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Lagrange Piecewise-Quadratic Interpolation Based on Planar Unordered Reduced Data
[chapter]
2015
Lecture Notes in Computer Science
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Once the order on points is imposed a piecewise-quadratic interpolationγ2 combined with the socalled cumulative chords is used to fit unordered reduced data. ...
The latter coincides with already established asymptotics derived for γ estimation via piecewise-quadratic interpolation based on ordered reduced data and cumulative chords. ...
In doing so, first an Algorithm 1 for generating an interpolation schemeγ 2 based on planar unordered reduced data setQ m = {q i } m i=0 is introduced. ...
doi:10.1007/978-3-319-24369-6_35
fatcat:lhoy5tovqvcrdinfffls35t2ji
Multidimensional curve fitting to unorganized data points by nonlinear minimization
1995
Computer-Aided Design
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The paper presents a method for generating a piecewise continuous parametric curve from a set of unordered and error-filled data points. ...
Successive quadratic programming is applied to find the optimal solution. A physical model is also supplied to facilitate an intuitive understanding of the mathematical background. ...
The paper presents a method for generating a piecewise continuous parametric curve from a set of unordered and error-filled data points. ...
doi:10.1016/0010-4485(95)90752-2
fatcat:byxmopfuxvberday6nbbbnbuti
DesigningN-PolyVector Fields with Complex Polynomials
2014
Computer graphics forum (Print)
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We show how to compute smooth N-PolyVector fields with prescribed bounds on angles. 3. We show how to compute conjugate N-PolyVector fields for remeshing with planar elements. ...
Such fields are necessary in the remeshing of surfaces using planar quad (PQ) and planar hexagonal elements. ...
The problem reduces to projecting u 0 , v 0 on the quadric parametrized by H, which is a specific quadraticallyconstrained quadratic program problem. ...
doi:10.1111/cgf.12426
fatcat:egi3mzoxhbeqtg3dn4mfhtyynu
Quadratic Serendipity Finite Elements on Polygons Using Generalized Barycentric Coordinates
[article]
2012
arXiv
pre-print
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We introduce a finite element construction for use on the class of convex, planar polygons and show it obtains a quadratic error convergence estimate. ...
On a convex n-gon satisfying simple geometric criteria, our construction produces 2n basis functions, associated in a Lagrange-like fashion to each vertex and each edge midpoint, by transforming and combining ...
Harmonic coordinates λ Har are defined as the solution to Laplace's equation on the polygon with piecewise linear boundary data satisfying B6 [21, 25, 7] . ...
arXiv:1109.3259v2
fatcat:7ahznwvzund3rjafraxjoh5udq
Quadratic serendipity finite elements on polygons using generalized barycentric coordinates
2014
Mathematics of Computation
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We introduce a finite element construction for use on the class of convex, planar polygons and show it obtains a quadratic error convergence estimate. ...
On a convex n-gon satisfying simple geometric criteria, our construction produces 2n basis functions, associated in a Lagrange-like fashion to each vertex and each edge midpoint, by transforming and combining ...
Harmonic coordinates λ Har are defined as the solution to Laplace's equation on the polygon with piecewise linear boundary data satisfying B6 [21, 25, 7] . ...
doi:10.1090/s0025-5718-2014-02807-x
fatcat:uz26lzmadrhdlev6ygzxy6z3vy
QUADRATIC SERENDIPITY FINITE ELEMENTS ON POLYGONS USING GENERALIZED BARYCENTRIC COORDINATES
2014
Mathematics of Computation
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We introduce a finite element construction for use on the class of convex, planar polygons and show it obtains a quadratic error convergence estimate. ...
On a convex n-gon, our construction produces 2n basis functions, associated in a Lagrange-like fashion to each vertex and each edge midpoint, by transforming and combining a set of n(n + 1)/2 basis functions ...
Harmonic coordinates λ Har are defined as the solution to Laplace's equation on the polygon with piecewise linear boundary data satisfying B6 [7, 21, 25] . ...
pmid:25301974
pmcid:PMC4188447
fatcat:ena5fkz4dvd3jkkkv5rca437c4
Reduction and decomposition of differential automata: Theory and applications
[chapter]
1998
Lecture Notes in Computer Science
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by unevenly spaced
points, Lagrange interpolation formula, Divided Difference, Newton's
General interpolation Formula. ...
SIMULINK (and/or similar package) based experiments on graphical
synthesis of systems; Control synthesis for typical dynamical systems. ...
doi:10.1007/3-540-64358-3_48
fatcat:hqwvar3zbfftdhg4cybpjwogde
Fitting curves and surfaces to point clouds in the presence of obstacles
2009
Computer Aided Geometric Design
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We examine two families of obstacles: first, the point cloud itself is interpreted as obstacle, e.g. to reconstruct any apparant boundaries of the data set. ...
