Previous Data Structures Research Articles

Dynamic Ray Shooting and Shortest Paths in Planar Subdivisions via Balanced Geodesic Triangulations

We give new methods for maintaining a data structure that supports ray-shooting and shortest-path queries in a dynamically changing connected planar subdivision S. Our approach is based on a new dynamic method for maintaining a balanced decomposition of a simple polygon via geodesic triangles. We maintain such triangulations by viewing their dual trees as balanced trees. We show that rotations in these trees can be implemented via simple “diagonal swapping” operations performed on the corresponding geodesic triangles, and that edge insertion and deletion can be implemented on these trees using operations akin to the standardsplitandspliceoperations. We also maintain a dynamic point location structure on the geodesic triangulation, so that we may implement ray-shooting queries by first locating the ray's endpoint and then walking along the ray from geodesic triangle to geodesic triangle until we hit the boundary of some region of S. The shortest path between two points in the same region is obtained by locating the two points and then walking from geodesic triangle to geodesic triangle either following a boundary or taking a shortcut through a common tangent. Our data structure usesO(n) space and supports queries and updates inO(log2n) worst-case time, wherenis the current size of S. It outperforms the previous best data structure for this problem by a lognfactor in all the complexity measures (space, query times, and update times).

Filtering, Clustering and Hierarchy Construction: a New Solution for Ray‐Tracing Complex Scenes

AbstractData structures that handle very complex scenes (hundreds of thousands of objects) have in the past either been laboriously built by hand, or have required the determination of unintuitive parameter values by the user. It is often the case that an incorrect choice of these parameters can result in greedy memory requirements or severely degraded performance. As a remedy to this problem we propose a new data structure which is fully automatic since it does not require the user to determine any input parameters. The structure is built by first filtering the input objects by size, subsequently applying a clustering step to objects of the same size and finally building a hierarchy of uniform grids . We then show that this data structure can be efficiently constructed. The implementation of the shows that the new structure is stable since it's memory requirements grow linearly with the size of the scene, and that it presents a satisfactory compromise between memory usage and computational efficiency. A detailed comparison with previous data structures is also presented in the results.

Point location among hyperplanes and unidirectional ray-shooting

We present an algorithm for locating a query point q in an arrangement of n hyperplanes in R d . The size of the data structure is O( n d ) and the time to answer any query is O(log n). Unlike previous data structures, our solution will also report, in addition to the face of the arrangement that contains q, the first hyperplane that is hit (if any) by shooting the point q in some fixed direction. Actually, if this ray-shooting capability is all that is needed, or if one only desires to know a single vertex of the face enclosing q, then the storage can be reduced to O( n d /(log n) ⌈ d/2⌉-ϵ ), for any fixed ϵ >0.