A new polynomial-time algorithm for linear programming
Combinatorica
Graph-Based Algorithms for Boolean Function Manipulation
IEEE Transactions on Computers
Fast constructive-solid geometry display in the pixel-powers graphics system
SIGGRAPH '86 Proceedings of the 13th annual conference on Computer graphics and interactive techniques
Constructive solid geometry for polyhedral objects
SIGGRAPH '86 Proceedings of the 13th annual conference on Computer graphics and interactive techniques
Set operations on polyhedra using binary space partitioning trees
SIGGRAPH '87 Proceedings of the 14th annual conference on Computer graphics and interactive techniques
Marching cubes: A high resolution 3D surface construction algorithm
SIGGRAPH '87 Proceedings of the 14th annual conference on Computer graphics and interactive techniques
ACM Transactions on Graphics (TOG)
Geometric and solid modeling: an introduction
Geometric and solid modeling: an introduction
Merging BSP trees yields polyhedral set operations
SIGGRAPH '90 Proceedings of the 17th annual conference on Computer graphics and interactive techniques
Linear programming and convex hulls made easy
SCG '90 Proceedings of the sixth annual symposium on Computational geometry
BRep-Index: a multidimensional space partitioning tree
SMA '91 Proceedings of the first ACM symposium on Solid modeling foundations and CAD/CAM applications
Las Vegas algorithms for linear and integer programming when the dimension is small
Journal of the ACM (JACM)
An efficient surface intersection algorithm based on lower-dimensional formulation
ACM Transactions on Graphics (TOG)
An improved z-buffer CSG rendering algorithm
HWWS '98 Proceedings of the ACM SIGGRAPH/EUROGRAPHICS workshop on Graphics hardware
Efficient algorithms for geometric optimization
ACM Computing Surveys (CSUR)
Exact arithmetic at low cost—a case study in linear programming
Computational Geometry: Theory and Applications
SIGGRAPH '85 Proceedings of the 12th annual conference on Computer graphics and interactive techniques
Representations for Rigid Solids: Theory, Methods, and Systems
ACM Computing Surveys (CSUR)
A null-object detection algorithm for constructive solid geometry
Communications of the ACM
Dual contouring of hermite data
Proceedings of the 29th annual conference on Computer graphics and interactive techniques
A Combinatorial Bound for Linear Programming and Related Problems
STACS '92 Proceedings of the 9th Annual Symposium on Theoretical Aspects of Computer Science
On visible surface generation by a priori tree structures
SIGGRAPH '80 Proceedings of the 7th annual conference on Computer graphics and interactive techniques
Constructive Solid Geometry for Triangulated Polyhedra
Constructive Solid Geometry for Triangulated Polyhedra
Application of binary space partitioning trees to geometric modeling and ray-tracing
Application of binary space partitioning trees to geometric modeling and ray-tracing
Three-dimensional binary space partitioning tree and constructive solid geometry tree construction from algebraic boundary representations
Blister: GPU-based rendering of Boolean combinations of free-form triangulated shapes
ACM SIGGRAPH 2005 Papers
Visualization of large ISO-Surfaces based on nested clip-boxes
SIGGRAPH '05 ACM SIGGRAPH 2005 Posters
Progressive dimension-independent Boolean operations
SM '04 Proceedings of the ninth ACM symposium on Solid modeling and applications
Realtime constructive solid geometry
ACM SIGGRAPH 2007 posters
Set Membership Classification: A Unified Approach to Geometric Intersection Problems
IEEE Transactions on Computers
Technical section: Point in solid strategies
Computers and Graphics
Exact solutions to linear programming problems
Operations Research Letters
SGP '09 Proceedings of the Symposium on Geometry Processing
| Hi-index | 0.00 |
This paper presents a new method for evaluating boolean set operations between Binary Space Partition (BSP) trees. Our algorithm has many desirable features, including both numerical robustness and O(n) output sensitive time complexity, while simultaneously admitting a straightforward implementation. To achieve these properties, we present two key algorithmic improvements. The first is a method for eliminating null regions within a BSP tree using linear programming. This replaces previous techniques based on polygon cutting and tree splitting. The second is an improved method for compressing BSP trees based on a similar approach within binary decision diagrams. The performance of the new method is analyzed both theoretically and experimentally. Given the importance of boolean set operations, our algorithms can be directly applied to many problems in graphics, CAD and computational geometry.