Techniques of reliable computing like interval arithmetic can be used to

guarantee a reliable solution even in the presence of numerical round-off

errors. The need to trace bounds for the error function separately can be

eliminated using these techniques. In this talk, we focus on some

demonstrations 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.

An octree is a common hierarchical data structure to represent 3D

geometrical objects in solid modeling systems or to reconstruct a real

scene. The solid representation is based on recursive cell decompositions

of the space. Unfortunately, the data structure may require a large amount

of memory when it uses a set of very small cubic nodes to approximate a

solid.

In this talk, we present a novel generalization of the octree model created

from a CSG object that uses interval arithmetic and allows us to extend the

tests for classifying points in space as inside, on the boundary or outside

the object to handle 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.

Furthermore, this talk is concerned with interval-based algorithms for

reliable proximity queries between the extended octrees and with further

processing of the structure. We conclude the talk with some examples of

implementations.