Constrained Interpolation And Shape Preserving Approximation By Space Curves [QA297.6. K82 2006 f rb].

Dua jenis masalah rekabentuk lengkung telah ipertimbangkan. Terlebih dahulu kami mempertimbangkan interpolasi satu set titik data ruang yang bertertib dengan satu lengkung licin tertakluk kepada satu set satah kekangan yang berbentuk terhingga atau tak terhingga di mana garis cebis demi cebis yang menyambung titik data secara berturutan tidak bersilang dengan satah kekangan. Two types of curve designing problem have been considered. We first consider the interpolation of a given set of ordered spatial data points by a smooth curve in the presence of a set of finite or infinite constraint planes, where the polyline joining consecutive data points does not intersect with the constraint planes

Shape Preserving Interpolation Using C

This paper discusses the construction of new C2 rational cubic spline interpolant with cubic numerator and quadratic denominator. The idea has been extended to shape preserving interpolation for positive data using the constructed rational cubic spline interpolation. The rational cubic spline has three parameters αi, βi, and γi. The sufficient conditions for the positivity are derived on one parameter γi while the other two parameters αi and βi are free parameters that can be used to change the final shape of the resulting interpolating curves. This will enable the user to produce many varieties of the positive interpolating curves. Cubic spline interpolation with C2 continuity is not able to preserve the shape of the positive data. Notably our scheme is easy to use and does not require knots insertion and C2 continuity can be achieved by solving tridiagonal systems of linear equations for the unknown first derivatives di, i=1,…,n-1. Comparisons with existing schemes also have been done in detail. From all presented numerical results the new C2 rational cubic spline gives very smooth interpolating curves compared to some established rational cubic schemes. An error analysis when the function to be interpolated is ft∈C3t0,tn is also investigated in detail

Positivity Preserving Interpolation Using Rational Bicubic Spline

This paper discusses the positivity preserving interpolation for positive surfaces data by extending the C1 rational cubic spline interpolant of Karim and Kong to the bivariate cases. The partially blended rational bicubic spline has 12 parameters in the descriptions where 8 of them are free parameters. The sufficient conditions for the positivity are derived on every four boundary curves network on the rectangular patch. Numerical comparison with existing schemes also has been done in detail. Based on Root Mean Square Error (RMSE), our partially blended rational bicubic spline is on a par with the established methods