Therefore, we describe the fitting problem as optimization problem and employ an iterative procedure to solve it -the presence of obstacles poses constraints on this minimization process. ...
(Lin and Wang, 2002) tightly border planar point clouds resembling curves by B-spline interpolation of their boundary points. ...
doi:10.1016/j.cagd.2008.04.003
fatcat:4iritpxk7fhftbl3qxvzgwqjgm
Stable Simplex Spline Bases for $$C^3$$ C 3 Quintics on the Powell–Sabin 12-Split
2016
Constructive approximation
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The bases are stable in the L∞ norm with a condition number independent of the geometry, have a well-conditioned Lagrange interpolant at the domain points, and a quasi-interpolant with local approximation ...
For the space of C 3 quintics on the Powell-Sabin 12-split of a triangle, we determine explicitly the six symmetric simplex spline bases that reduce to a B-spline basis on each edge, have a positive partition ...
simplex spline bases B of S 3 5 that reduce to a Bspline basis on the boundary. ...
doi:10.1007/s00365-016-9332-8
fatcat:4kuwtttjyzdk3cdlhgobdltwwu
Stable simplex spline bases for C^3 quintics on the Powell-Sabin 12-split
[article]
2015
arXiv
pre-print
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The bases are stable in the L_∞ norm with a condition number independent of the geometry, have a well-conditioned Lagrange interpolant at the domain points, and a quasi-interpolant with local approximation ...
For the space of C^3 quintics on the Powell-Sabin 12-split of a triangle, we determine explicitly the six symmetric simplex spline bases that reduce to a B-spline basis on each edge, have a positive partition ...
Hence, there is a well-conditioned Lagrange interpolant at the domain points of the basis B c . ...
arXiv:1504.02628v2
fatcat:ufp3d4exsrgfxgadqcttrnu6ve
Survey on sparsity in geometric modeling and processing
2015
Graphical Models
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However, sparsity based methods in geometric processing is far from popular than its applications in these areas. ...
This review paper highlights a few representative examples of how the interaction between sparsity based methods and geometric processing can enrich both fields, and raises a number of open questions for ...
In LOP/WLOP, the majority of the time is spent on the evaluation of the attractive forces from all points in P, Preiner et al. [19] efficiently reduce the set P of unordered input points to a much more ...
doi:10.1016/j.gmod.2015.06.012
fatcat:owpftxk3ivdp3a7dnzxhz2xvxm
14th International Symposium on Mathematical Programming
1990
Mathematical programming
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Keywords: Lagrange interpolation -Richardson extrapolation -optimization methods One of the intriguing problems of interpolation theory posed by Erd os in 1961 is the problem of nding a set of interpolation ...
Our approach is particularly well suited for special classes of graphs such as planar graphs and graphs based on grid structures. ...
basis : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : 276 reduced cost xing : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : 118 reduced order systems ...
doi:10.1007/bf01580875
fatcat:3jtclwmntzgjxkqs5uecombdaa
Symmetry-preserving discretization of variational field theories
[article]
2015
arXiv
pre-print
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The present paper develops a variational theory of discrete fields defined on abstract cellular complexes. ...
The discrete formulation is derived solely from a variational principle associated to a discrete Lagrangian density on a discrete bundle, and developed up to the notion of symmetries and conservation laws ...
data. ...
arXiv:1509.08750v1
fatcat:s6fdgk7mkzgpvlidj5q5qqvkiy
A penalized likelihood approach to image warping
2001
Journal of The Royal Statistical Society Series B-statistical Methodology
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A conjugate gradient algorithm is used to estimate the warping function, which is numerically approximated by a piecewise bilinear function. ...
Fourier±von Mises image model We thank Professor Dryden for generalizing our result on the distribution of Y f , conditional on A Y f , when Y f is a Gaussian random ®eld. ...
In the paper we focused on point estimation and were concerned about computing time, so we did no more than to point out the opportunities for a Bayesian approach. ...
doi:10.1111/1467-9868.00295
fatcat:t7nswwlnlrf3div7z5wcklgzgm
Interactive numerical flow visualization using stream surfaces
1990
Computing Systems in Engineering
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The balance of my committee, Fred Brooks, James Coggins, and Henry Fuchs, allowed me the freedom to pursue my research on the other end of the country. I thank each of them very much. ...
Trilinear Interpolation Most flow visualization software uses a cell-local trilinear interpolating function. This produces a piecewise-linear reconstruction of the ideal flow field. ...
This copying isolates the interpolation software from the format of the data files, it reduces the time required to interpolate field values at successive query points in the same cell, and it supports ...
doi:10.1016/0956-0521(90)90021-c
fatcat:he3jcf3wzff2pervtrhsxwuvu4
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