Interpolation of data on the surface of a sphere

@article{Renka1984InterpolationOD,
  title={Interpolation of data on the surface of a sphere},
  author={Robert J. Renka},
  journal={ACM Trans. Math. Softw.},
  year={1984},
  volume={10},
  pages={417-436}
}
  • R. Renka
  • Published 1984
  • Mathematics, Computer Science
  • ACM Trans. Math. Softw.
The problem treated is that of constructing a C ~ interpolant of data values associated with arbitrarily distributed nodes on the surface of a sphere. A local interpolation method that has proved very successful for fitting data on the plane consists of generating a triangulation of the nodes, estimating gradients at the nodes, and constructing a triangle-based mterpolant of the data and gradient estamates Methods and software that extend thas solution procedure to the surface of the sphere are… Expand
Interpolation over a sphere based upon a minimum norm network
TLDR
A new method for interpolating data over a spherical domain is presented, based upon a functional minimization that characterizes a curve network that produces a smooth function defined on the surface of the sphere that interpolates the given dependent data values. Expand
Interpolation of scattered data on closed surfaces
TLDR
Techniques for the construction and visualization of a function defined over a closed surface domain which depends on a discrete sample of measurements at arbitrary locations on the domain surface and transparent surface graphs projected from the domain are presented. Expand
Interpolation on surfaces using minimum norm networks
  • H. Pottmann
  • Mathematics, Computer Science
  • Comput. Aided Geom. Des.
  • 1992
TLDR
New methods for interpolating scattered data on a surface using a functional minimization that characterizes the restriction of the final interpolant to curves which form the edges in a triangulation of the domain surface are presented. Expand
Modified multiquadric methods for scattered data interpolation over a sphere
Abstract Given arbitrary points on a sphere and associated real values, we address the problem of constructing a smooth function defined over the sphere which interpolates the given data. SeveralExpand
Algorithm 773: SSRFPACK: interpolation of scattered data on the surface of a sphere with a surface under tension
  • R. Renka
  • Mathematics, Computer Science
  • TOMS
  • 1997
SSRFPACK is a Fortran 77 software package that constructs a smooth interpolatory or approximating surface to data values associated with arbitrarily distributed points on the surface of a sphere. ItExpand
Fitting scattered data on spherelike surfaces using tensor products of trigonometric and polynomial splines
SummaryA method is presented for fitting a function defined on a general smooth spherelike surfaceS, given measurements on the function at a set of scattered points lying onS. The approximatingExpand
Surfaces defined on surfaces
TLDR
Two methods for constructing interpolants to data arbitrarily located on convex surfaces are presented, one a modified Shepard's method and the other a triangular-based method. Expand
The map and blend scattered data interpolant on a sphere
Abstract The map and blend technique constructs a function defined over the sphere that interpolates to a discrete sample of measurements at arbitrary locations on the sphere. This technique consistsExpand
Difference formulas for the surface Laplacian on a triangulated surface
Abstract Different approximating expressions for the surface Laplacian operator on a triangulated surface are derived. They are evaluated on a triangulated spherical surface for which the analyticalExpand
Scattered Data Techniques for Surfaces
  • S. Lodha, R. Franke
  • Mathematics, Computer Science
  • Scientific Visualization Conference (dagstuhl '97)
  • 1997
This survey presents several techniques for solving variants of the following scattered data interpolation problem: given a finite set of N points in R3, find a surface that interpolates the givenExpand
...
1
2
3
4
5
...

References

SHOWING 1-10 OF 19 REFERENCES
$C^1$ surface interpolation for scattered data on a sphere
An algorithm is described for constructing a smooth computable function, f, defined over the surface of a sphere and interpolating a set of n data values, u sub i, associated with n locations, P subExpand
Software for C1 Surface Interpolation
Publisher Summary This chapter discusses algorithm and underlying theory of software for C1 surface interpolation. There has been practically no theory to guide the development of algorithms forExpand
The side-vertex method for interpolation in triangles☆
Abstract Interpolation schemes which assume prescribed values on the boundary of a triangle are presented. The development of these interpolants is based upon univariate interpolation along lineExpand
A Method of Bivariate Interpolation and Smooth Surface Fitting for Irregularly Distributed Data Points
  • H. Akima
  • Mathematics, Computer Science
  • TOMS
  • 1978
TLDR
A method of blvariate interpolation and smooth surface fitting is developed for z values given at points irregularly distributed in the x-y plane for Bivariate Interpolation and Smooth Surface Fitting for Irregularly Distributed Data Points. Expand
Smooth interpolation in triangles
Abstract The purpose of this paper is to describe new schemes of interpolation to the boundary values of a function defined on a triangle. These schemes are affine-invariant and combine severalExpand
A triangle-based $C^1$ interpolation method
This paper discusses methods and software for C/sup 1/ interpolation at arbitrarily distributed data points in the plane. The primary results presented here are derivative-estimation procedures whichExpand
Two Dimensional Interpolation from Random Data
A method is described for smooth interpolation between random data points in two or more dimensions. The method gives a smooth surface passing exactly through the given data points, and is suitableExpand
A Critical Comparison of Some Methods for Interpolation of Scattered Data
Abstract : This report is concerned with methods for solving the scattered data interpolation problem: Given points (X sub K, Y sub k, F sub k), k = 1, ..., N, construct a smooth function, F(x,y), soExpand
A Storage-efficient Method for Construction of a Thiessen Triangulation
This paper describes a storage-efficient method and associated algorithms for constructing and representing a triangulation of arbitrarily distributed points in the plane.
Spline Interpolation and Smoothing on the Sphere
We extend the notion of periodic polynomial splines on the circle and thin plate splines on Euclidean d-space to splines on the sphere which are invariant under arbitrary rotations of the coordinat...
...
1
2
...