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Four point parabolic interpolation

Michael A. Lachance, Arthur J. Schwartz
1991 Computer Aided Geometric Design  
Four point parabolic interpolation, Computer Aided Geometric Design 8 (1991) 143-149.  ...  We show that four points in the plane may be interpolated by one or two parabolas or possibly by no parabola, depending on the configuration of points.  ...  For q defined above q, + q2 + q3 = 1 and q, = 0 if and only if Q is collinear with Q, and Qk, the points distinct from Q,. We turn our attention to the four point interpolation problem.  ... 
doi:10.1016/0167-8396(91)90039-e fatcat:4yztmzk7yzh3rbxfjeqfxrxtgq

A simple technique for adding tension to parabolic blending interpolation

W. Schneider
1986 Computers and Mathematics with Applications  
Rodin A~tract--An extension of Overhauser's parabolic blending interpolation is given by introducing a tension-like behaviour to the interpolation curves.  ...  This is achieved by pulling Overhauser's parabolas towards the chords between the data points by means of straightness factors, and establishing at the same time the smoothness of the interpolation curves  ...  As a final example, Fig. 6 gives an f~ = 0.5 modified parabola interpolation, again for four data points (convex case).  ... 
doi:10.1016/0898-1221(86)90019-2 fatcat:nowg43xvyrgzzofvc3s3pnhoa4

Interpolating sampled contours in 3-D: analyses of variability and bias

Paul A. Warren, Laurence T. Maloney, Michael S. Landy
2002 Vision Research  
We varied (1) contour type (linear or parabolic), (2) orientation of the plane containing the contour and (3) the number of points on a sampled contour.  ...  Interpolation performance was very accurate, comparable to results from Vernier tasks. Setting variability was highest along the line of sight and for the parabolic contour.  ...  of parabolic interpolation between four and eight points (now that eight points fall within the curvilinear interpolation area).  ... 
doi:10.1016/s0042-6989(02)00266-3 pmid:12367742 fatcat:m4giwioc2vezxnii2ogezxjh2u

A piecewise parabolic C1 approximation technique for curved boundaries

Robin J.Y. McLeod, A.R. Mitchell
1979 Computers and Mathematics with Applications  
The four degrees of freedom are specified locally by Hermite interpolation. This piecewise curve approximation can then be thought of as a locally defined C' spline.  ...  It is essential that such points are chosen as nodes, since a parabola does not have an inflexion point. Each parabolic arc has four degrees of freedom.  ...  There are four inflexion points and the approximation (solid line) comprises eight parabolic arcs. Fig. 3 . 3 The digitisation produced 219 data points.  ... 
doi:10.1016/0898-1221(79)90088-9 fatcat:3eptuhpyfney3nalzychb5im4u

Interpolation methods for time-delay estimation using cross-correlation method for blood velocity measurement

Xiaoming Lai, H. Torp
1999 IEEE Transactions on Ultrasonics, Ferroelectrics and Frequency Control  
In this study, four different methods are suggested to improve the estimation accuracy: (1) Parabolic interpolation with bias-compensation, derived from a theoretical signal model. (2) Parabolic interpolation  ...  combined with linear filter interpolation of the correlation function. (3) Parabolic interpolation to the complex correlation function envelope. (4) Matched filter interpolation applied to the correlation  ...  Parabolic-fit Interpolation Combined with Linear Filter Interpolation The parabolic-fit interpolation uses a few correlation coefficients in the vicinity of the maximum discrete point.  ... 
doi:10.1109/58.753016 pmid:18238424 fatcat:yqfdzlik3zcxla7mpk3qanvbie

Page 102 of American Society of Civil Engineers. Proceedings of the American Society of Civil Engineers Vol. 87, Issue HY4 [page]

1961 American Society of Civil Engineers. Proceedings of the American Society of Civil Engineers  
Linear interpolation is based on two adjacent points, parabolic on three. There are, thus, two intervals between points in which interpolation can be ac- complished.  ...  Continuous parabolic interpolation is accomplished with a 3-point solution equivalent to fitting a simple parabola.  ... 

Interpolating sampled contours in 3D: perturbation analyses

Paul A. Warren, Laurence T. Maloney, Michael S. Landy
2004 Vision Research  
In four experiments, observers interpolated parabolic sampled contours confined to planes in three-dimensional space.  ...  Influence fell rapidly to zero as distance from the interpolated point increased, indicating that human visual interpolation of parabolic contours is local.  ...  Adding extra points beyond the three or four used for parabolic interpolation did not enhance performance.  ... 
doi:10.1016/j.visres.2003.11.007 pmid:14967207 fatcat:3t2hmfcinvd5pes6qyqqrnwwlq

