Polygonization of implicit surfaces
Computer Aided Geometric Design
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
Interval methods for multi-point collisions between time-dependent curved surfaces
SIGGRAPH '93 Proceedings of the 20th annual conference on Computer graphics and interactive techniques
Feature sensitive surface extraction from volume data
Proceedings of the 28th annual conference on Computer graphics and interactive techniques
Rasterizing Algebraic Curves and Surfaces
IEEE Computer Graphics and Applications
Interval and Affine Arithmetic for Surface Location of Power- and Bernstein-Form Polynomials
Proceedings of the 9th IMA Conference on the Mathematics of Surfaces
Efficient collision detection of complex deformable models using AABB trees
Journal of Graphics Tools
Interval Methods in Geometric Modeling
GMP '00 Proceedings of the Geometric Modeling and Processing 2000
Verified spatial subdivision of implicit objects using implicit linear interval estimations
Proceedings of the 7th international conference on Curves and Surfaces
A practical approach for airport spatial modeling
Proceedings of the 13th International Conference on Computer Systems and Technologies
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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 algorithm that has been implemented and tested for implicit surfaces.