Very Fast Algorithms for the Area of the Union of Many Circles (Classic Reprint) - Softcover

Inhaltsangabe

Compute the area of a union of circles with efficient, practical methods.

This book presents algorithms that scale beyond naive checks, including exact-arithmetic approaches and Monte Carlo techniques, to estimate or compute the union’s area in two dimensions. In clear, accessible terms, you’ll see how the plane is partitioned into circular-arc segments and how to manage these components as you add circles. The text covers both deterministic and probabilistic methods, from straightforward 0(n^2) procedures to linear Monte Carlo ideas, with discussions of time and space efficiency and practical preprocessing ideas such as Voronoi-based queries.

• How to represent the evolving union with arc lists and how to update them efficiently as new circles are added.
• Exact-area strategies alongside Monte Carlo approaches, including error bounds and sampling considerations.
• Concepts like boundary descriptions, Voronoi preprocessing, and probabilistic estimators that scale to many circles.

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