Ray Shooting Amidst Fat Convex Polyhedra in 3-Space
نویسندگان
چکیده
We present a data structure for ray-shooting queries in a set of convex fat polyhedra of total complexity n in R. The data structure uses O(n) storage and preprocessing time, and queries can be answered in O(log n) time. A trade-off between storage and query time is also possible: for any m with n < m < n, we can construct a structure that uses O(m) storage and preprocessing time such that queries take O((n/ √ m) log n) time.
منابع مشابه
Ray Shooting Amidst Spheres in Three Dimensions and Related Problems
We consider the problem of ray shooting amidst spheres in 3-space: given n arbitrary (possibly intersecting) spheres in 3-space and any " > 0, we show how to preprocess the spheres in time O(n 3+"), into a data structure of size O(n 3+"), so that any ray-shooting query can be answered in time O(n "). Our result improves previous techniques (see 3, 5]), where roughly O(n 4) storage was required ...
متن کاملRay Shooting amidst Convex Polyhedra and Polyhedral Terrains in Three Dimensions
We consider the problem of ray shooting in a 3-dimensional scene consisting of m (possibly intersecting) convex polyhedra or polyhedral terrains with a total of n faces, i.e., we want to preprocess them into a data structure, so that the rst intersection point of a query ray and the given polyhedra can be determined quickly. We present a technique that requires O((mn) 2+") preprocessing time an...
متن کاملShooting amidst Convex Polyhedra and Polyhedral Terrains in Three Dimensions
We consider the problem of ray shooting in a three-dimensional scene consisting of m (possibly intersecting) convex polyhedra or polyhedral terrains with a total of n faces, i.e., we want to preprocess them into a data structure, so that the first intersection point of a query ray and the given polyhedra can be determined quickly. We present a technique that requires O ((mn):+) preprocessing ti...
متن کاملVertical ray shooting and computing depth orders of fat objects
We present new results for three problems dealing with a set P of n convex constantcomplexity fat polyhedra in 3-space. (i) We describe a data structure for vertical ray shooting in P that has O(log n) query time and uses O(n log n) storage. (ii) We give an algorithm to compute in O(n log n) time a depth order on P if it exists. (iii) We give an algorithm to verify in O(n log n) time whether a ...
متن کاملRay-Shooting on Triangles in 3-Space1
We present a uniform approach to problems involving lines in 3-space. This approach is based on mapping lines in R 3 into points and hyperplanes in 5-dimensional projective space (Pl ucker space). We obtain new results on the following problems: 1. Preprocess n triangles so as to eeciently answer the query: \Given a ray, which is the rst triangle hit?" (Ray-shooting problem). We discuss the ray...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
دوره شماره
صفحات -
تاریخ انتشار 2005