Curves: Automatic Tension Adjustment for Interpolatory Splines

Authors:
Yates Fletcher;David F. McAllister
Affiliations:
-;-
Venue:
IEEE Computer Graphics and Applications
Year:
1990

Citing 4
Cited 2

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Computer Aided Geometric Design
An analysis of tension methods for convexity-preserving interpolation

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A New Method of Interpolation and Smooth Curve Fitting Based on Local Procedures

Journal of the ACM (JACM)
Scalar- and planar-valued curve fitting using splines under tension

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Interpolation with slackness and continuity control and convexity-preservation using singular blending

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C-B-spline singular blending interpolating

ICCOMP'06 Proceedings of the 10th WSEAS international conference on Computers

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Abstract

The authors deal with anomalous oscillations often exhibited by cubic spline interpolating curves. These oscillations, which are not suggested by the data, can be treated with a shaping parameter called tension, which is introduced by generalizing the cubic spline formation in some fashion. The authors consider the associated problem of estimating the magnitude of the tensions necessary to achieve a desired shape. The analysis is based on a theory they reported earlier, called convexity interval analysis, and it leads to an algorithm that produces suitable tension values for given data automatically, without experimentation or interactive user direction. Three examples are given to illustrate the concepts.