# Efficient Piecewise-Cubic Polynomial Curve Approximation Using Uniform Metric

• Kim, Jae-Hoon (Division of Computer Engineering, Pusan University of Foreign Studies)
• Published : 2008.09.30
• 46 6

#### Abstract

We present efficient algorithms for solving the piecewise-cubic approximation problems in the plane. Given a set D of n points in the plane, we find a piecewise-cubic polynomial curve passing through only the points of a subset S of D and approximating the other points using the uniform metric. The goal is to minimize the size of S for a given error tolerance $\varepsilon$, called the min-# problem, or to minimize the error tolerance $\varepsilon$ for a given size of S, called the min-$\varepsilon$ problem. We give algorithms with running times O($n^2$ logn) and O($n^3$) for both problems, respectively.

#### Keywords

piecewise-cubic;approximation;uniform metric

#### References

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