Technology roadmap for flexible sensors

Humans rely increasingly on sensors to address grand challenges and to improve quality of life in the era of digitalization and big data. For ubiquitous sensing, flexible sensors are developed to overcome the limitations of conventional rigid counterparts. Despite rapid advancement in bench-side research over the last decade, the market adoption of flexible sensors remains limited. To ease and to expedite their deployment, here, we identify bottlenecks hindering the maturation of flexible sensors and propose promising solutions. We first analyze challenges in achieving satisfactory sensing performance for real-world applications and then summarize issues in compatible sensor-biology interfaces, followed by brief discussions on powering and connecting sensor networks. Issues en route to commercialization and for sustainable growth of the sector are also analyzed, highlighting environmental concerns and emphasizing nontechnical issues such as business, regulatory, and ethical considerations. Additionally, we look at future intelligent flexible sensors. In proposing a comprehensive roadmap, we hope to steer research efforts towards common goals and to guide coordinated development strategies from disparate communities. Through such collaborative efforts, scientific breakthroughs can be made sooner and capitalized for the betterment of humanity.Agency for Science, Technology and Research (A*STAR)National Research Foundation (NRF)Submitted/Accepted versionY.L., Z.L., M.Z., and X.C. acknowledge the National Research Foundation, Singapore (NRF) under NRF’s Medium Sized Centre: Singapore Hybrid-Integrated Next-Generation μElectronics (SHINE) Centre funding programme, and AME programming funding scheme of Cyber Physiochemical Interface (CPI) project (no. A18A1b0045). Y.L. acknowledges National Natural Science Foundation of China (62201243). C.J. acknowledges funding support from the National Key R&D Program of China (no. 2019YFA0706100), the National Natural Science Foundation of China (82151305), Lingang Laboratory (LG-QS-202202-09). T.Q.T. and N.E.L. acknowledge support by the Basic Science Research Program (no. 2020R1A2C3013480) through the National Research Foundation of Korea (NRF) funded by the Ministry of Science and ICT. A.F. acknowledges the AFOSR (grant FA9550-22-1-0423). Y.L. and Y.Z. would like to acknowledge the NSF (award no. 2134664) and NIH (award no. R01HD108473) for financial support. X.F. acknowledges the support from the National Natural Science Foundation of China (grant no. U20A6001). L.Y. would like to thank the A*STAR Central Research Fund (CRF) and the AME Programmatic A18A1b0045 (Cyber Physiochemical Interfaces) for funding support. C.F.G. acknowledges the National Natural Science Foundation of China (no. T2225017). T.Q.T. acknowledges the Brain Pool Program (No. 2020H1D3A2A02111068) through the National Research Foundation (NRF) funded by the Ministry of Science. Z.L. acknowledges the support from RIE2020 AME Programmatic Grant funded by A*STAR-SERC, Singapore (Grant No. A18A1b0045). X.G. acknowledges funding support through the Shanghai Science and Technology Commission (grant no. 19JC1412400), the National Science Fund for Excellent Young Scholars (grant no. 61922057). C.D. acknowledges National Science Foundation CAREER: Conformable Piezoelectrics for Soft Tissue Imaging (grant no. 2044688) and MIT Media Lab Consortium funding. D.K. and O.G.S. acknowledge Leibniz Association and the German Research Foundation DFG (Gottfried Wilhelm Leibniz Program SCHM 1298/22-1, KA5051/1-1 and KA 5051/3-1), as well as the Leibniz association (Leibniz Transfer Program T62/2019). C.W. acknowledges the National Key Research and Development Program of China (grant no. 2021YFA1202600), National Natural Science Foundation of China (grant no. 62174082). A.V.-Y.T., E.Z., Y.Z., X.Z., and J.P. acknowledge the National Research Foundation, Singapore (NRF) under NRF’s Medium Sized Centre: Singapore Hybrid-Integrated Next-Generation μElectronics (SHINE) Centre funding programme, and AME programming funding scheme of Cyber Physiochemical Interface (CPI) project (no. A18A1b0045). R.Z. acknowledges National Natural Science Foundation of China (grant no. 51735007) and Beijing Natural Science Foundation (grant no. 3191001). N.M. acknowledges the support by JST PRESTO Grant Number JPMJPR20B7 and JST Adaptable and Seamless Technology transfer Program through Target-driven R&D (ASTEP) grant number JPMJTM22BK. C.P. acknowledges the Korean government (Ministry of Science and ICT, MSIT) (2022R1A4A3032923). M.W. acknowledges the National Key R&D Program of China under Grant (2021YFB3601200). X.Z. acknowledges National Natural Science Foundation of China (no. 62074029). S.X. acknowledges the 3M nontenured faculty award. T.-W.L. and D.-G.S. acknowledge the Pioneer Research Center Program through the National Research Foundation of Korea funded by the Ministry of Science, ICT & Future Planning (grant no. NRF-2022M3C1A3081211). C.T.L. would like to acknowledge support from the Institute for Health Innovation and Technology (iHealthtech), the MechanoBioEngineering Laboratory at the Department of Biomedical Engineering and the Institute for Functional Intelligent Materials (I-FIM) at the National University of Singapore (NUS). C.T.L. also acknowledges support from the National Research Foundation and A*STAR, under its RIE2020 Industry Alignment Fund − Industry Collaboration Projects (IAF-ICP) (grant no. I2001E0059) − SIA-NUS Digital Aviation Corp Lab and the NUS ARTIC Research (grant no. HFM-RP1). X.Y. acknowledges funding support by City University of Hong Kong (grant no. 9667221). T.X. and X.Z. acknowledge National Natural Science Foundation of China (22234006). B.C.K.T. acknowledges Cyber-Physiochemical Interfaces CPI, A*STAR A18A1b0045. H.G. acknowledges a research start-up grant (002479-00001) from Nanyang Technological University and the Agency for Science, Technology and Research (A*STAR) in Singapore. W.G. acknowledges National Science Foundation grant 2145802. D.J.L. acknowledges support from the US National Science Foundation grant number CBET-2223566. G.Y. acknowledges support from The Welch Foundation award F-1861, and Camille Dreyfus Teacher-Scholar Award. M.D.D. acknowledges funding support from NSF (grant no. EEC1160483). J.-H.A acknowledges the National Research Foundation of Korea (NRF-2015R1A3A2066337). J.C. acknowledges the Henry Samueli School of Engineering & Applied Science and the Department of Bioengineering at the University of California, Los Angeles for startup support and a Brain & Behavior Research Foundation Young Investigator Grant. K.T. acknowledges JST AIP Accelerated Program (no. JPMJCR21U1) and JSPS KAKENHI (grant no. JP22H00594). P.S.W. acknowledges the National Science Foundation (CMMI1636136) for support. A.M.A., M.C.H., and P.S.W. thank the National Institute on Drug Abuse (DA045550) for support. S.M. and X.C. appreciated the support from the Smart Grippers for Soft Robotics (SGSR) Programme under the National Research Foundation, Prime Minister’s Office, Singapore under its Campus of Research Excellence and Technological Enterprise (CREATE) programme