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Lagrange Piecewise-Quadratic Interpolation Based on Planar Unordered Reduced Data
[chapter]

2015
*
Lecture Notes in Computer Science
*

Once the order

doi:10.1007/978-3-319-24369-6_35
fatcat:lhoy5tovqvcrdinfffls35t2ji
*on*points is imposed a*piecewise*-*quadratic**interpolation*γ2 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. ...##
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Multidimensional curve fitting to unorganized data points by nonlinear minimization

1995
*
Computer-Aided Design
*

The paper presents a method for generating a

doi:10.1016/0010-4485(95)90752-2
fatcat:byxmopfuxvberday6nbbbnbuti
*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. ...##
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DesigningN-PolyVector Fields with Complex Polynomials

2014
*
Computer graphics forum (Print)
*

We show how to compute smooth N-PolyVector fields with prescribed bounds

doi:10.1111/cgf.12426
fatcat:egi3mzoxhbeqtg3dn4mfhtyynu
*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. ...##
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Quadratic Serendipity Finite Elements on Polygons Using Generalized Barycentric Coordinates
[article]

2012
*
arXiv
*
pre-print

We introduce a finite element construction for use

arXiv:1109.3259v2
fatcat:7ahznwvzund3rjafraxjoh5udq
*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] . ...##
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Quadratic serendipity finite elements on polygons using generalized barycentric coordinates

2014
*
Mathematics of Computation
*

We introduce a finite element construction for use

doi:10.1090/s0025-5718-2014-02807-x
fatcat:uz26lzmadrhdlev6ygzxy6z3vy
*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] . ...##
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QUADRATIC SERENDIPITY FINITE ELEMENTS ON POLYGONS USING GENERALIZED BARYCENTRIC COORDINATES

2014
*
Mathematics of Computation
*

We introduce a finite element construction for use

pmid:25301974
pmcid:PMC4188447
fatcat:ena5fkz4dvd3jkkkv5rca437c4
*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] . ...##
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Reduction and decomposition of differential automata: Theory and applications
[chapter]

1998
*
Lecture Notes in Computer Science
*

by unevenly spaced
points,

doi:10.1007/3-540-64358-3_48
fatcat:hqwvar3zbfftdhg4cybpjwogde
*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. ...##
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Fitting curves and surfaces to point clouds in the presence of obstacles

2009
*
Computer Aided Geometric Design
*

We examine two families of obstacles: first, the point cloud itself is interpreted as obstacle, e.g. to reconstruct any apparant boundaries of the

doi:10.1016/j.cagd.2008.04.003
fatcat:4iritpxk7fhftbl3qxvzgwqjgm
*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. ...##
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Stable Simplex Spline Bases for $$C^3$$ C 3 Quintics on the Powell–Sabin 12-Split

2016
*
Constructive approximation
*

The

doi:10.1007/s00365-016-9332-8
fatcat:4kuwtttjyzdk3cdlhgobdltwwu
*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. ...##
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Stable simplex spline bases for C^3 quintics on the Powell-Sabin 12-split
[article]

2015
*
arXiv
*
pre-print

The

arXiv:1504.02628v2
fatcat:ufp3d4exsrgfxgadqcttrnu6ve
*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 . ...##
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Survey on sparsity in geometric modeling and processing

2015
*
Graphical Models
*

However, sparsity

doi:10.1016/j.gmod.2015.06.012
fatcat:owpftxk3ivdp3a7dnzxhz2xvxm
*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 ...##
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14th International Symposium on Mathematical Programming

1990
*
Mathematical programming
*

Keywords:

doi:10.1007/bf01580875
fatcat:3jtclwmntzgjxkqs5uecombdaa
*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 ...##
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Symmetry-preserving discretization of variational field theories
[article]

2015
*
arXiv
*
pre-print

The present paper develops a variational theory of discrete fields defined

arXiv:1509.08750v1
fatcat:s6fdgk7mkzgpvlidj5q5qqvkiy
*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*. ...##
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A penalized likelihood approach to image warping

2001
*
Journal of The Royal Statistical Society Series B-statistical Methodology
*

A conjugate gradient algorithm is used to estimate the warping function, which is numerically approximated by a

doi:10.1111/1467-9868.00295
fatcat:t7nswwlnlrf3div7z5wcklgzgm
*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. ...##
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Interactive numerical flow visualization using stream surfaces

1990
*
Computing Systems in Engineering
*

The balance of my committee, Fred Brooks, James Coggins, and Henry Fuchs, allowed me the freedom to pursue my research

doi:10.1016/0956-0521(90)90021-c
fatcat:he3jcf3wzff2pervtrhsxwuvu4
*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 ...
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