Dual Sweep Line Technique
2-D Intervals (Rectangles) Union
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In this article, we will see how Sweep Line Technique can be used to compute union of rectangles.
Let's suppose a list of (axis-aligned) rectangles and each rectangle is represented as [x1, y1, x2, y2] , where (x1, y1) are the coordinates of the bottom-left corner, and (x2, y2) are the coordinates of the top-right corner of the ith rectangle.
Our objective is to find the total area covered by all rectangles in the plane.
This problem can be solved very easily using Sweep Line technique, using the concepts of events and active events. However, to solve this problem we would need Dual Sweep Line Technique, where we will have to sweep line along both x-axis and y-axis. The algorithm and code below explains the technique very well.
In-depth Algorithm Discussion and Code Implementation:
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Related Must-Read Topics:
- 1d Range Search
- Closest Pair
- Convex Hull
2D Intervals Union
& Skyline Problem
- Overlapping 1D Intervals
- Merging Overlapping 1D Intervals
- Separating Overlapping 1D Intervals
Senior SDE | Chief Architect
Microsoft | University of Florida
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