Solid representation and operation using extended octrees
ACM Transactions on Graphics (TOG)
Solving the Collision Detection Problem
IEEE Computer Graphics and Applications
An efficient collision detection algorithm using range data for walk-through systems
VRST '97 Proceedings of the ACM symposium on Virtual reality software and technology
PODS '97 Proceedings of the sixteenth ACM SIGACT-SIGMOD-SIGART symposium on Principles of database systems
Parallel processing for 2-1/2D machining simulation
Proceedings of the sixth ACM symposium on Solid modeling and applications
Collision Detection and Response for Computer Animation
SIGGRAPH '88 Proceedings of the 15th annual conference on Computer graphics and interactive techniques
A procedure for computing the symmetric difference of regions defined by polygonal curves
Journal of Symbolic Computation
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Geometric set operations play an integral role in systems for CAD/CAM, for robot planning, and for modeling objects such as underground formations from empirical data. Two major issues in the implementation of geometric set operations are efficiency in the search for geometric intersections and effectiveness in the treatment of singular intersection cases. This article presents an algorithm for geometric set operations on planar polyhedral nonmanifold objects that addresses both these issues. First, an efficient search for geometric intersections is obtained by localizing the search to small regions of object space through a cellular subdivision scheme using the polytree data structure. Second, an effective treatment of singular intersection cases is obtained by mapping each singular intersection occurring in a region into one of a small set of cases.