Abstract
We present a data structure for ray-shooting queries in a set of convex fat polyhedra of total complexity n in R 3 . The data structure uses O ( n 2 + ε ) storage and preprocessing time, and queries can be answered in O ( log 2 n ) time. A trade-off between storage and query time is also possible: for any m with n < m < n 2 , we can construct a structure that uses O ( m 1 + ε ) storage and preprocessing time such that queries take O ( ( n / m ) log 2 n ) time. We also describe a data structure for simplex intersection queries in a set of n convex fat constant-complexity polyhedra in R 3 . For any m with n < m < n 3 , we can construct a structure that uses O ( m 1 + ε ) storage and preprocessing time such that all polyhedra intersecting a query simplex can be reported in O ( ( n / m 1 / 3 ) log n + k ) time, where k is the number of answers.
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