Synopsis
Three techniques to solve geometric retrieval problems with efficient data structures
This book presents practical methods to answer complex geometric questions quickly. It shows how to balance preprocessing, space, and query time to handle large sets of points in multiple dimensions.
This edition focuses on triangle and wedge retrieval, half-space queries in 3D, and related problems in higher dimensions. It explains how to partition query space, reuse information across nearby regions, and apply divide-and-conquer to break hard problems into smaller ones. The discussion includes clear descriptions of data-structure design, time costs, and space requirements, with many approaches that extend beyond two dimensions.- Three robust techniques for organizing geometric queries: partitioning, coherence, and divide-and-conquer.
- Concrete solutions for triangle retrieval, wedge problems, and half-space retrieval in 2D and 3D.
- Strategies to manage space and preprocessing time while keeping query times practical.
- Extensions to higher dimensions and related retrieval problems, with performance considerations.
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