixels is reduced to at least 2.568%. The method is significant to improve the on-orbit autonomous operating capability and on-orbit application efficiency of space camera.

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“…Thus the appropriate boundary conditions could be imposed on the model for any value of turbulence over the foil. The Not-a-Knot cubic spline interpolation, proposed by De Boor [27], was used as the type does not exert 'super-convergence' at the knot points. This is achieved through setting a boundary condition where two points either-side of the interval are set to be equal (eqn:F.23).…”

Section: F15 Evaluating Turbulence Depreciationmentioning

confidence: 99%

Tidal Energy and Coastal Models: Improved Turbine Simulation

Gwenter¹

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Marine renewable energy is a continually growing topic of both commercial and academic research sectors. While not as developed as other renewable technologies such as those deployed within the wind sector, there is substantial technological crossover coupled with the inherent high energy density of water, that has helped push marine renewables into the wider renewable agenda. Thus, an ever expanding range of projects are in various stages of development.As with all technological developments, there are a range of factors that can con-tribute to the rate of development or eventual success. One of the main difficulties, when looking at marine renewable technologies in a comparative view to other en-ergy generation technologies, is that the operational environment is physically more complex: Energy must be supplied in diverse physical conditions, that temporally fluctuate with a range of time scales. The constant questions to the iteration to the local ecology. The increased operational fatigue of deployed devices. The financial risk associated within a recent sector.This work presents the continual research related to the computational research development of different marine renewable technologies that were under develop-ment of several institutional bodies at the time of writing this document.The scope has a wide envelopment as the nature of novel projects means that the project failure rate is high. Thus, forced through a combination of reasons related to financial, useful purpose and intellectual property, the research covers distinct projects.

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The not-a-knot piecewise interpolatory cubic polynomial

Cited by 7 publications

References 7 publications

Trajectory optimization of space vehicle in rendezvous proximity operation with evolutionary feasibility conserving techniques

Trajectory optimization of space vehicle in rendezvous proximity operation with evolutionary feasibility conserving techniques

An Automatic Exposure Method of Plane Array Remote Sensing Image Based on Two-Dimensional Entropy

Tidal Energy and Coastal Models: Improved Turbine Simulation

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