Filters








33 Hits in 4.7 sec

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

Ryszard Kozera, Piotr Szmielew
2015 Lecture Notes in Computer Science  
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

Lian Fang, David C Gossard
1995 Computer-Aided Design  
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

Olga Diamanti, Amir Vaxman, Daniele Panozzo, Olga Sorkine-Hornung
2014 Computer graphics forum (Print)  
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]

Alexander Rand, Andrew Gillette, Chandrajit Bajaj
2012 arXiv   pre-print
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

Alexander Rand, Andrew Gillette, Chandrajit Bajaj
2014 Mathematics of Computation  
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

Alexander Rand, Andrew Gillette, Chandrajit Bajaj
2014 Mathematics of Computation  
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]

Alexey S. Matveev, Andrey V. Savkin
1998 Lecture Notes in Computer Science  
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

Simon Flöry
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 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

Tom Lyche, Georg Muntingh
2016 Constructive approximation  
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]

Tom Lyche, Georg Muntingh
2015 arXiv   pre-print
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

Linlin Xu, Ruimin Wang, Juyong Zhang, Zhouwang Yang, Jiansong Deng, Falai Chen, Ligang Liu
2015 Graphical Models  
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  
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]

A.C. Casimiro, C. Rodrigo
2015 arXiv   pre-print
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

C. A. Glasbey, K. V. Mardia
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 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

J.P.M. Hultquist
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 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
« Previous Showing results 1 — 15 out of 33 results