A Reliable Extended Octree Representation of CSG Objects with an Adaptive Subdivision Depth

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.