3,897 research outputs found
Shape preserving interpolatory subdivision schemes
Stationary interpolatory subdivision schemes which preserve shape properties such as convexity or monotonicity are constructed. The schemes are rational in the data and generate limit functions that are at least . The emphasis is on a class of six-point convexity preserving subdivision schemes that generate limit functions. In addition, a class of six-point monotonicity preserving schemes that also leads to limit functions is introduced. As the algebra is far too complicated for an analytical proof of smoothness, validation has been performed by a simple numerical methodology
Fitting Constrained Continuous Spline Curves.
Fitting a curve through a set of planar data which represents a positive quantity requires that the curve stays above the horizontal axis, The more general problem of designing parametric and non-parametric curves which do not cross the given constraint boundaries is considered. Several methods will be presented
Constrained Interpolation By Parametric Rational Cubic Splines
Interpolasi terkekang adalah berguna dalam masalah seperti mereka bentuk
sebuah Iengkung yang perlu dihadkan dalam suatu kawasan tertentu. Dalam disertasi ini,
kami membincangkan interpolasi terkekang dengan menggunakan splin kubik nisbah
yang diperkenalkan dalam (Goodman et aI, 1991). Terdapat dua kaedah pengubahsuaian
lengkung disarankan, kaedah yang melibatkan modifikasi pemberat a,p berkaitan
dengan titik hujung segmen lengkung dibincangkan dalam disertasi ini. Skim ini
memperoleh sebuah G2 lengkung interpolasi yang terletak di sebelah garis-garis yang
diberikan seperti data yang diberikan. Sebagai perkembangan daripada kertas ini, kami
akan memperoleh satu skim interpolasi terkekang altematif dengan menggunakan
lengkung kubik nisbah. Pemberat n, e yang berkaitan dengan titik kawalan dalaman
diubah suai untuk memperoleh sebuah G1 lengkung interpolasi yang terletak di sebelah
garis-garis yang diberikan seperti data yang diberikan.
Constrained interpolation could be useful in problem like designing a curve that
must be restricted within a specified region. In this dissertation, we discuss constrained
interpolation using rational cubic splines introduced in (Goodman et aI, 1991). There are
two curve modification methods suggested and the one which involves modification of
the weights a ,fJ associated with the end points of the curve segments is discussed in
this dissertation. This scheme obtains a G2 interpolating curve which lies on one side of
the given lines as the given data. Extension from this paper, we will derive an alternative
constrained interpolation scheme using rational cubic curve. The weights Q , e
associated with the inner control points are modified to obtain a G1 interpolating curve
which lies on one side of the given lines as the given data
Gauge Invariant Framework for Shape Analysis of Surfaces
This paper describes a novel framework for computing geodesic paths in shape
spaces of spherical surfaces under an elastic Riemannian metric. The novelty
lies in defining this Riemannian metric directly on the quotient (shape) space,
rather than inheriting it from pre-shape space, and using it to formulate a
path energy that measures only the normal components of velocities along the
path. In other words, this paper defines and solves for geodesics directly on
the shape space and avoids complications resulting from the quotient operation.
This comprehensive framework is invariant to arbitrary parameterizations of
surfaces along paths, a phenomenon termed as gauge invariance. Additionally,
this paper makes a link between different elastic metrics used in the computer
science literature on one hand, and the mathematical literature on the other
hand, and provides a geometrical interpretation of the terms involved. Examples
using real and simulated 3D objects are provided to help illustrate the main
ideas.Comment: 15 pages, 11 Figures, to appear in IEEE Transactions on Pattern
Analysis and Machine Intelligence in a better resolutio
Positive Data Visualization Using Trigonometric Function
A piecewise rational trigonometric cubic function with four shape parameters has been constructed to address the problem of visualizing positive data. Simple data-dependent constraints on shape parameters are derived to preserve positivity and assure smoothness. The method is then extended to positive surface data by rational trigonometric bicubic function. The order of approximation of developed interpolant is
An Arbitrary Curvilinear Coordinate Method for Particle-In-Cell Modeling
A new approach to the kinetic simulation of plasmas in complex geometries,
based on the Particle-in- Cell (PIC) simulation method, is explored. In the two
dimensional (2d) electrostatic version of our method, called the Arbitrary
Curvilinear Coordinate PIC (ACC-PIC) method, all essential PIC operations are
carried out in 2d on a uniform grid on the unit square logical domain, and
mapped to a nonuniform boundary-fitted grid on the physical domain. As the
resulting logical grid equations of motion are not separable, we have developed
an extension of the semi-implicit Modified Leapfrog (ML) integration technique
to preserve the symplectic nature of the logical grid particle mover. A
generalized, curvilinear coordinate formulation of Poisson's equations to solve
for the electrostatic fields on the uniform logical grid is also developed. By
our formulation, we compute the plasma charge density on the logical grid based
on the particles' positions on the logical domain. That is, the plasma
particles are weighted to the uniform logical grid and the self-consistent mean
electrostatic fields obtained from the solution of the logical grid Poisson
equation are interpolated to the particle positions on the logical grid. This
process eliminates the complexity associated with the weighting and
interpolation processes on the nonuniform physical grid and allows us to run
the PIC method on arbitrary boundary-fitted meshes.Comment: Submitted to Computational Science & Discovery December 201
Numerical Testing of a New Positivity-Preserving Interpolation Algorithm
An important component of a number of computational modeling algorithms is an
interpolation method that preserves the positivity of the function being
interpolated. This report describes the numerical testing of a new
positivity-preserving algorithm that is designed to be used when interpolating
from a solution defined on one grid to different spatial grid. The motivating
application is a numerical weather prediction (NWP) code that uses spectral
elements as the discretization choice for its dynamics core and Cartesian
product meshes for the evaluation of its physics routines. This combination of
spectral elements, which use nonuniformly spaced quadrature/collocation points,
and uniformly-spaced Cartesian meshes combined with the desire to maintain
positivity when moving between these necessitates our work. This new approach
is evaluated against several typical algorithms in use on a range of test
problems in one or more space dimensions. The results obtained show that the
new method is competitive in terms of observed accuracy while at the same time
preserving the underlying positivity of the functions being interpolated.Comment: 58 pages, 17 figure
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