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Fast algorithms for minimum matrix norm with application in computer graphics

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Abstract

In this paper we consider the following problem. Given (r 1,r 2, ...,r n)∈ R n, for anyI= (I 1,I 2,...,I n)∈ Z n, letE 1=(e ij), wheree ij=(r i−rj)−(I i−Ij), findI ∈ Z n such that |E I| is minimized, where |·| is a matrix norm. This problem arises from optimal curve rasterization in computer graphics, where minimum distortion of curve dynamic context is sought. Until now, there has been no polynomial-time solution to this computer graphics problem. We present a very simpleO(n lgn)-time algorithm to solve this problem under various matrix norms.

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Authors and Affiliations

  1. Department of Computer Science, Beijing Computer Institute, Beijing, China

    Shouwen Tang

  2. Department of Computer Science, University of Western Ontario, N6A 5B7, London, Ontario, Canada

    Kaizhong Zhang & Xiaolin Wu

Authors
  1. Shouwen Tang
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  2. Kaizhong Zhang
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  3. Xiaolin Wu
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Additional information

Communicated by D. T. Lee.

This research was supported by the Natural Sciences and Engineering Research Council of Canada under Grant OGP0046373.

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Tang, S., Zhang, K. & Wu, X. Fast algorithms for minimum matrix norm with application in computer graphics. Algorithmica 15, 68–81 (1996). https://doi.org/10.1007/BF01942607

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  • DOI: https://doi.org/10.1007/BF01942607

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