Voronoi diagram of a polygon in chessboard metric and maskless lithographic applications

Hayong Shin, Seyoun Park, Eonjin Park, Deok Soo Kim

Research output: Contribution to journalArticlepeer-review


Lithography using photomasks has been the major workhorse in manufacturing printed circuit boards, semiconductors, and flat panel display devices. However, the cost of photomask is so high that it often becomes the bottleneck, especially when the production volume is low. For this reason, maskless lithography technology is recently gaining more attention, and hence, the computation of efficient lithography path becomes of greater importance than ever in order to obtain high throughput of lithography process. The target machine of this paper has a numerically controlled XY table on which a substrate is located and a variable size (square-shape) aperture in front of the light source. In this paper, we present an approach to efficient lithography path generation using Voronoi diagram and medial axis transform in chessboard metric. The properties and construction method of Voronoi diagram of a polygonal object in chessboard metric are examined. Then, lithography path generation scheme is explained. The proposed idea can also be applied to the fabrication of photomask itself and the rapid prototyping of a 3D model via layered lithography.

Original languageEnglish (US)
Pages (from-to)357-371
Number of pages15
JournalInternational Journal of Computational Geometry and Applications
Issue number4
StatePublished - Aug 2008
Externally publishedYes


  • Chessboard metric
  • Maskless lithography
  • Medial axis transform
  • Voronoi diagram

ASJC Scopus subject areas

  • Theoretical Computer Science
  • Geometry and Topology
  • Computational Theory and Mathematics
  • Computational Mathematics
  • Applied Mathematics


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