Influence function for visual interpolation

Alex K. Hon, Laurence T. Maloney, Michael S. Landy, Bernice E. Rogowitz, Thrasyvoulos N. Pappas
1997 Human Vision and Electronic Imaging II  
We present three experiments in which observers were asked to interpolate parabolic sampled contours.  ...  visible points contributed to the interpolation judgment.  ...  Their interpolated points lay very close to the unique, invisible, parabolic contour containing the points that the experimenters had selected.  ... 
doi:10.1117/12.274538 dblp:conf/hvei/HonML97 fatcat:tdexmcq3dfgcrfojym6iebor6q

A PSF-Shape-Based Beamforming Strategy for Robust 2D Motion Estimation in Ultrafast Data

Anne Saris, Stein Fekkes, Maartje Nillesen, Hendrik Hansen, Chris de Korte
2018 Applied Sciences  
The proposed methodology was compared to data beamformed on a conventionally spaced grid, combined with the commonly used 1D parabolic interpolation.  ...  It describes a novel approach for determining the sampling grid for ultrafast data based on the system's point-spread-function (PSF).  ...  Large bias, SD and RMSE values were found when 1D parabolic interpolation was used for CCF interpolation.  ... 
doi:10.3390/app8030429 fatcat:m3q6urbnvra5lfi5kw3hkhfjdi

Page 3098 of American Society of Civil Engineers. Collected Journals Vol. 117, Issue 10 [page]

1991 American Society of Civil Engineers. Collected Journals  
Although the variation is parabolic, very little error is introduced by in- stalling only one linear interpolation point (at the 0.2-point) between the cusp and midspan.  ...  Recalling that interpolating above the parabolic variation between two relative span stations in the three-span bridge may overestimate the moment ratio by up to 6%, one may obtain a value for the four-span  ... 

Novel Embedding Secrecy within Images Utilizing an Improved Interpolation-Based Reversible Data Hiding Scheme

Fatuma Saeid Hassan, Adnan Gutub
2020 Journal of King Saud University: Computer and Information Sciences  
We investigated the interpolation techniques improving the parabolic interpolation (PI) method to scale-up the original image, then embedding within it the secret data using newly proposed embedding technique  ...  On the other hand, the proposed circle interpolation (CIRI) achieved less PSNR value than PI showing interesting remarks.  ...  The scheme used four interpolation techniques that were proposed as variation of the given parabolic interpolation PI in the literature.  ... 
doi:10.1016/j.jksuci.2020.07.008 fatcat:pdd5nn4xd5hsfpi5yf64ylqa2u

Study on Dune Morphology in Computer Mapping Based on 3S Technology [chapter]

Zhidan Ba
2021 Frontiers in Artificial Intelligence and Applications  
The result shows that the parabolic dune showed U shape in plane, and dune arms point to the west which was also wind direction.  ...  Take the parabolic dune of Hobq desert in Inner Mongolia as research object.  ...  to the query point and applies weights to these samples proportionally based on the region size to interpolate.  ... 
doi:10.3233/faia210391 fatcat:oh52fqfquzcd7hhtuixgz4mkhu

A novel interpolation strategy for estimating subsample speckle motion

Beth J Geiman, Laurence N Bohs, Martin E Anderson, Sean M Breit, Gregg E Trahey
2000 Physics in Medicine and Biology  
Computer simulations were performed to compare grid slopes with two conventional interpolation schemes, parabolic fit and cubic spline.  ...  Results of computer simulations show that parabolic fit and cubic spline performed poorly at translations greater than 0.5 samples, and translations less than 0.5 samples were subject to an estimation  ...  We therefore chose to evaluate parabolic interpolation, as well as the more common method for interpolation of three points, cubic spline.  ... 
doi:10.1088/0031-9155/45/6/310 pmid:10870709 fatcat:wiv4ls7ojbavfnaujccti5zceu

Page 1157 of SMPTE Motion Imaging Journal Vol. 91, Issue 12 [page]

1982 SMPTE Motion Imaging Journal  
The op- timum parabola interpolator (based on four points) appeared to perform bet- ter than a cubic algorithm passing through the same four samples.  ...  The implementation of parabolic interpolators can be further simplified in the case where N is a power of two, say 2’.  ... 

Finite Element and Finite Difference Methods for Elliptic and Parabolic Differential Equations [chapter]

Aklilu T. G. Giorges
2011 Numerical Analysis - Theory and Application  
The interpolation functions for a linear rectangular element with four nodes are defined in (Eq. 12).  ...  For simplicity, we use a linear rectangular element with four nodes and also we use a matrix notation ( ) to represent all nodal points of the elements instead of writing each node point contribution.  ...  Finite Element and Finite Difference Methods for Elliptic and Parabolic Differential Equations, Numerical Analysis -Theory and Application, Prof.  ... 
doi:10.5772/23839 fatcat:y5dc5fbnh5gr5l3mi4cqdgx6qy
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