Div-free minimizing splines under tension
نویسنده
چکیده
Vector field approximation is a problem involving the reconstruction of physical fields from a set of scattered observed data. In this paper, we address the problem of interpolation of divergence-free vector fields in three dimensional space by thin plate spline under tension. The problem is formulated as a minimization problem where the cost is related to the equilibrium energy of thin plate with tension. The existence and uniqueness of an analytical solution is provided. We give some numerical examples to illustrate this theory.
منابع مشابه
The Visual Computer ( to appear 2007 )
Fair webs are energy-minimizing curve networks. Obtained via an extension of cubic splines or splines in tension to networks of curves, they are efficiently computable and possess a variety of interesting applications. We present properties of fair webs and their discrete counterparts, i.e., fair polygon networks. Applications of fair curve and polygon networks include fair surface design and a...
متن کاملTENSION TRIGONOMETRIC SPLINES INTERPOLATION METHOD FOR SOLVING A LINEAR BOUNDARY VALUE PROBLEM
By using the trigonometric uniform splines of order 3 with a real tension factor, a numericalmethod is developed for solving a linear second order boundary value problems (2VBP) withDirichlet, Neumann and Cauchy types boundary conditions. The moment at the knots isapproximated by central finite-difference method. The order of convergence of the methodand the theory is illustrated by solving tes...
متن کاملPseudo-polyharmonic div-curl splines and elastic splines
Vector field reconstruction is a problem that arises in many scientific applications. In this paper we study a div-curl approximation of vector fields by pseudo-polyharmonic splines and elastic splines. This leads to the variational smoothing and interpolating spline problems with minimization of an energy involving the rotational and the divergence of the vector field.
متن کاملEnergy Formulations of Algebraic Splines
A-splines are implicit real algebraic curves in Bernstein-B ezier (BB) form that are smooth. We develop a spectrum of physical A-spline curve models using various energy formulations based on the theory of elasticity. Our bending and stretching energy formulations yield interactive physically based modeling with A-splines while preserving the advantages of free-form modeling of complex shapes. ...
متن کاملDiv-Curl weighted thin plate splines approximation
The paper deals with Div-Curl approximation problem by weighted thin plate splines. The weighted thin plate splines are an extension of the well known thin plate splines and are radial basis functions which allow the approximation and interpolation of a scalar functions from a given scattered data. We show how the weighted thin plate splines may also be used for the approximation and interpolat...
متن کامل