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Computational geometry: an introduction
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IEEE Computer Graphics and Applications
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Data Structures for Range Searching
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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
Near real-time shaded display of rigid objects
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Localized set operations for solid modeling
SIGGRAPH '83 Proceedings of the 10th annual conference on Computer graphics and interactive techniques
On visible surface generation by a priori tree structures
SIGGRAPH '80 Proceedings of the 7th annual conference on Computer graphics and interactive techniques
A priori based techniques for determining visibility priority for 3-d scenes
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Application of binary space partitioning trees to geometric modeling and ray-tracing
Application of binary space partitioning trees to geometric modeling and ray-tracing
Specifying composite illustrations with communicative goals
UIST '89 Proceedings of the 2nd annual ACM SIGGRAPH symposium on User interface software and technology
Near real-time shadow generation using BSP trees
SIGGRAPH '89 Proceedings of the 16th annual conference on Computer graphics and interactive techniques
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SIGGRAPH '90 Proceedings of the 17th annual conference on Computer graphics and interactive techniques
Adaptive mesh generation for global diffuse illumination
SIGGRAPH '90 Proceedings of the 17th annual conference on Computer graphics and interactive techniques
Worlds within worlds: metaphors for exploring n-dimensional virtual worlds
UIST '90 Proceedings of the 3rd annual ACM SIGGRAPH symposium on User interface software and technology
On constructing binary space partitioning trees
CSC '90 Proceedings of the 1990 ACM annual conference on Cooperation
Hidden surface removal with respect to a moving view point
STOC '91 Proceedings of the twenty-third annual ACM symposium on Theory of computing
BRep-Index: a multidimensional space partitioning tree
SMA '91 Proceedings of the first ACM symposium on Solid modeling foundations and CAD/CAM applications
A rapid hierarchical radiosity algorithm
Proceedings of the 18th annual conference on Computer graphics and interactive techniques
Interval arithmetic recursive subdivision for implicit functions and constructive solid geometry
SIGGRAPH '92 Proceedings of the 19th annual conference on Computer graphics and interactive techniques
Fast object-precision shadow generation for area light sources using BSP trees
I3D '92 Proceedings of the 1992 symposium on Interactive 3D graphics
Collaborative multimedia scientific design in SHASTRA
MULTIMEDIA '93 Proceedings of the first ACM international conference on Multimedia
Shastra: Multimedia Collaborative Design Environment
IEEE MultiMedia
Computer-generated pen-and-ink illustration
SIGGRAPH '94 Proceedings of the 21st annual conference on Computer graphics and interactive techniques
Shadow volume BSP trees for computation of shadows in dynamic scenes
I3D '95 Proceedings of the 1995 symposium on Interactive 3D graphics
I-COLLIDE: an interactive and exact collision detection system for large-scale environments
I3D '95 Proceedings of the 1995 symposium on Interactive 3D graphics
Geometric programming: a programming approach to geometric design
ACM Transactions on Graphics (TOG)
Separability of polyhedra for optimal filtering of spatial and constraint data
PODS '95 Proceedings of the fourteenth ACM SIGACT-SIGMOD-SIGART symposium on Principles of database systems
Approximating polyhedra with spheres for time-critical collision detection
ACM Transactions on Graphics (TOG)
The feudal priority algorithm on hidden-surface removal
SIGGRAPH '96 Proceedings of the 23rd annual conference on Computer graphics and interactive techniques
Splitting a complex of convex polytopes in any dimension
Proceedings of the twelfth annual symposium on Computational geometry
Consistent solid and boundary representations from arbitrary polygonal data
Proceedings of the 1997 symposium on Interactive 3D graphics
Interactive Boolean operations for conceptual design of 3-D solids
Proceedings of the 24th annual conference on Computer graphics and interactive techniques
Output-senstitive rendering and communication in dynamic virtual environments
VRST '97 Proceedings of the ACM symposium on Virtual reality software and technology
Cylindrical static and kinetic binary space partitions
SCG '97 Proceedings of the thirteenth annual symposium on Computational geometry
Practical techniques for constructing binary space partitions for orthogonal rectangles
SCG '97 Proceedings of the thirteenth annual symposium on Computational geometry
Parallel hierarchical computation of specular radiosity
PRS '97 Proceedings of the IEEE symposium on Parallel rendering
Hardware-assisted virtual collisions
VRST '98 Proceedings of the ACM symposium on Virtual reality software and technology
Kinetic binary space partitions for intersecting segments and disjoint triangles
Proceedings of the ninth annual ACM-SIAM symposium on Discrete algorithms
Optimal binary space partitions for orthogonal objects
SODA '90 Proceedings of the first annual ACM-SIAM symposium on Discrete algorithms
Fast CSG voxelization by frame buffer pixel mapping
VVS '00 Proceedings of the 2000 IEEE symposium on Volume visualization
A segment-tree based kinetic BSP
SCG '01 Proceedings of the seventeenth annual symposium on Computational geometry
Binary space partitions for axis-parallel segments, rectangles, and hyperrectangles
