# Scanline algorithms on a grid

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DOI: 10.1007/BF01934088

- Cite this article as:
- Karlsson, R.G. & Overmars, M.H. BIT (1988) 28: 227. doi:10.1007/BF01934088

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## Abstract

A number of important problems in computational geometry are solved efficiently on 2- or 3-dimensional grids by means of scanline techniques. In the time complexity of solutions to the maximal elements and closure problems, a factor log*n* is substituted by loglog*n*, where*n* is the number of elements. Next, by using a data structure introduced in the paper, the interval trie, previous solutions to the rectangle intersection and connected component problems are improved upon. Finally, a fast intersection finding algorithm for arbitrarily oriented line segments is presented.