Space division for ray tracing in CSG
IEEE Computer Graphics and Applications
The design and analysis of spatial data structures
The design and analysis of spatial data structures
Solid representation and operation using extended octrees
ACM Transactions on Graphics (TOG)
Interval analysis for computer graphics
SIGGRAPH '92 Proceedings of the 19th 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
Geometric computations with interval and new robust methods: applications in computer graphics, GIS and computational geometry
Continuous collision detection for articulated models using Taylor models and temporal culling
ACM SIGGRAPH 2007 papers
A Hierarchical Data Structure for Representing the Spatial Decomposition of 3-D Objects
IEEE Computer Graphics and Applications
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Reliable computing techniques, like interval arithmetic, can be used to guarantee reliable solutions even in the presence of numerical round-off errors. The use of such techniques can eliminate the need to trace bounds for the error function separately. In this paper, we show how the techniques and algorithms of reliable computing can be applied to the construction and further processing of hierarchical solid representations, using the octree model as an example.