Computational geometry: an introduction
Computational geometry: an introduction
Computer graphics: principles and practice (2nd ed.)
Computer graphics: principles and practice (2nd ed.)
Graphics gems IV
On the complexity of point-in-polygon algorithms
Computers & Geosciences
Computational geometry: algorithms and applications
Computational geometry: algorithms and applications
Handbook of discrete and computational geometry
Union and split operations on dynamic trapezoidal maps
Computational Geometry: Theory and Applications
The point in polygon problem for arbitrary polygons
Computational Geometry: Theory and Applications
Introduction to Algorithms: A Creative Approach
Introduction to Algorithms: A Creative Approach
A cell-based point-in-polygon algorithm suitable for large sets of points
Computers & Geosciences
On Compatible Star Decompositions of Simple Polygons
IEEE Transactions on Visualization and Computer Graphics
The Power of Non-Rectilinear Holes
Proceedings of the 9th Colloquium on Automata, Languages and Programming
Approximate convex decomposition of polygons
Computational Geometry: Theory and Applications
Technical section: 2D point-in-polygon test by classifying edges into layers
Computers and Graphics
A new hierarchical triangle-based point-in-polygon data structure
Computers & Geosciences
Voronoi representation for areal data processing in data-rich environments
ISI'09 Proceedings of the 2009 IEEE international conference on Intelligence and security informatics
| Hi-index | 0.00 |
The paper presents a new algorithm for point-in-polygon queries. By decomposing a polygon into a set of convex polygons and then constructing a BSP tree, the algorithm performs an inclusion query against the polygon in two steps. In the first step, it finds the convex polygon that is most likely to contain the query point through the BSP tree, and then in the second step, it tests whether the query point is in the convex polygon by employing advanced techniques for point-in-convex-polygon queries. The new algorithm is immune of singularity and has a performance of conducting a query by time demand in O(logn), and storage requirement in O(n). The time complexity of the preprocessing is O(nlogn) for convex decomposition and BSP tree construction. The new algorithm has its performance in various aspects comparable to the state-of-art algorithms based on trapezoidation. Furthermore, as the number of convex polygons is always much fewer than the number of trapezoids in partitioning a polygon, and a high-quality search tree can always be constructed to manage the convex polygons, the new algorithm can run much faster than the trapezoidation-based algorithms, up to over double folds in maximum.