Computational geometry: an introduction
Computational geometry: an introduction
Graph-Based Algorithms for Boolean Function Manipulation
IEEE Transactions on Computers
Ray tracing complex models containing surface tessellations
SIGGRAPH '87 Proceedings of the 14th annual conference on Computer graphics and interactive techniques
An efficient ray-polygon intersection
Graphics gems
Oriented projective geometry
Faster line segment intersection
Graphics Gems III
Symbolic Boolean manipulation with ordered binary-decision diagrams
ACM Computing Surveys (CSUR)
Graphics gems IV
Improving the Variable Ordering of OBDDs Is NP-Complete
IEEE Transactions on Computers
Algorithm 112: Position of point relative to polygon
Communications of the ACM
Certification of Algorithm 112: Position of point relative to polygon
Communications of the ACM
An efficient algorithm for finding the CSG representation of a simple polygon
SIGGRAPH '88 Proceedings of the 15th annual conference on Computer graphics and interactive techniques
How Reliable Are Practical Point-in-Polygon Strategies?
ESA '08 Proceedings of the 16th annual European symposium on Algorithms
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We investigate the use of a constructive solid geometry (CSG) representation in testing if a query point falls inside a polygon; in particular, we use a CSG tree whose leaves correspond to halfplanes defined by edges and whose internal nodes are intersections or unions of the regions defined by their subtrees. By preprocessing polygons into this representation, we obtain a linear-space data structure for point-in-polygon tests that has a tight inner loop that can prune unnecessary edge tests during evaluation. We experiment with opportunities to optimize the pruning by permuting children of nodes. The resulting test is less memory-intensive than grid methods and faster than existing one-shot methods. It also extends to ray-shooting in 3-space.