Fast Algorithms for Minimum Matrix Norm with Application in Computer Graphics

Shouwen Tang, Kaizhong Zhang, Xiaolin Wu

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.