A technical report on how to answer complex geometric queries fast in arrangements of segments.
It covers ray shooting, implicit point location, and related problems with efficient, implicit representations.
The work adapts partition-tree techniques to handle implicit data and batched queries, striving for subquadratic preprocessing and space with near-linear query time. It presents methods for ray shooting in non-simple polygons and for a variety of practical applications in placement queries and three-dimensional visibility.
- How to preprocess segment arrangements to enable fast point location and related queries.
- Techniques that achieve subquadratic preprocessing and near-linear query time using partition trees.
- Applications to ray shooting in complex planar and three-dimensional settings.
- Practical problem areas like polygon placement and implicit hidden surface removal in graphics.
Ideal for readers of computational geometry and graphics research looking for scalable, implicit representations and efficient query handling.