Computational geometry: an introduction
Computational geometry: an introduction
Eliminating the flag in threaded binary search trees
Information Processing Letters
A dynamic screen technique for shaded graphics display of slice-represented objects
Computer Vision, Graphics, and Image Processing
Applications of spatial data structures: Computer graphics, image processing, and GIS
Applications of spatial data structures: Computer graphics, image processing, and GIS
The design and analysis of spatial data structures
The design and analysis of spatial data structures
Computer graphics: principles and practice (2nd ed.)
Computer graphics: principles and practice (2nd ed.)
An introduction to ray tracing
An introduction to ray tracing
Grid intersection graphs and boxicity
Discrete Mathematics - Special issue on combinatorics and algorithms
Bucket-like space partitioning data structures with applications to ray-tracing
SCG '97 Proceedings of the thirteenth annual symposium on Computational geometry
Occlusion horizons for driving through urban scenery
I3D '01 Proceedings of the 2001 symposium on Interactive 3D graphics
Volume Visualization (Tutorial)
Volume Visualization (Tutorial)
The Design and Analysis of Computer Algorithms
The Design and Analysis of Computer Algorithms
Front-to-Back Display of BSP Trees
IEEE Computer Graphics and Applications
Foundations of Multidimensional and Metric Data Structures (The Morgan Kaufmann Series in Computer Graphics and Geometric Modeling)
Optimal spanners for axis-aligned rectangles
Computational Geometry: Theory and Applications
Back-to-Front Display of Voxel Based Objects
IEEE Computer Graphics and Applications
A survey of visibility for walkthrough applications
IEEE Transactions on Visualization and Computer Graphics
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The framework of boxels is developed to represent 2.5D datasets, such as urban environments. Boxels are axis-aligned non-intersecting boxes which can be used to directly represent objects in the scene or as bounding volumes. Guibas and Yao have shown that axis-aligned disjoint rectangles in the plane can be ordered into four total orders so that any ray meets them in one of the four orders. This is also applicable to boxels, and it is shown that there exist four different partitionings of the boxels into ordered sequences of disjoint sets, called antichains, so that boxels in one antichain can act as occluders of the boxels in subsequent antichains. The expected runtime for the antichain partitioning is O(nlogn), where n is the number of boxels. This partitioning can be used for the efficient implementation of virtual drivethroughs and ray tracing. Boxels can also be easily organized into hierarchies to speed up the rendering. For drivethroughs, the antichains are processed in front-to-back order together with a run-length encoding of the boxel horizon, yielding real-time rendering of scenes with up to 300,000 buildings. For ray tracing, a ray intersects at most one boxel in an antichain, and the time to determine that boxel is O(1) for most ''natural'' scenes, and at worst, logarithmic in the size of the antichain. Objects which are not axis-aligned can also be handled by a simple modification. Boxel rendering can also be parallelized for multi-core machines.