Visualization and collision detection are two of the most important problems connected with implicit objects. Enumeration algorithms can be used either directly or as preprocessing step for many algorithms solving these problems. In general, enumeration algorithms based on recursive space subdivision are reliable tools to encounter those parts in space, where the object might be located. But the bad performance and the huge number of computed enclosing cells, if high precision is required, are grave drawbacks. Implicit Linear Interval Estimations (ILIEs) introduced in this paper are implicit interval (hyper-)planes providing oriented tight bounds of the object within given cells. It turns out that the use of ILIEs highly improves the performance of the classical enumeration algorithm and the quality of the results. The theoretical background as well as a fast and simple technique to compute ILIEs are presented. The applicability of ILIEs is demonstrated by means of a modified enumeration algorithmthat has been implemented and tested for implicit surfaces.
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