论文信息 - MQ—curves are curves in tension

MQ—curves are curves in tension

Abstract This paper studies properties of curves with multiquadrics as basis functions (MQ–curves). Firstly, MQ–curves with constant precision are considered. Especially, it is pointed out that the interpolating MQ–curve is a curve in tension. Secondly, a very special MQ–curve with linear precision depending only on four coefficients is used to derive a local basis of C2–continuous MQ–splines in tension which are an alternative to the well–known exponential C2–spline in tension.

Matthias Eck

[1] C. Micchelli. Interpolation of scattered data: Distance matrices and conditionally positive definite functions , 1986 .

[2] Steven Pruess,et al. Alternatives to the exponential spline in tension , 1979 .

[3] R. L. Hardy. Theory and applications of the multiquadric-biharmonic method : 20 years of discovery 1968-1988 , 1990 .

[4] R. L. Hardy. Multiquadric equations of topography and other irregular surfaces , 1971 .

[5] R. Franke. Scattered data interpolation: tests of some methods , 1982 .

[6] Helmut Pottmann,et al. Modified multiquadric methods for scattered data interpolation over a sphere , 1990, Comput. Aided Geom. Des..

[7] M. J. D. Powell,et al. Univariate multiquadric approximation: Quasi-interpolation to scattered data , 1992 .

[8] E. Kansa. Multiquadrics—A scattered data approximation scheme with applications to computational fluid-dynamics—I surface approximations and partial derivative estimates , 1990 .