12,030 research outputs found
Smooth approximation of data on the sphere with splines
A computable function, defined over the sphere, is constructed, which is of classC1 at least and which approximates a given set of data. The construction is based upon tensor product spline basisfunctions, while at the poles of the spherical system of coordinates modified basisfunctions, suggested by the spherical harmonics expansion, are introduced to recover the continuity order at these points. Convergence experiments, refining the grid, are performed and results are compared with similar results available in literature.\ud
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The approximation accuracy is compared with that of the expansion in terms of spherical harmonics. The use of piecewise approximation, with locally supported basisfunctions, versus approximation with spherical harmonics is discussed
Curve network interpolation by quadratic B-spline surfaces
In this paper we investigate the problem of interpolating a B-spline curve
network, in order to create a surface satisfying such a constraint and defined
by blending functions spanning the space of bivariate quadratic splines
on criss-cross triangulations. We prove the existence and uniqueness of the
surface, providing a constructive algorithm for its generation. We also present
numerical and graphical results and comparisons with other methods.Comment: With respect to the previous version, this version of the paper is
improved. The results have been reorganized and it is more general since it
deals with non uniform knot partitions. Accepted for publication in Computer
Aided Geometric Design, October 201
Error analysis for quadratic spline quasi-interpolants on non-uniform criss-cross triangulations of bounded rectangular domains
Given a non-uniform criss-cross partition of a rectangular domain ,
we analyse the error between a function defined on and two types
of -quadratic spline quasi-interpolants (QIs) obtained as linear
combinations of B-splines with discrete functionals as coefficients. The main
novelties are the facts that supports of B-splines are contained in
and that data sites also lie inside or on the boundary of . Moreover,
the infinity norms of these QIs are small and do not depend on the
triangulation: as the two QIs are exact on quadratic polynomials, they give the
optimal approximation order for smooth functions. Our analysis is done for
and its partial derivatives of the first and second orders and a particular
effort has been made in order to give the best possible error bounds in terms
of the smoothness of and of the mesh ratios of the triangulation
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Irregular C2 surface construction using bi-polynomial rectangular patches
The construction of C2 surfaces using bi-polynomial
parametric rectangular patches is studied. In particular, the analy-
sis of the C2 continuity conditions for the case of n patches meeting at
an n-vertex is developed
C2 piecewise cubic quasi-interpolants on a 6-direction mesh
We study two kinds of quasi-interpolants (abbr. QI) in the space of C2 piecewise cubics in the plane, or in a rectangular domain, endowed with the highly symmetric triangulation generated by a uniform 6-direction mesh. It has been proved recently that this space is generated by the integer translates of two multi-box splines. One kind of QIs is of differential type and the other of discrete type. As those QIs are exact on the space of cubic polynomials, their approximation order is 4 for sufficiently smooth functions. In addition, they exhibit nice superconvergent properties at some specific points. Moreover, the infinite norms of the discrete QIs being small, they give excellent approximations of a smooth function and of its first order partial derivatives. The approximation properties of the QIs are illustrated by numerical examples
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Smooth parametric surfaces and n-sided patches
The theory of 'geometric continuity' within the subject of CAGD is reviewed. In particular, we are concerned with how parametric surface patches for CAGD can be pieced together to form a smooth Ck surface. The theory is applied to the problem of filling an n-sided hole occurring within a smooth rectangular patch complex. A number of solutions to this problem are surveyed
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