Geometric modeling
Computational geometry: an introduction
Computational geometry: an introduction
Intersection algorithms for lines and circles
ACM Transactions on Graphics (TOG)
Computer graphics: principles and practice (2nd ed.)
Computer graphics: principles and practice (2nd ed.)
Faster line segment intersection
Graphics Gems III
Computational geometry in C
On the complexity of point-in-polygon algorithms
Computers & Geosciences
Computational geometry: algorithms and applications
Computational geometry: algorithms and applications
Two efficient algorithms for determining intersection points between simple polygons
Computers & Geosciences
A cell-based point-in-polygon algorithm suitable for large sets of points
Computers & Geosciences
Point-in-polygon tests for geometric buffers
Computers & Geosciences
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The paper presents an algorithm for constructing the geometric outlines of a given set of line segments, using a sweep-line approach. The algorithm works in four steps: creating the basic geometric outlines, identifying the intersection points between them, constructing cycles, and determining the spatial relationships amongst the cycles. In the worst case, when each basic geometric buffer intersects all the other, the time complexity of the algorithm is O(n2 log n), where n is the number of input line segments. However, in practice, the expected time complexity is much lower, and this has been confirmed by experiments--it has been shown that O(n log n) time complexity is a good estimation in most situations. The algorithm has been used in GIS applications over a period and has proved to be successful.