# Topology-Oriented Approach to Robust Geometric Computation

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## Abstract

The topology-oriented approach is a principle for translating geometric algorithms into practically valid computer software. In this principle, the highest priority is placed on the topological consistency of the geometric objects; numerical values are used as lower-priority information. The resulting software is completely robust in the sense that no matter how large numerical errors arise, the algorithm never fail. The basic idea of this approach and various examples are surveyed.

## Keywords

Convex Hull Voronoi Diagram Computational Geometry Convex Polyhedron Voronoi Region
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