Robotics Research Technical Report: An Algorithm for Generalized Point Location and Its Applications (Classic Reprint) - Hardcover
Synopsis
A new framework for fast geometric queries that scales to complex spaces.
This book presents a data‑structure approach to solving the generalized point location problem in high dimensions and with nonlinear boundaries. It shows how to turn Collins’ cylindrical algebraic decomposition into a practical tool for fast searching, with careful handling of real algebraic predicates and witnesses.
The work explains how to transform algebraic descriptions into a searchable structure, balancing preprocessing effort, storage needs, and query speed. It highlights how the method connects to classic problems in computational geometry and what it means for real‑world performance, including bit‑level considerations and arithmetic costs.
- Extends point location to arbitrary algebraic varieties and describes a scalable data structure for fast queries.
- Offers concrete bounds on size, preprocessing time, and query time under realistic computational models.
- Discusses the role of algebraic tools, bit complexity, and practical tradeoffs in implementation.
- Shows how the framework yields subquadratic solutions to a range of geometric problems and related applications.
Ideal for readers who want a solid, theory‑grounded approach to multidimensional searching and its applications in computational geometry.
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