line-intersection

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line-intersection

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Last edited May 25, 2016

Created on May 25, 2016

This interactive visualization demonstrates the Bentley–Ottmann algorithm for finding line segment intersections. Users can drag line endpoints to reposition them, click to add new segments, and right-click to remove them. The algorithm sweeps a horizontal line from top to bottom, maintaining the order of segment x-positions at the current y (shown in the right panel). Instead of checking all O(n²) segment pairs, only adjacent segments are tested for intersections as they start, end, or cross, yielding O(n log n + I log n) time for I intersections. The SVG rendering highlights intersection points as they are discovered, providing an intuitive view of the sweep-line process.

AI-generated description

The Bentley–Ottmann algorithm finds all the intersections that occur in a set of line segments. Drag the endpoints of the line to move, click to add and right click to remove.

Instead of calculating the intersection of every pair of segments, which would require O(n²) comparisons for a set of n lines, the algorithm uses a sweep line. Starting at the top of the screen and moving down, it keeps track of the order of the lines' x positions at the current y position (represented by the figure on the right). As lines start, end or intersect, new pairs of lines become adjacent in the x ordering and are checked for intersections.

A set of lines with I intersections ends up only requiring O(n log n + I log n) operations. Computational Geometry: Algorithms and Applications, chapter 2 has a proof and a more detailed explanation.

forked from <a href='http://bl.ocks.org/1wheel/'>1wheel</a>'s block: <a href='http://bl.ocks.org/1wheel/464141fe9b940153e636'>line-intersection</a>

forked from <a href='http://bl.ocks.org/apburnes/'>apburnes</a>'s block: <a href='http://bl.ocks.org/apburnes/68f69b32d86f6d987ddfd0e2c48d2872'>line-intersection</a>

forked from <a href='http://bl.ocks.org/apburnes/'>apburnes</a>'s block: <a href='http://bl.ocks.org/apburnes/c0d53f70215d4a49a200d24a5c0e6b3a'>line-intersection</a>

forked from <a href='http://bl.ocks.org/apburnes/'>apburnes</a>'s block: <a href='http://bl.ocks.org/apburnes/42118e82a0756867276c9afe5567e0c5'>line-intersection</a>

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