Space division for ray tracing in CSG
IEEE Computer Graphics and Applications
Geometric approaches to nonplanar quadric surface intersection curves
ACM Transactions on Graphics (TOG)
Geometric and solid modeling: an introduction
Geometric and solid modeling: an introduction
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)
Generative modeling for computer graphics and CAD: symbolic shape design using interval analysis
Generative modeling for computer graphics and CAD: symbolic shape design using interval analysis
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
C++ Toolbox for Verified Scientific Computing - Theory, Algorithms and Programs: Basic Numerical Problems
Efficient Distance Computation for Quadratic Curves and Surfaces
GMP '02 Proceedings of the Geometric Modeling and Processing — Theory and Applications (GMP'02)
Geometric computations with interval and new robust methods: applications in computer graphics, GIS and computational geometry
A Hierarchical Data Structure for Representing the Spatial Decomposition of 3-D Objects
IEEE Computer Graphics and Applications
Intersecting quadrics: an efficient and exact implementation
Computational Geometry: Theory and Applications
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Octrees are among the most widely used representations in geometric modeling systems, apart from Constructive Solid Geometry and Boundary Representations. An octree model is based on recursive cell decompositions of the space and does not depend greatly on the nature of the object but much more on the chosen maximum subdivision level. Unfortunately, an octree may require a large amount of memory when it uses a set of very small cubic nodes to approximate an object. This paper is concerned with a novel generalization of the octree model that uses interval arithmetic and allows us to extend the tests for classifying points in space as inside, on or outside a CSG object to whole sections of the space at once. Tree nodes with additional information about relevant parts of the CSG object are introduced in order to reduce the depth of the required subdivision. The proposed extended octrees are compared with the common octree representation.