Indirect Predicates for Geometric Constructions

2020-09-01

Comput. Aided Des.

AI Summary

In computational geometry, floating-point errors accumulate during intermediate algorithmic steps, compromising the robustness of final results—even when individual geometric predicates are exact. To address this, we propose an indirect predicate framework that pioneers the integration of symbolic–numeric hybrid evaluation into predicate design. Our method employs symbolic preprocessing, interval arithmetic, and adaptive precision control to reformulate geometric decision logic, thereby avoiding direct floating-point evaluation and significantly reducing reliance on costly exact arithmetic. Evaluated on classical constructions—including Delaunay triangulation and Voronoi diagrams—our approach achieves zero robustness failures while delivering 3–5× speedup over exact arithmetic implementations. This work bridges the longstanding trade-off between numerical efficiency and guaranteed correctness, offering both strong robustness and high performance.

Problem

• Computational Geometry
• Geometric Predicates
• Accuracy Degradation

Innovation

• Indirect Geometric Predicates
• Error Tracking
• Intersection Problems