Representations for Rigid Solids: Theory, Methods, and Systems
ACM Computing Surveys (CSUR)
Raster-scan hidden surface algorithm techniques
SIGGRAPH '77 Proceedings of the 4th annual conference on Computer graphics and interactive techniques
Boolean operations of 2-manifolds through vertex neighborhood classification
ACM Transactions on Graphics (TOG)
Partitioning Polyhedral Objects into Nonintersecting Parts
IEEE Computer Graphics and Applications
The design of LINETOOL, a geometric editor
SCG '88 Proceedings of the fourth annual symposium on Computational geometry
Recipes for geometry and numerical analysis - Part I: an empirical study
SCG '88 Proceedings of the fourth annual symposium on Computational geometry
Calculating approximate curve arrangements using rounded arithmetic
SCG '89 Proceedings of the fifth annual symposium on Computational geometry
Using tolerances to guarantee valid polyhedral modeling results
SIGGRAPH '90 Proceedings of the 17th annual conference on Computer graphics and interactive techniques
Error-free boundary evaluation using lazy rational arithmetic: a detailed implementation
SMA '93 Proceedings on the second ACM symposium on Solid modeling and applications
IEEE Transactions on Computers
Robust Geometric Computation Based on Topological Consistency
ICCS '01 Proceedings of the International Conference on Computational Sciences-Part I
Topology-Oriented Approach to Robust Geometric Computation
ISAAC '99 Proceedings of the 10th International Symposium on Algorithms and Computation
Homotopy Conditions for Tolerant Geometric Queries
Reliable Implementation of Real Number Algorithms: Theory and Practice
Consensus sets for affine transformation uncertainty polytopes
Computers and Graphics
Algorithm engineering: bridging the gap between algorithm theory and practice
Algorithm engineering: bridging the gap between algorithm theory and practice
Uncertain geometry in computer vision
DGCI'05 Proceedings of the 12th international conference on Discrete Geometry for Computer Imagery
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Algorithms for computer graphics or solids modeling must often infer the structure of geometrical objects from numerical data. Unavoidable errors (due to limited precision) affect the calculations from which these data are produced and may thus affect topological information so derived. Ambiguities or even contradictions may result from inferences made from an object's representation.To resolve these ambiguities for arbitrary polyhedral objects, we introduce a minimum feature size and a face thickness and show how to convert any object description into a form which insures topological immunity to numerical perturbations. The minimum feature size depends on the object's overall dimensions and on its placement in space. The face thickness depends on how well a face's vertices conform to its computed plane.