Join Our Newsletter

Free Online Productivity Tools
i2Speak
i2Symbol
i2OCR
iTex2Img
iWeb2Print
iWeb2Shot
i2Type
iPdf2Split
iPdf2Merge
i2Bopomofo
i2Pinyin
i2Cantonese
i2Cangjie
i2Arabic
i2Style
i2Image
i2PDF
iLatex2Rtf
Sci2ools

SIAMCOMP

1998

1998

Motivated by applications in computer graphics, visualization, and scienti c computation, we study the computational complexity of the following problem: Given a set S of n points sampled from a bivariate function f(x;y) and an input parameter " > 0, compute a piecewise linear function (x;y) of minimum complexity (that is, a xy-monotone polyhedral surface, with a minimum number of vertices, edges, or faces) such that j (xp;yp) ? zpj "; for all (xp;yp;zp) 2 S: We prove that the decision version of this problem is NP-Hard. The main result of our paper is a polynomial-time approximation algorithm that computes a piecewise linear surface of size O(Ko logKo), where Ko is the complexityof an optimalsurface satisfying the constraints of the problem. The technique developed in our paper is more general and applies to several other problems that deal with partitioning of points (or other objects) subject to certain geometric constraints. For instance, we get the same approximation...

Related Content

Added |
23 Dec 2010 |

Updated |
23 Dec 2010 |

Type |
Journal |

Year |
1998 |

Where |
SIAMCOMP |

Authors |
Pankaj K. Agarwal, Subhash Suri |

Comments (0)