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Fast, Exact, Linear Booleans
Author(s) -
Bernstein Gilbert,
Fussell Don
Publication year - 2009
Publication title -
computer graphics forum
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.578
H-Index - 120
eISSN - 1467-8659
pISSN - 0167-7055
DOI - 10.1111/j.1467-8659.2009.01504.x
Subject(s) - polyhedron , polygon (computer graphics) , computer science , computation , regular polygon , monotone polygon , subroutine , tree (set theory) , theoretical computer science , algorithm , boolean data type , discrete mathematics , mathematics , combinatorics , programming language , telecommunications , geometry , frame (networking)
We present a new system for robustly performing Boolean operations on linear, 3D polyhedra. Our system is exact, meaning that all internal numeric predicates are exactly decided in the sense of exact geometric computation. Our BSP‐tree based system is 16‐28× faster at performing iterative computations than CGAL's Nef Polyhedra based system, the current best practice in robust Boolean operations, while being only twice as slow as the non‐robust modeler Maya. Meanwhile, we achieve a much smaller substrate of geometric subroutines than previous work, comprised of only 4 predicates, a convex polygon constructor, and a convex polygon splitting routine. The use of a BSP‐tree based Boolean algorithm atop this substrate allows us to explicitly handle all geometric degeneracies without treating a large number of cases.