SCG '01 Proceedings of the seventeenth annual symposium on Computational geometry
View management for virtual and augmented reality
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A new BSP tree framework incorporating dynamic LoD models
VRST '00 Proceedings of the ACM symposium on Virtual reality software and technology
Separability of Polyhedra for Optimal Filtering of Spatial and Constraint Data
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Binary space partitions for axis-paralles line segments: size-height tradeoffs
Information Processing Letters
Collision Detection for Interactive Graphics Applications
IEEE Transactions on Visualization and Computer Graphics
Converting Discrete Images to Partitioning Trees
IEEE Transactions on Visualization and Computer Graphics
Dynamic Scene Occlusion Culling
IEEE Transactions on Visualization and Computer Graphics
Hierarchical Data Structures and Algorithms for Computer Graphics
IEEE Computer Graphics and Applications
Near Real-Time CSG Rendering Using Tree Normalization and Geometric Pruning
IEEE Computer Graphics and Applications
Binary space partitions for 3D subdivisions
SODA '03 Proceedings of the fourteenth annual ACM-SIAM symposium on Discrete algorithms
Fast and Accurate Collision Detection for Virtual Environments
Dagstuhl '97, Scientific Visualization
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ESA '98 Proceedings of the 6th Annual European Symposium on Algorithms
Image-Based Techniques in a Hybrid Collision Detector
IEEE Transactions on Visualization and Computer Graphics
Local polyhedra and geometric graphs
Proceedings of the nineteenth annual symposium on Computational geometry
An object-oriented shadow generation algorithm for real-time application
WORDS '97 Proceedings of the 3rd Workshop on Object-Oriented Real-Time Dependable Systems - (WORDS '97)
Shadow Generation Using Discretized Shadow Volume in Angular Coordinates
PG '03 Proceedings of the 11th Pacific Conference on Computer Graphics and Applications
Representing medical images with partitioning trees
VIS '92 Proceedings of the 3rd conference on Visualization '92
Image-based collision detection
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SCG '04 Proceedings of the twentieth annual symposium on Computational geometry
Local polyhedra and geometric graphs
Computational Geometry: Theory and Applications - Special issue on the 19th annual symposium on computational geometry - SoCG 2003
Counting Cases in Marching Cubes: Toward a Generic Algorithm for Producing Substitopes
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Proceedings of the eleventh international conference on 3D web technology
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Computational Geometry: Theory and Applications
The number of guillotine partitions in d dimensions
Information Processing Letters
Computer-Aided Design
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Journal of Electronic Testing: Theory and Applications
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Approximate range searching using binary space partitions
Computational Geometry: Theory and Applications
Local polyhedra and geometric graphs
Computational Geometry: Theory and Applications - Special issue on the 19th annual symposium on computational geometry - SoCG 2003
The number of guillotine partitions in d dimensions
Information Processing Letters
SGP '09 Proceedings of the Symposium on Geometry Processing
Volume and complexity bounded simplification of solid model represented by binary space partition
Proceedings of the 14th ACM Symposium on Solid and Physical Modeling
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ICCOMP'06 Proceedings of the 10th WSEAS international conference on Computers
Approximate range searching using binary space partitions
FSTTCS'04 Proceedings of the 24th international conference on Foundations of Software Technology and Theoretical Computer Science
Technical note: Fast and robust Booleans on polyhedra
Computer-Aided Design
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Energy efficient in-network data indexing for mobile wireless sensor networks
SSTD'13 Proceedings of the 13th international conference on Advances in Spatial and Temporal Databases
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We introduce a new representation for polyhedra by showing how Binary Space Partitioning Trees (BSP trees) can be used to represent regular sets. We then show how they may be used in evaluating set operations on polyhedra. The BSP tree is a binary tree representing a recursive partitioning of d-space by (sub-)hyperplanes, for any dimension d. Their previous application to computer graphics has been to organize an arbitrary set of polygons so that a fast solution to the visible surface problem could be obtained. We retain this property (in 3D) and show how BSP trees can also provide an exact representation of arbitrary polyhedra of any dimension. Conversion from a boundary representation (B-reps) of polyhedra to a BSP tree representation is described. This technique leads to a new method for evaluating arbitrary set theoretic (boolean) expressions on B-reps, represented as a CSG tree, producing a BSP tree as the result. Results from our language-driven implmentation of this CSG evaluator are discussed. Finally, we show how to modify a BSP tree to represent the result of a set operation between the BSP tree and a B-rep. We describe the embodiment of this approach in an interactive 3D object design program that allows incremental modification of an object with a tool. Placement of the tool, selection of views, and performance of the set operation are all performed at interactive speeds for modestly complex objects.